Abstract:
  The counting of the dimension of the space of $U(N) \times U(N) \times U(N)$
polynomial invariants of a complex $3$-index tensor as a function of degree $n$
is known in terms of a sum of squares of Kronecker coefficients. For $n \le N$,
the formula can be expressed in terms of a sum of symmetry factors of
partitions of $n$ denoted $Z_3(n)$. We derive the large $n$ all-orders
asymptotic formula for $ Z_3(n)$ making contact with high order results
previously obtained numerically. The derivation relies on the dominance in the
sum, of partitions with many parts of length $1$. The dominance of other small
parts in restricted partition sums leads to related asymptotic results. The
result for the $3$-index tensor observables gives the large $n$ asymptotic
expansion for the counting of bipartite ribbon graphs with $n$ edges, and for
the dimension of the associated Kronecker permutation centralizer algebra. We
explain how the different terms in the asymptotics are associated with
probability distributions over ribbon graphs. The large $n$ dominance of small
parts also leads to conjectured formulae for the asymptotics of invariants for
general $d$-index tensors. The coefficients of $ 1/n$ in these expansions
involve Stirling numbers of the second kind along with restricted partition
sums.


Abstract:
  Text generation has received a lot of attention in computational
argumentation research as of recent. A particularly challenging task is the
generation of counter-arguments. So far, approaches primarily focus on
rebutting a given conclusion, yet other ways to counter an argument exist. In
this work, we go beyond previous research by exploring argument undermining,
that is, countering an argument by attacking one of its premises. We
hypothesize that identifying the argument's weak premises is key to effective
countering. Accordingly, we propose a pipeline approach that first assesses the
premises' strength and then generates a counter-argument targeting the weak
ones. On the one hand, both manual and automatic evaluation proves the
importance of identifying weak premises in counter-argument generation. On the
other hand, when considering correctness and content richness, human annotators
favored our approach over state-of-the-art counter-argument generation.


Abstract:
  We introduce a novel method for reconstructing the projected matter
distributions of galaxy clusters with weak-lensing (WL) data based on
convolutional neural network (CNN). Training datasets are generated with
ray-tracing through cosmological simulations. We control the noise level of the
galaxy shear catalog such that it mimics the typical properties of the existing
ground-based WL observations of galaxy clusters. We find that the mass
reconstruction by our multi-layered CNN with the architecture of alternating
convolution and trans-convolution filters significantly outperforms the
traditional reconstruction methods. The CNN method provides better
pixel-to-pixel correlations with the truth, restores more accurate positions of
the mass peaks, and more efficiently suppresses artifacts near the field edges.
In addition, the CNN mass reconstruction lifts the mass-sheet degeneracy when
applied to our projected cluster mass estimation from sufficiently large
fields. This implies that this CNN algorithm can be used to measure cluster
masses in a model-independent way for future wide-field WL surveys.


Abstract:
  For homogeneous bilinear control systems, the control sets are characterized
using a Lie algebra rank condition for the induced systems on projective space.
This is based on a classical Diophantine approximation result. For affine
control systems, the control sets around the equilibria for constant controls
are characterized with particular attention to the question when the control
sets are unbounded.


Abstract:
  A sudden loss of vacuum can be catastrophic for particle accelerators. In
such an event, air leaks into the liquid-helium-cooled accelerator beamline
tube and condenses on its inner surface, causing rapid boiling of the helium
and dangerous pressure build-up. Understanding the coupled heat and mass
transfer processes is important for the design of beamline cryogenic systems.
Our past experimental study on nitrogen gas propagating in a copper tube cooled
by normal liquid helium (He I) has revealed a nearly exponential slowing down
of the gas front. A theoretical model that accounts for the interplay of the
gas dynamics and the condensation was developed, which successfully reproduced
various key observations. However, since many accelerator beamlines are
actually cooled by the superfluid phase of helium (He II) in which the heat
transfer is via a non-classical thermal-counterflow mode, we need to extend our
work to the He II cooled tube. This paper reports our systematic measurements
using He II and the numerical simulations based on a modified model that
accounts for the He II heat-transfer characteristics. By tuning the He II peak
heat-flux parameter in our model, we have reproduced the observed gas dynamics
in all experimental runs. The fine-tuned model is then utilized to reliably
evaluate the heat deposition in He II. This work not only advances our
understanding of condensing gas dynamics but also has practical implications to
the design codes for beamline safety.


Abstract:
  We present unconditionally energy stable Runge-Kutta (RK) discontinuous
Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our
algorithm is geared toward arbitrarily high order approximations in both space
and time, while energy dissipation remains preserved without imposing any
restriction on time steps and meshes. We achieve this in two steps. First,
taking advantage of the penalty free DG method introduced by Liu and Yin [J
Sci. Comput. 77:467--501, 2018] for spatial discretization, we reformulate an
extended linearized ODE system by the energy quadratization (EQ) approach.
Second, we apply an s-stage algebraically stable RK method for temporal
discretization. The resulting fully discrete DG schemes are linear and
unconditionally energy stable. In addition, we introduce a
prediction-correction procedure to improve both the accuracy and stability of
the scheme. We illustrate the effectiveness of the proposed schemes by
numerical tests with benchmark problems.


Abstract:
  Iron selenide (FeSe) - the structurally simplest iron-based superconductor,
has attracted tremendous interest in the past years. While the transition
temperature (Tc) of bulk FeSe is $\sim$ 8 K, it can be significantly enhanced
to 40 - 50 K by various ways of electron doping. However, the underlying
physics for such great enhancement of Tc and so the Cooper pairing mechanism
still remain puzzles. Here, we report a systematic study of the
superconducting- and normal-state properties of FeSe films via ionic liquid
gating. With fine tuning, Tc evolves continuously from below 10 K to above 40
K; in situ two-coil mutual inductance measurements unambiguously confirm the
gating is a uniform bulk effect. Close to Tc, the normal-state resistivity
shows a linear dependence on temperature and the linearity extends to lower
temperatures with the superconductivity suppressed by high magnetic fields. At
high fields, the normal-state magnetoresistance exhibits a linear-in-field
dependence and obeys a simple scaling relation between applied field and
temperature. Consistent behaviors are observed for different-Tc states
throughout the gating process, suggesting the pairing mechanism very likely
remains the same from low- to high-Tc state. Importantly, the coefficient of
the linear-in-temperature resistivity is positively correlated with Tc,
similarly to the observations in cuprates, Bechgaard salts and iron pnictide
superconductors. Our study points to a short-range antiferromagnetic exchange
interaction mediated pairing mechanism in FeSe.


Abstract:
  Nowadays, with the vigorous expansion and development of gaming video
streaming techniques and services, the expectation of users, especially the
mobile phone users, for higher quality of experience is also growing swiftly.
As most of the existing research focuses on traditional video streaming, there
is a clear lack of both subjective study and objective quality models that are
tailored for quality assessment of mobile gaming content. To this end, in this
study, we first present a brand new Tencent Gaming Video dataset containing
1293 mobile gaming sequences encoded with three different codecs. Second, we
propose an objective quality framework, namely Efficient hard-RAnk Quality
Estimator (ERAQUE), that is equipped with (1) a novel hard pairwise ranking
loss, which forces the model to put more emphasis on differentiating similar
pairs; (2) an adapted model distillation strategy, which could be utilized to
compress the proposed model efficiently without causing significant performance
drop. Extensive experiments demonstrate the efficiency and robustness of our
model.


Abstract:
  In this paper, we introduce a novel visual representation learning which
relies on a handful of adaptively learned tokens, and which is applicable to
both image and video understanding tasks. Instead of relying on hand-designed
splitting strategies to obtain visual tokens and processing a large number of
densely sampled patches for attention, our approach learns to mine important
tokens in visual data. This results in efficiently and effectively finding a
few important visual tokens and enables modeling of pairwise attention between
such tokens, over a longer temporal horizon for videos, or the spatial content
in images. Our experiments demonstrate strong performance on several
challenging benchmarks for both image and video recognition tasks. Importantly,
due to our tokens being adaptive, we accomplish competitive results at
significantly reduced compute amount. We obtain comparable results to the
state-of-the-arts on ImageNet while being computationally more efficient. We
establish new state-of-the-arts on multiple video datasets, including
Kinetics-400, Kinetics-600, Charades, and AViD.
  The code is available at:
https://github.com/google-research/scenic/tree/main/scenic/projects/token_learner


Abstract:
  Multi-target prediction (MTP) serves as an umbrella term for machine learning
tasks that concern the simultaneous prediction of multiple target variables.
Classical instantiations are multi-label classification, multivariate
regression, multi-task learning, dyadic prediction, zero-shot learning, network
inference, and matrix completion. Despite the significant similarities, all
these domains have evolved separately into distinct research areas over the
last two decades. This led to the development of a plethora of
highly-engineered methods, and created a substantially-high entrance barrier
for machine learning practitioners that are not experts in the field. In this
work we present a generic deep learning methodology that can be used for a wide
range of multi-target prediction problems. We introduce a flexible multi-branch
neural network architecture, partially configured via a questionnaire that
helps end-users to select a suitable MTP problem setting for their needs.
Experimental results for a wide range of domains illustrate that the proposed
methodology manifests a competitive performance compared to methods from
specific MTP domains.


Abstract:
  Extreme-scale cosmological simulations have been widely used by today's
researchers and scientists on leadership supercomputers. A new generation of
error-bounded lossy compressors has been used in workflows to reduce storage
requirements and minimize the impact of throughput limitations while saving
large snapshots of high-fidelity data for post-hoc analysis. In this paper, we
propose to adaptively provide compression configurations to compute partitions
of cosmological simulations with newly designed post-analysis aware
rate-quality modeling. The contribution is fourfold: (1) We propose a novel
adaptive approach to select feasible error bounds for different partitions,
showing the possibility and efficiency of adaptively configuring lossy
compression for each partition individually. (2) We build models to estimate
the overall loss of post-analysis result due to lossy compression and to
estimate compression ratio, based on the property of each partition. (3) We
develop an efficient optimization guideline to determine the best-fit
configuration of error bounds combination in order to maximize the compression
ratio under acceptable post-analysis quality loss. (4) Our approach introduces
negligible overheads for feature extraction and error-bound optimization for
each partition, enabling post-analysis-aware in situ lossy compression for
cosmological simulations. Experiments show that our proposed models are highly
accurate and reliable. Our fine-grained adaptive configuration approach
improves the compression ratio of up to 73% on the tested datasets with the
same post-analysis distortion with only 1% performance overhead.


Abstract:
  Sequence-to-sequence (seq2seq) models are competitive with hybrid models for
automatic speech recognition (ASR) tasks when large amounts of training data
are available. However, data sparsity and domain adaptation are more
problematic for seq2seq models than their hybrid counterparts. We examine
corpora of five languages from the IARPA MATERIAL program where the transcribed
data is conversational telephone speech (CTS) and evaluation data is broadcast
news (BN). We show that there is a sizable initial gap in such a data condition
between hybrid and seq2seq models, and the hybrid model is able to further
improve through the use of additional language model (LM) data. We use an
additional set of untranscribed data primarily in the BN domain for
semisupervised training. In semisupervised training, a seed model trained on
transcribed data generates hypothesized transcripts for unlabeled
domain-matched data for further training. By using a hybrid model with an
expanded language model for pseudotranscription, we are able to improve our
seq2seq model from an average word error rate (WER) of 66.7% across all five
languages to 29.0% WER. While this puts the seq2seq model at a competitive
operating point, hybrid models are still able to use additional LM data to
maintain an advantage.


Abstract:
  The anthology of spoken languages today is inundated with textual
information, necessitating the development of automatic summarization models.
In this manuscript, we propose an extractor-paraphraser based abstractive
summarization system that exploits semantic overlap as opposed to its
predecessors that focus more on syntactic information overlap. Our model
outperforms the state-of-the-art baselines in terms of ROUGE, METEOR and word
mover similarity (WMS), establishing the superiority of the proposed system via
extensive ablation experiments. We have also challenged the summarization
capabilities of the state of the art Pointer Generator Network (PGN), and
through thorough experimentation, shown that PGN is more of a paraphraser,
contrary to the prevailing notion of a summarizer; illustrating it's
incapability to accumulate information across multiple sentences.


Abstract:
  We consider the problem of computing reachable sets directly from noisy data
without a given system model. Several reachability algorithms are presented,
and their accuracy is shown to depend on the underlying system generating the
data. First, an algorithm for computing over-approximated reachable sets based
on matrix zonotopes is proposed for linear systems. Constrained matrix
zonotopes are introduced to provide less conservative reachable sets at the
cost of increased computational expenses and utilized to incorporate prior
knowledge about the unknown system model. Then we extend the approach to
polynomial systems and under the assumption of Lipschitz continuity to
nonlinear systems. Theoretical guarantees are given for these algorithms in
that they give a proper over-approximative reachable set containing the true
reachable set. Multiple numerical examples show the applicability of the
introduced algorithms, and accuracy comparisons are made between algorithms.


Abstract:
  Epitaxially-grown quantum well and quantum dot solar cells suffer from weak
light absorption, strongly limiting their performance. Light trapping based on
optical resonances is particularly relevant for such devices to increase light
absorption and thereby current generation. Compared to homogeneous media, the
position of the quantum layers within the device is an additional parameter
that can strongly influence resonant absorption. However, this effect has so
far received little attention from the photovoltaic community. In this work, we
develop a theoretical framework to evaluate and optimize resonant light
absorption in a thin slab with multiple quantum layers. Using numerical
simulations, we show that the position of the layers can make the difference
between strong absorption enhancement and completely suppressed absorption, and
that an optimal position leads to an absorption enhancement twice larger than
average. We confirm these results experimentally by measuring the absorption
enhancement from photoluminescence spectra in InAs/GaAs quantum dot samples.
Overall, this work provides an additional degree of freedom to substantially
improve absorption, encouraging the development of quantum wells and quantum
dots-based devices such as intermediate-band solar cells.


Abstract:
  In this paper we develop the stability rules for NASICON structured
materials, as an example of compounds with complex bond topology and
composition. By applying machine learning to the ab-initio computed phase
stability of 3881 potential NASICONs we can extract a simple two-dimensional
descriptor that is extremely good at separating stable from unstable NASICONS.
This machine-learned "tolerance factor" contains information on the Na content,
the radii and electronegativities of the elements, and the Madelung energy. We
test the predictive capability of this approach by selecting six predicted
NASICON compositions. Five out of the six resulted in a phase pure NASICON
while the sixth composition led to a NASICON that coexisted with other phases,
validating the efficacy of this approach. This work not only provide tools to
understand synthetic accessibility of NASICON-type materials, but also
demonstrate an efficient paradigm for discovering new materials with complicate
composition and atomic structure.


Abstract:
  Humans often communicate by using imprecise language, suggesting that fuzzy
concepts with unclear boundaries are prevalent in language use. In this paper,
we test the extent to which models trained to capture the distributional
statistics of language show correspondence to fuzzy-membership patterns. Using
the task of natural language inference, we test a recent state of the art model
on the classical case of temperature, by examining its mapping of temperature
data to fuzzy-perceptions such as "cool", "hot", etc. We find the model to show
patterns that are similar to classical fuzzy-set theoretic formulations of
linguistic hedges, albeit with a substantial amount of noise, suggesting that
models trained solely on language show promise in encoding fuzziness.


Abstract:
  Elements with low First Ionization Potential (FIP) are known to be three to
four times more abundant in active region loops of the solar corona than in the
photosphere. There have been observations suggesting that this observed "FIP
bias" may be different in other parts of the solar corona and such observations
are thus important in understanding the underlying mechanism. The Solar X-ray
Monitor (XSM) on board the Chandrayaan-2 mission carried out spectroscopic
observations of the Sun in soft X-rays during the 2019-20 solar minimum,
considered to be the quietest solar minimum of the past century. These
observations provided a unique opportunity to study soft X-ray spectra of the
quiescent solar corona in the absence of any active regions. By modelling high
resolution broadband X-ray spectra from XSM, we estimate the temperature and
emission measure during periods of possibly the lowest solar X-ray intensity.
We find that the derived parameters remain nearly constant over time with a
temperature around 2 MK, suggesting the emission is dominated by X-ray Bright
Points (XBPs). We also obtain the abundances of Mg, Al, and Si relative to H,
and find that the FIP bias is ~2, lower than the values observed in active
regions.


Abstract:
  Datasets displaying temporal dependencies abound in science and engineering
applications, with Markov models representing a simplified and popular view of
the temporal dependence structure. In this paper, we consider Bayesian settings
that place prior distributions over the parameters of the transition kernel of
a Markov model, and seeks to characterize the resulting, typically intractable,
posterior distributions. We present a PAC-Bayesian analysis of variational
Bayes (VB) approximations to tempered Bayesian posterior distributions,
bounding the model risk of the VB approximations. Tempered posteriors are known
to be robust to model misspecification, and their variational approximations do
not suffer the usual problems of over confident approximations. Our results tie
the risk bounds to the mixing and ergodic properties of the Markov data
generating model. We illustrate the PAC-Bayes bounds through a number of
example Markov models, and also consider the situation where the Markov model
is misspecified.


Abstract:
  We present an approach for Task-Motion Planning (TMP) using Iterative
Deepened AND/OR Graph Networks (TMP-IDAN) that uses an AND/OR graph network
based novel abstraction for compactly representing the task-level states and
actions. While retrieving a target object from clutter, the number of object
re-arrangements required to grasp the target is not known ahead of time. To
address this challenge, in contrast to traditional AND/OR graph-based planners,
we grow the AND/OR graph online until the target grasp is feasible and thereby
obtain a network of AND/OR graphs. The AND/OR graph network allows faster
computations than traditional task planners. We validate our approach and
evaluate its capabilities using a Baxter robot and a state-of-the-art robotics
simulator in several challenging non-trivial cluttered table-top scenarios. The
experiments show that our approach is readily scalable to increasing number of
objects and different degrees of clutter.


Abstract:
  In this paper we consider PDE's problems involving the anisotropic Laplacian
operator, with Robin boundary conditions. By means of Talenti techniques,
widely used in the last decades, we prove a comparison result between the
solutions of the above-mentioned problems and the solutions of the symmetrized
ones. As a consequence of these results, a Bossel-Daners type inequality can be
shown in dimension 2.


Abstract:
  In a recent Letter [Phys. Rev. Lett. 126, 063902 (2021)], M. A. Carroll et
al. derived a model to analytically determine regimes of thermal, collective
anti-bunching, and laser emission for emitters in a cavity. According to their
model, nanolasers exhibit a distinct threshold at which the coherent laser
field emerges from a bifurcation at a finite pump rate. The amplitude of this
coherent field increases with a further increase in the pump rate. Such a
behavior contrasts the usual view of the transition to lasing in single-mode
high-$\beta$ nanolasers, according to which strong spontaneous emission into
the lasing mode results in a smooth transformation from the thermal state to
the coherent state as the pump rate increases. Here, we demonstrate that the
authors have ignored important terms in the equations of their model, which
caused the bifurcation and the ideally monochromatic field to emerge at a
finite pump rate.


Abstract:
  In this paper, we propose a clearing model for prices in a financial markets
due to margin calls on short sold assets. In doing so, we construct an explicit
formulation for the prices that would result immediately following asset
purchases and a margin call. The key result of this work is the determination
of a threshold short interest ratio which, if exceeded, results in the
discontinuity of the clearing prices due to a feedback loop.


Abstract:
  A central question in resource theory is whether one can construct a set of
monotones that completely characterise the allowed transitions dictated by a
set of free operations. A similar question is whether two distinct sets of free
operations generate the same class of transitions. These questions are part of
the more general problem of whether it is possible to pass from one
characterisation of a resource theory to another. In the present letter we
prove that in the context of quantum resource theories this class of problems
is undecidable in general. This is done by proving the undecidability of the
membership problem for CPTP maps, which subsumes all the other results.


Abstract:
  The Covid-19 pandemic caused disruptive effects for individuals, firms, and
societies. In this paper, we offer insights on the major issues and challenges
firms are facing in the Covid-19 pandemic, as well as their concerns for
Corporate Social Responsibility (CSR) themes. To do so, we investigate large
Italian firms' discussion on Twitter in the first nine months of the pandemic.
We downloaded all Twitter posts from 1st of March, 2020, to 17th of November,
2020 by the accounts of the largest Italian firms, i.e. those with 250 or more
employees. We then built the bipartite network of accounts and hashtags and,
using an entropy-based null model as a benchmark, we projected the information
contained in the network into the accounts layers, identifying a network of
accounts in which a link indicates a non trivial similarity in terms of their
usage of hashtags. We find that the conversation is focused around 13
communities, 10 of which include Covid-19 themes. The core of the network is
formed of 5 communities, which deal with environmental sustainability, digital
innovation and safety. Firms' ownership type does not seem to influence the
conversation. 10 communities out of 13 mention hashtags related to CSR, with
the environmental and social dimensions as the prevalent ones. Interestingly
enough, the social dimension seems more relevant in the communities dealing
with digital innovation and safety. However, the relevance of CSR hashtags is
very small at the single message level, but with some peculiarities arising in
specific communities. Overall, our paper highlights the role of network methods
on Twitter data as a tool which can support managers and policy makers to
design their strategies and decision making, capturing firms' emerging issues
and relevant themes.


Abstract:
  Recommender systems (RSs) are becoming an inseparable part of our everyday
lives. They help us find our favorite items to purchase, our friends on social
networks, and our favorite movies to watch. Traditionally, the recommendation
problem was considered as a simple classification or prediction problem;
however, the sequential nature of the recommendation problem has been shown.
Accordingly, it can be formulated as a Markov decision process (MDP) and
reinforcement learning (RL) methods can be employed to solve it. In fact,
recent advances in combining deep learning with traditional RL methods, i.e.
deep reinforcement learning (DRL), has made it possible to apply RL to the
recommendation problem with massive state and action spaces. In this paper, a
survey on reinforcement learning based recommender systems (RLRSs) is
presented. We first recognize the fact that algorithms developed for RLRSs can
be generally classified into RL- and DRL-based methods. Then, we present these
RL- and DRL-based methods in a classified manner based on the specific RL
algorithm, e.g., Q-learning, SARSA, and REINFORCE, that is used to optimize the
recommendation policy. Furthermore, some tables are presented that contain
detailed information about the MDP formulation of these methods, as well as
about their evaluation schemes. Finally, we discuss important aspects and
challenges that can be addressed in the future.


Abstract:
  We show that a class of compounds with $I$4/$mcm$ crystalline symmetry hosts
three-dimensional semi-Dirac fermions. Unlike the known two-dimensional
semi-Dirac points, the degeneracy of these three-dimensional semi-Dirac points
is not lifted by spin-orbit coupling due to the protection by a nonsymmorphic
symmetry -- screw rotation in the $a-b$ plane and a translation along the $c$
axis. This crystalline symmetry is found in tetragonal perovskite oxides,
realizable in thin films by epitaxial strain that results in
a$^0$a$^0$c$^-$-type octahedral rotation. Interestingly, with broken
time-reversal symmetry, two pairs of Weyl points emerge from the semi-Dirac
points within the Brillouin zone, and an additional lattice distortion leads to
enhanced intrinsic anomalous Hall effect. The ability to tune the Berry phase
by epitaxial strain can be useful in novel oxide-based electronic devices.


Abstract:
  Hydrogels hold promise in agriculture as reservoirs of water in dry soil,
potentially alleviating the burden of irrigation. However, confinement in soil
can markedly reduce the ability of hydrogels to absorb water and swell,
limiting their widespread adoption. Unfortunately, the underlying reason
remains unknown. By directly visualizing the swelling of hydrogels confined in
three-dimensional granular media, we demonstrate that the extent of hydrogel
swelling is determined by the competition between the force exerted by the
hydrogel due to osmotic swelling and the confining force transmitted by the
surrounding grains. Furthermore, the medium can itself be restructured by
hydrogel swelling, as set by the balance between the osmotic swelling force,
the confining force, and intergrain friction. Together, our results provide
quantitative principles to predict how hydrogels behave in confinement,
potentially improving their use in agriculture as well as informing other
applications such as oil recovery, construction, mechanobiology, and
filtration.


Abstract:
  We present a method for a real time visualization and automatic processing
for detection and classification of untouched cancer cells in blood during
stain free imaging flow cytometry using digital holographic microscopy and
machine learning in throughput of 15 cells per second. As a preliminary model
for circulating tumor cells in blood, we automatically classified primary and
metastatic colon cancer cells, where the two types of cancer cells were
isolated from the same individual, as well as four types of blood cells. We
used low-coherence off-axis interferometric phase microscopy and a microfluidic
channel to quantitatively image cells during flow. The acquired images were
processed and classified based on their morphology and quantitative phase
features during the cell flow. We achieved high accuracy of 92.56 percent for
distinguishing between the cells, paving the way for future automatic
label-free cancer cell classification in blood samples.


Abstract:
  Self-attention mechanism recently achieves impressive advancement in Natural
Language Processing (NLP) and Image Processing domains. And its permutation
invariance property makes it ideally suitable for point cloud processing.
Inspired by this remarkable success, we propose an end-to-end architecture,
dubbed Cross-Level Cross-Scale Cross-Attention Network (CLCSCANet), for point
cloud representation learning. First, a point-wise feature pyramid module is
introduced to hierarchically extract features from different scales or
resolutions. Then a cross-level cross-attention is designed to model long-range
inter-level and intra-level dependencies. Finally, we develop a cross-scale
cross-attention module to capture interactions between-and-within scales for
representation enhancement. Compared with state-of-the-art approaches, our
network can obtain competitive performance on challenging 3D object
classification, point cloud segmentation tasks via comprehensive experimental
evaluation.


Abstract:
  Space-filling designs are important in computer experiments, which are
critical for building a cheap surrogate model that adequately approximates an
expensive computer code. Many design construction techniques in the existing
literature are only applicable for rectangular bounded space, but in real world
applications, the input space can often be non-rectangular because of
constraints on the input variables. One solution to generate designs in a
constrained space is to first generate uniformly distributed samples in the
feasible region, and then use them as the candidate set to construct the
designs. Sequentially Constrained Monte Carlo (SCMC) is the state-of-the-art
technique for candidate generation, but it still requires large number of
constraint evaluations, which is problematic especially when the constraints
are expensive to evaluate. Thus, to reduce constraint evaluations and improve
efficiency, we propose the Constrained Minimum Energy Design (CoMinED) that
utilizes recent advances in deterministic sampling methods. Extensive
simulation results on 15 benchmark problems with dimensions ranging from 2 to
13 are provided for demonstrating the improved performance of CoMinED over the
existing methods.


Abstract:
  In this report, we summarize the set partition enumeration problems and
thoroughly explain the algorithms used to solve them. These algorithms iterate
through the partitions in lexicographic order and are easy to understand and
implement in modern high-level programming languages, without recursive
structures and jump logic. We show that they require linear space in respect to
the set cardinality and advance the enumeration in constant amortized time. The
methods discussed in this document are not novel. Our goal is to demonstrate
the process of enumerating set partitions and highlight the ideas behind it.
This work is an aid for learners approaching this enumeration problem and
programmers undertaking the task of implementing it.


Abstract:
  In this paper we prove new bounds for sums of convex or concave functions.
Specifically, we prove that for all $A,B \subseteq \mathbb R$ finite sets, and
for all $f,g$ convex or concave functions, we have
  $$|A + B|^{38}|f(A) + g(B)|^{38} \gtrsim |A|^{49}|B|^{49}.$$
  This result can be used to obtain bounds on a number of two-variable
expanders of interest, as well as to the asymmetric sum-product problem. We
also adjust our technique to also prove the three-variable expansion result
  \[
  |AB+A|\gtrsim |A|^{\frac32 +\frac3{170}}\,.
  \]
  Our methods follow a series of recent developments in the sum-product
literature, presenting a unified picture. Of particular interest is an
adaptation of a regularisation technique of Xue, that enables us to find
positive proportion subsets with certain desirable properties.


Abstract:
  The Group Quantization formalism is a scheme for constructing a functional
space that is an irreducible infinite dimensional representation of the Lie
algebra belonging to a dynamical symmetry group. We apply this formalism to the
construction of functional space and operators for quadratic potentials --
gaussian pricing kernels in finance. We describe the Black-Scholes theory, the
Ho-Lee interest rate model and the Euclidean repulsive and attractive
oscillators. The symmetry group used in this work has the structure of a
principal bundle with base (dynamical) group a semi-direct extension of the
Heisenberg-Weyl group by SL(2,R), and structure group (fiber) the positive real
line.


Abstract:
  Recent works leveraging Graph Neural Networks to approach graph matching
tasks have shown promising results. Recent progress in learning discrete
distributions poses new opportunities for learning graph matching models. In
this work, we propose a new model, Stochastic Iterative Graph MAtching (SIGMA),
to address the graph matching problem. Our model defines a distribution of
matchings for a graph pair so the model can explore a wide range of possible
matchings. We further introduce a novel multi-step matching procedure, which
learns how to refine a graph pair's matching results incrementally. The model
also includes dummy nodes so that the model does not have to find matchings for
nodes without correspondence. We fit this model to data via scalable stochastic
optimization. We conduct extensive experiments across synthetic graph datasets
as well as biochemistry and computer vision applications. Across all tasks, our
results show that SIGMA can produce significantly improved graph matching
results compared to state-of-the-art models. Ablation studies verify that each
of our components (stochastic training, iterative matching, and dummy nodes)
offers noticeable improvement.


Abstract:
  This is a contribution to the program of dynamical approach to mean curvature
flow initiated by Colding and Minicozzi. In this paper, we prove two main
theorems. The first one is local in nature and the second one is global. In
this first result, we pursue the stream of ideas of \cite{CM3} and get a slight
refinement of their results. We apply the invariant manifold theory from
hyperbolic dynamics to study the dynamics close to a closed shrinker that is
not a sphere. In the second theorem, we show that if a hypersurface under the
rescaled mean curvature flow converges to a closed shrinker that is not a
sphere, then a generic perturbation on initial data would make the flow leave a
small neighborhood of the shrinker and never come back.


Abstract:
  For treatment effects - one of the core issues in modern econometric analysis
- prediction and estimation are two sides of the same coin. As it turns out,
machine learning methods are the tool for generalized prediction models.
Combined with econometric theory, they allow us to estimate not only the
average but a personalized treatment effect - the conditional average treatment
effect (CATE). In this tutorial, we give an overview of novel methods, explain
them in detail, and apply them via Quantlets in real data applications. We
study the effect that microcredit availability has on the amount of money
borrowed and if 401(k) pension plan eligibility has an impact on net financial
assets, as two empirical examples. The presented toolbox of methods contains
meta-learners, like the Doubly-Robust, R-, T- and X-learner, and methods that
are specially designed to estimate the CATE like the causal BART and the
generalized random forest. In both, the microcredit and 401(k) example, we find
a positive treatment effect for all observations but conflicting evidence of
treatment effect heterogeneity. An additional simulation study, where the true
treatment effect is known, allows us to compare the different methods and to
observe patterns and similarities.


Abstract:
  Intense light-matter interactions and unique structural and electrical
properties make Van der Waals heterostructures composed by Graphene (Gr) and
monolayer transition metal dichalcogenides (TMD) promising building blocks for
tunnelling transistors, flexible electronics, as well as optoelectronic
devices, including photodetectors, photovoltaics and QLEDs, bright and
narrow-line emitters using minimal amounts of active absorber material. The
performance of such devices is critically ruled by interlayer interactions
which are still poorly understood in many respects. Specifically, two classes
of coupling mechanisms have been proposed: charge transfer (CT) and energy
transfer (ET), but their relative efficiency and the underlying physics is an
open question. Here, building on a time resolved Raman scattering experiment,
we determine the electronic temperature profile of Gr in response to TMD
photo-excitation, tracking the picosecond dynamics of the G and 2D bands.
Compelling evidence for a dominant role ET process accomplished within a
characteristic time of ~ 3 ps is provided. Our results suggest the existence of
an intermediate process between the observed picosecond ET and the generation
of a net charge underlying the slower electric signals detected in
optoelectronic applications.


Abstract:
  We introduce LTrack, a new tracking attack on LTE that allows an attacker to
stealthily extract user devices' locations and permanent identifiers (IMSI). To
remain stealthy, the localization of devices in LTrack is fully passive,
relying on our new uplink/downlink sniffer. Our sniffer records both the times
of arrival of LTE messages and the contents of the Timing Advance Commands,
based on which LTrack calculates locations. LTrack is the first to show the
feasibility of a passive localization in LTE through implementation on
software-defined radio.
  Passive localization attacks reveal a user's location traces but can at best
link these traces to a device's pseudonymous temporary identifier (TMSI),
making tracking in dense areas or over a long time-period challenging. LTrack
overcomes this challenge by introducing and implementing a new type of IMSI
Catcher named IMSI Extractor. It extracts a device's IMSI and binds it to its
current TMSI. Instead of relying on fake base stations like existing IMSI
Catchers, which are detectable due to their continuous transmission, IMSI
Extractor relies on our uplink/downlink sniffer enhanced with surgical message
overshadowing. This makes our IMSI Extractor the stealthiest IMSI Catcher to
date.
  We evaluate LTrack through a series of experiments and show that in
line-of-sight conditions, the attacker can estimate the location of a phone
with less than 6m error in 90% of the cases. We successfully tested our IMSI
Extractor against a set of 17 modern smartphones connected to our
industry-grade LTE testbed. We further validated our uplink/downlink sniffer
and IMSI Extractor in a test facility of an operator.


Abstract:
  We perform a short review of the history of quantum mechanics, with a focus
on the historical problems with describing ionization theoretically in the
context of quantum mechanics. The essentials of the theory of resonances are
presented. The exterior complex scaling method for obtaining resonance
parameters within the context of the Schrodinger equation is detailed. We
explain how this is implemented for a numerical solution using a finite element
method for the scaled variable. Results for the resonance parameters of a
one-dimensional hydrogen model in an external direct current (DC) electric
field are presented as proof of the independence of the theory from the scaling
angle. We apply the theory to the real hydrogen atom in a DC field and present
results which agree with literature values. The resonance parameters for singly
ionized helium are also presented. Using a model potential energy for the water
molecule, we solve for the energy eigenvalues. We then solve for the resonance
parameters of the water molecule in a DC field and compare to literature
results. Our widths for the valence orbital are shown to agree well with the
so-called "coupled-cluster singles and doubles with perturbative triples
excitations" method.


Abstract:
  We consider the problem of online scheduling on a single machine in order to
minimize weighted flow time. The existing algorithms for this problem (STOC
'01, SODA '03, FOCS '18) all require exact knowledge of the processing time of
each job. This assumption is crucial, as even a slight perturbation of the
processing time would lead to polynomial competitive ratio. However, this
assumption very rarely holds in real-life scenarios.
  In this paper, we present the first algorithm for weighted flow time which do
not require exact knowledge of the processing times of jobs. Specifically, we
introduce the Scheduling with Predicted Processing Time (SPPT) problem, where
the algorithm is given a prediction for the processing time of each job,
instead of its real processing time. For the case of a constant factor
distortion between the predictions and the real processing time, our algorithms
match all the best known competitiveness bounds for weighted flow time --
namely $O(\log P), O(\log D)$ and $O(\log W)$, where $P,D,W$ are the maximum
ratios of processing times, densities, and weights, respectively. For larger
errors, the competitiveness of our algorithms degrades gracefully.


Abstract:
  This paper presents a new ridesharing simulation platform that accounts for
dynamic driver supply and passenger demand, and complex interactions between
drivers and passengers. The proposed simulation platform explicitly considers
driver and passenger acceptance/rejection on the matching options, and
cancellation before/after being matched. New simulation events, procedures and
modules have been developed to handle these realistic interactions. The
capabilities of the simulation platform are illustrated using numerical
experiments. The experiments confirm the importance of considering supply and
demand interactions and provide new insights to ridesharing operations. Results
show that increase of driver supply does not always increase matching option
accept rate, and larger matching window could have negative impacts on overall
ridesharing success rate. These results emphasize the importance of a careful
planning of a ridesharing system.


Abstract:
  We investigate a model of interacting Dirac fermions in $2+1$ dimensions with
$M$ flavors and $N$ colors having the $\mathrm{U}(M)\times \mathrm{SU}(N)$
symmetry. In the large-$N$ limit, we find that the $\mathrm{U}(M)$ symmetry is
spontaneously broken in a variety of ways. In the vacuum, when the
parity-breaking flavor-singlet mass is varied, the ground state undergoes a
sequence of $M$ first-order phase transitions, experiencing $M+1$ phases
characterized by symmetry breaking $\mathrm{U}(M)\to \mathrm{U}(M-k)\times
\mathrm{U}(k)$ with $k\in\{0,1,2,\cdots,M\}$, bearing a close resemblance to
the vacuum structure of three-dimensional QCD. At finite temperature and
chemical potential, a rich phase diagram with first and second-order phase
transitions and tricritical points is observed. Also exotic phases with
spontaneous symmetry breaking of the form as $\mathrm{U}(3)\to
\mathrm{U}(1)^3$, $\mathrm{U}(4)\to \mathrm{U}(2)\times \mathrm{U}(1)^2$, and
$\mathrm{U}(5)\to \mathrm{U}(2)^2\times \mathrm{U}(1)$ exist. For a large
flavor-singlet mass, the increase of the chemical potential $\mu$ brings about
$M$ consecutive first-order transitions that separate the low-$\mu$ phase
diagram with vanishing fermion density from the high-$\mu$ region with a high
fermion density.


Abstract:
  In contrast to conventional pipeline Spoken Language Understanding (SLU)
which consists of automatic speech recognition (ASR) and natural language
understanding (NLU), end-to-end SLU infers the semantic meaning directly from
speech and overcomes the error propagation caused by ASR. End-to-end slot
filling (SF) from speech is an essential component of end-to-end SLU, and is
usually regarded as a sequence-to-sequence generation problem, heavily relied
on the performance of language model of ASR. However, it is hard to generate a
correct slot when the slot is out-of-vovabulary (OOV) in training data,
especially when a slot is an anti-linguistic entity without grammatical rule.
Inspired by object detection in computer vision that is to detect the object
from an image, we consider SF as the task of slot detection from speech. In
this paper, we formulate the SF task as a matching task and propose an
end-to-end knowledge-based SF model, named Speech-to-Slot (Speech2Slot), to
leverage knowledge to detect the boundary of a slot from the speech. We also
release a large-scale dataset of Chinese speech for slot filling, containing
more than 830,000 samples. The experiments show that our approach is markedly
superior to the conventional pipeline SLU approach, and outperforms the
state-of-the-art end-to-end SF approach with 12.51% accuracy improvement.


Abstract:
  While the techniques in optimal control theory are often model-based, the
policy optimization (PO) approach can directly optimize the performance metric
of interest without explicit dynamical models, and is an essential approach for
reinforcement learning problems. However, it usually leads to a non-convex
optimization problem in most cases, where there is little theoretical
understanding on its performance. In this paper, we focus on the
risk-constrained Linear Quadratic Regulator (LQR) problem with noisy input via
the PO approach, which results in a challenging non-convex problem. To this
end, we first build on our earlier result that the optimal policy has an affine
structure to show that the associated Lagrangian function is locally gradient
dominated with respect to the policy, based on which we establish strong
duality. Then, we design policy gradient primal-dual methods with global
convergence guarantees to find an optimal policy-multiplier pair in both
model-based and sample-based settings. Finally, we use samples of system
trajectories in simulations to validate our policy gradient primal-dual
methods.


Abstract:
  The connectivity and resource-constrained nature of single-board devices
opens up to cybersecurity concerns affecting Internet of Things (IoT)
scenarios. One of the most important is the presence of evil IoT twins. Evil
IoT twins are malicious devices, with identical hardware and software
configurations to authorized ones, that can provoke sensitive information
leakages, data poisoning, or privilege escalation in IoT scenarios. Combining
behavioral fingerprinting and Machine/Deep Learning (ML/DL) techniques is a
promising solution to identify evil IoT twins by detecting minor performance
differences generated by imperfections in manufacturing. However, existing
solutions are not suitable for single-board devices because they do not
consider their hardware and software limitations, underestimate critical
aspects such as fingerprint stability, and do not explore the potential of
ML/DL techniques. To improve it, this work proposes an ML/DL-oriented
methodology that uses behavioral fingerprinting to identify identical
single-board devices. The methodology leverages the different built-in
components of the system, comparing their internal behavior with each other to
detect variations that occurred in manufacturing processes. The validation has
been performed in a real environment composed of identical Raspberry Pi 4 Model
B and Raspberry Pi 3 Model B+ devices, obtaining a 92.6\% average accuracy with
a Random Forest model and achieving the identification for all devices by
setting a 50\% threshold in the evaluation process. Finally, a discussion
compares the proposed solution with related work and provides important lessons
learned and limitations.


Abstract:
  The advent of deep learning has led to the prevalence of deep neural network
architectures for monaural music source separation, with end-to-end approaches
that operate directly on the waveform level increasingly receiving research
attention. Among these approaches, transformation of the input mixture to a
learned latent space, and multiplicative application of a soft mask to the
latent mixture, achieves the best performance, but is prone to the introduction
of artifacts to the source estimate. To alleviate this problem, in this paper
we propose a hybrid time-domain approach, termed the HTMD-Net, combining a
lightweight masking component and a denoising module, based on skip
connections, in order to refine the source estimated by the masking procedure.
Evaluation of our approach in the task of monaural singing voice separation in
the musdb18 dataset indicates that our proposed method achieves competitive
performance compared to methods based purely on masking when trained under the
same conditions, especially regarding the behavior during silent segments,
while achieving higher computational efficiency.


Abstract:
  Cache advertisements reduce the access cost by allowing users to skip the
cache when it does not contain their datum. Such advertisements are used in
multiple networked domains such as 5G networks, wide area networks, and
information-centric networking. The selection of an advertisement strategy
exposes a trade-off between the access cost and bandwidth consumption. Still,
existing works mostly apply a trial-and-error approach for selecting the best
strategy, as the rigorous foundations required for optimizing such decisions is
lacking. Our work shows that the desired advertisement policy depends on
numerous parameters such as the cache policy, the workload, the cache size, and
the available bandwidth. In particular, we show that there is no ideal single
configuration. Therefore, we design an adaptive, self-adjusting algorithm that
periodically selects an advertisement policy. Our algorithm does not require
any prior information about the cache policy, cache size, or workload, and does
not require any apriori configuration. Through extensive simulations, using
several state-of-the-art cache policies, and real workloads, we show that our
approach attains a similar cost to that of the best static configuration (which
is only identified in retrospect) in each case.


Abstract:
  Lck (lymphocyte-specific protein tyrosine kinase) is an enzyme which plays a
number of important roles in the function of immune cells. It belongs to the
Src family of kinases which are known to undergo autophosphorylation. It turns
out that this leads to a remarkable variety of dynamical behaviour which can
occur during their activation. We prove that in the presence of
autophosphorylation one phenomenon, bistability, already occurs in a
mathematical model for a protein with a single phosphorylation site. We further
show that a certain model of Lck exhibits oscillations. Finally we discuss the
relations of these results to models in the literature which involve Lck and
describe specific biological processes, such as the early stages of T cell
activation and the stimulation of T cell responses resulting from the
suppression of PD-1 signalling which is important in immune checkpoint therapy
for cancer.


Abstract:
  Recent work has found that adversarially-robust deep networks used for image
classification are more interpretable: their feature attributions tend to be
sharper, and are more concentrated on the objects associated with the image's
ground-truth class. We show that smooth decision boundaries play an important
role in this enhanced interpretability, as the model's input gradients around
data points will more closely align with boundaries' normal vectors when they
are smooth. Thus, because robust models have smoother boundaries, the results
of gradient-based attribution methods, like Integrated Gradients and DeepLift,
will capture more accurate information about nearby decision boundaries. This
understanding of robust interpretability leads to our second contribution:
\emph{boundary attributions}, which aggregate information about the normal
vectors of local decision boundaries to explain a classification outcome. We
show that by leveraging the key factors underpinning robust interpretability,
boundary attributions produce sharper, more concentrated visual explanations --
even on non-robust models. Any example implementation can be found at
\url{https://github.com/zifanw/boundary}.


Abstract:
  Crustal deformation due to the 2016 earthquake sequence in Kumamoto, Japan,
that culminated in a preceding earthquake of magnitude M6.5 and a subsequent
M7.3 earthquake 28 hours later, caused stress perturbation on and around the
causative Futagawa-Hinagu fault zone. Monitoring changes in seismicity pattern
along this zone plays a role in understanding the process before and after
major earthquakes. For this purpose, stress-dependent laws in statistical
seismology can be used: the Gutenberg-Richter frequency-size law and the
Omori-Utsu aftershock-decay law. We review the results obtained by using these
laws in previous studies to show a zone of high stress near the eventual
epicenters of the M6.5 and M7.3 earthquakes before the start of the Kumamoto
sequence, and after it, showing a decreasing trend in stress along the
Futagawa-Hinagu fault zone. Detailed analysis suggests aseismic slips along the
causative fault zone. The aseismic preslip locally reduced stress just prior to
the M7.3 earthquake near its epicenter. Recently, a system was proposed by
Gulia and Wiemer (2019) that utilizes the Gutenberg-Richter frequency-size law
to judge, immediately after a large earthquake, whether it was the mainshock or
a foreshock to a future event. Based on the reviewed results and our new
results, further research that takes into account the spatial variation of
frequency-size distribution, allowing the exploration of the possibility of a
local preslip of a future nearby earthquake, is needed to improve this system.


Abstract:
  Magnitude pruning is a common, effective technique to identify sparse
subnetworks at little cost to accuracy. In this work, we ask whether a
particular architecture's accuracy-sparsity tradeoff can be improved by
combining pruning information across multiple runs of training. From a shared
ResNet-20 initialization, we train several network copies (\emph{siblings}) to
completion using different SGD data orders on CIFAR-10. While the siblings'
pruning masks are naively not much more similar than chance, starting sibling
training after a few epochs of shared pretraining significantly increases
pruning overlap. We then choose a subnetwork by either (1) taking all weights
that survive pruning in any sibling (mask union), or (2) taking only the
weights that survive pruning across all siblings (mask intersection). The
resulting subnetwork is retrained. Strikingly, we find that union and
intersection masks perform very similarly. Both methods match the
accuracy-sparsity tradeoffs of the one-shot magnitude pruning baseline, even
when we combine masks from up to $k = 10$ siblings.


Abstract:
  While checkpointing is typically combined with a restart of the whole
application, localized recovery permits all but the affected processes to
continue. In task-based cluster programming, for instance, the application can
then be finished on the intact nodes, and the lost tasks be reassigned.
  This extended abstract suggests to adapt a checkpointing and localized
recovery technique that has originally been developed for independent tasks to
nested fork-join programs. We consider a Cilk-like work stealing scheme with
work-first policy in a distributed memory setting, and describe the required
algorithmic changes. The original technique has checkpointing overheads below
1% and neglectable costs for recovery, we expect the new algorithm to achieve a
similar performance.


Abstract:
  Sentence embedding models aim to provide general purpose embeddings for
sentences. Most of the models studied in this paper claim to perform well on
STS tasks - but they do not report on their suitability for clustering. This
paper looks at four recent sentence embedding models (Universal Sentence
Encoder (Cer et al., 2018), Sentence-BERT (Reimers and Gurevych, 2019), LASER
(Artetxe and Schwenk, 2019), and DeCLUTR (Giorgi et al., 2020)). It gives a
brief overview of the ideas behind their implementations. It then investigates
how well topic classes in two text classification datasets (Amazon Reviews (Ni
et al., 2019) and News Category Dataset (Misra, 2018)) map to clusters in their
corresponding sentence embedding space. While the performance of the resulting
classification model is far from perfect, it is better than random. This is
interesting because the classification model has been constructed in an
unsupervised way. The topic classes in these real life topic classification
datasets can be partly reconstructed by clustering the corresponding sentence
embeddings.


Abstract:
  In this study, we analytically formulated the path integral representation of
the conditional probabilities for non-Markovian kinetic processes in terms of
the free energy of the thermodynamic system. We carry out analytically the
time-fractional kinetic equations for these processes. Thus, in a simple way,
we generalize path integral solutions of the Markovian to the non-Markovian
cases. We conclude that these pedagogical results can be applied to some
physical problems such as the deformed ion channels, internet networks and
non-equilibrium phase transition problems.


Abstract:
  Reconstruction of a quantum state is of prime importance for
quantum-information science. Specifically, means of efficient determination of
a state of atoms of room-temperature vapor may enable applications in quantum
computations and cryptography. To step toward such applications, here we
present a method of reconstruction of a collective density matrix of an atomic
ensemble, consisting of atoms with an $F=1$ ground state. Such a long-lived
state is often encountered in real systems (e.g., potassium, sodium, rubidium)
and hence may be practically utilized. Our theoretical treatment enables
derivation of explicit formulas relating optical signals (polarization rotation
and ellipticity change) with specific density-matrix elements. The analysis are
supported with numerical simulations, which allows to evaluate fidelity and
robustness of the algorithm. The tests show that our algorithm allows to obtain
the fidelity exceeded 0.95 even at noisy environment and/or significant atomic
manipulation imperfections.


Abstract:
  Our first experience of dimension typically comes in the intuitive Euclidean
sense: a line is one dimensional, a plane is two-dimensional, and a volume is
three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},
systems with a fractional dimension, ``fractals'', now play an important role
in science. The novelty of encountering fractional dimension, and the intrinsic
beauty of many fractals, have a strong appeal to students and provide a
powerful teaching tool. I describe here a low-cost and convenient experimental
method for observing fractal dimension, by measuring the power-law scaling of
the resistance of a fractal network of resistors. The experiments are quick to
perform, and the students enjoy both the construction of the network and the
collaboration required to create the largest networks. Learning outcomes
include analysis of resistor networks beyond the elementary series and parallel
combinations, scaling laws, and an introduction to fractional dimension.


Abstract:
  First described in 2014, Roli's cube $\mathcal{R}$ is a chiral $4$-polytope,
faithfully realized in Euclidean $4$-space (a situation earlier thought to be
impossible). Here we describe $\mathcal{R}$ in a new way, determine its minimal
regular cover, and reveal connections to the M\"{o}bius-Kantor configuration.


Abstract:
  A level set topology optimization approach that uses an auxiliary density
field to nucleate holes during the optimization process and achieves minimum
feature size control in optimized designs is explored. The level set field
determines the solid-void interface, and the density field describes the
distribution of a fictitious porous material using the solid isotropic material
with penalization. These fields are governed by two sets of independent
optimization variables which are initially coupled using a penalty for hole
nucleation. The strength of the density field penalization and projection are
gradually increased through the optimization process to promote a 0-1 density
distribution. This treatment of the density field combined with a second
penalty that regulates the evolution of the density field in the void phase,
mitigate the appearance of small design features. The minimum feature size of
optimized designs is controlled by the radius of the linear filter applied to
the density optimization variables. The structural response is predicted by the
extended finite element method, the sensitivities by the adjoint method, and
the optimization variables are updated by a gradient-based optimization
algorithm. Numerical examples investigate the robustness of this approach with
respect to algorithmic parameters and mesh refinement. The results show the
applicability of the combined density level set topology optimization approach
for both optimal hole nucleation and for minimum feature size control in 2D and
3D. This comes, however, at the cost of a more advanced problem formulation and
additional computational cost due to an increased number of optimization
variables.


Abstract:
  The Hamiltonian shape invariant of a domain $X \subset \mathbb R^4$, as a
subset of $\mathbb R^2$, describes the product Lagrangian tori which may be
embedded in $X$. We provide necessary and sufficient conditions to determine
whether or not a path in the shape invariant can lift, that is, be realized as
a smooth family of embedded Lagrangian tori, when $X$ is a basic
$4$-dimensional toric domain such as a ball $B^4(R)$, an ellipsoid $E(a,b)$
with $\frac{b}{a} \in {\mathbb N}_{\geq 2}$, or a polydisk $P(c,d)$. As
applications, via the path lifting, we can detect knotted embeddings of product
Lagrangian tori in many toric $X$. We also obtain novel obstructions to
symplectic embeddings between domains that are more general than toric concave
or toric convex.


Abstract:
  The interfacial band structures of multilayer systems play a crucial role for
the ultrafast charge and spin carrier dynamics at interfaces. Here, we study
the energy- and momentum-dependent quasiparticle lifetimes of excited states of
a lead monolayer film on Ag(111) prior and after the adsorption of a monolayer
of 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA). Using time-resolved
two-photon momentum microscopy, we show that the electron dynamics of the bare
Pb/Ag(111) bilayer system is dominated by isotropic intraband scattering
processes within the quantum well state as well as interband scattering
processes from the QWS into the Pb sideband. After the adsorption of PTCDA on
the Pb monolayer, the interband scattering is suppressed and the electron
dynamics is solely determined by intraband or inelastic scattering processes.
Our findings hence uncover a new possibility to selectively tune and control
scattering processes of quantum well systems by the adsorption of organic
molecules.


Abstract:
  Near-term quantum hardware can support two-qubit operations only on the
qubits that can interact with each other. Therefore, to execute an arbitrary
quantum circuit on the hardware, compilers have to first perform the task of
qubit routing, i.e., to transform the quantum circuit either by inserting
additional SWAP gates or by reversing existing CNOT gates to satisfy the
connectivity constraints of the target topology. We propose a procedure for
qubit routing that is architecture agnostic and that outperforms other
available routing implementations on various circuit benchmarks. The depth of
the transformed quantum circuits is minimised by utilizing the Monte Carlo tree
search to perform qubit routing, aided by a Graph neural network that evaluates
the value function and action probabilities for each state.


Abstract:
  We extend the model-free data-driven paradigm for rate-independent fracture
mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics,
Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical
fatigue. The problem is formulated by combining the balance governing equations
stemming from variational principles with a set of data points that encodes the
fracture constitutive behavior of the material. The solution is found as the
data point that best satisfies the meta-stability condition as given by the
variational procedure and following a distance minimization approach based on
closest-point-projection. The approach is tested on different setups adopting
different types of rate-dependent fracture and fatigue models affected or not
by white noise.


Abstract:
  Several proposed models for dark matter posit the existence of
self-interaction processes that can impact the shape of dark matter halos,
making them more spherical than the ellipsoidal halos of collisionless dark
matter. One method of probing the halo shapes, and thus the strength of the
dark matter self-interaction, is by measuring the shape of the X-ray gas that
traces the gravitational potential in relaxed elliptical galaxies. In this work
we identify a sample of 11 relaxed, isolated elliptical galaxies and measure
the ellipticity of the gravitating matter using X-ray images from the
XMM-Newton and Chandra telescopes. We explore a variety of different mass
configurations and find that the dark matter halos of these galaxies have
ellipticities around $\epsilon\approx 0.2-0.5$. While we find non-negligible
scatter in the ellipticity distribution, our results are consistent with some
degree of self-interaction at the scale of $\sigma/m \sim 1$ cm$^2$/g, yet they
also remain compatible with a cold dark matter scenario. We additionally
demonstrate how our results can be used to directly constrain specific dark
matter models and discuss implications for current and future simulations of
self-interacting dark matter models.


Abstract:
  The traditional design and development of metallic alloys has taken a
hill-climbing approach to date, with incremental advances. Throughout the last
century, aluminium (Al) alloy design has been essentially empirical and
iterative, based on lessons learned from in service use and human experience.
Incremental alloy development is costly, slow, and doesn't fully harness the
data that exists in the field of Al-alloy metallurgy. In the present work, an
attempt has been made to utilise a data science approach to develop a machine
learning (ML) model for Al-alloy design. An objective-optimisation process has
also been developed, to exploit the ML model, for user experience and practical
application. A successful model was developed and presented herein, along with
the open-access software.


Abstract:
  Coulomb interactions play an essential role in atomically-thin materials. On
one hand, they are strong and long-ranged in layered systems due to the lack of
environmental screening. On the other hand, they can be efficiently tuned by
means of surrounding dielectric materials. Thus all physical properties which
decisively depend on the exact structure of the electronic interactions can be
in principle efficiently controlled and manipulated from the outside via
Coulomb engineering. Here, we show how this concept can be used to create
fundamentally new plasmonic waveguides in metallic layered materials. We
discuss in detail how dielectrically structured environments can be utilized to
non-invasively confine plasmonic excitations in an otherwise homogeneous
metallic 2D system by modification of its many-body interactions. We define
optimal energy ranges for this mechanism and demonstrate plasmonic confinement
within several nanometers. In contrast to conventional functionalization
mechanisms, this scheme relies on a purely many-body concept and does not
involve any direct modifications to the active material itself.


Abstract:
  In this paper, we study the Erd\H{o}s-Falconer distance problem in five
dimensions for sets of Cartesian product structures. More precisely, we show
that for $A\subset \mathbb{F}_p$ with $|A|\gg p^{\frac{13}{22}}$, then
$\Delta(A^5)=\mathbb{F}_p$. When $|A-A|\sim |A|$, we obtain stronger statements
as follows:
  If $|A|\gg p^{\frac{13}{22}}$, then $(A-A)^2+A^2+A^2+A^2+A^2=\mathbb{F}_p.$
  If $|A|\gg p^{\frac{4}{7}}$, then
$(A-A)^2+(A-A)^2+A^2+A^2+A^2+A^2=\mathbb{F}_p.$
  We also prove that if $p^{4/7}\ll |A-A|=K|A|\le p^{5/8}$, then \[|A^2+A^2|\gg
\min \left\lbrace \frac{p}{K^4},
\frac{|A|^{8/3}}{K^{7/3}p^{2/3}}\right\rbrace.\] As a consequence,
$|A^2+A^2|\gg p$ when $|A|\gg p^{5/8}$ and $K\sim 1$, where $A^2=\{x^2\colon
x\in A\}$.


Abstract:
  A total coloring of a graph $G = (V, E)$ is an assignment of colors to
vertices and edges such that neither two adjacent vertices nor two incident
edges get the same color, and, for each edge, the end-points and the edge
itself receive different colors. Any valid total coloring induces a partition
of the elements of $G$ into total matchings, which are defined as subsets of
vertices and edges that can take the same color. In this paper, we propose
Integer Linear Programming models for both the Total Coloring and the Total
Matching problems, and we study the strength of the corresponding Linear
Programming relaxations. The total coloring is formulated as the problem of
finding the minimum number of total matchings that cover all the graph
elements, and we prove that this relaxation is tighter than a natural
assignment model. This covering formulation can be solved by a column
generation algorithm, where the pricing subproblem corresponds to the Weighted
Total Matching Problem. Hence, we study the Total Matching Polytope. We
introduce two families of nontrivial valid inequalities: congruent-2k3 cycle
inequalities based on the parity of the vertex set induced by the cycle, and
clique inequalities induced by complete subgraphs of even order. We prove that
congruent-2k3 cycle inequalities are facet-defining only when k = 4, while the
even cliques are always facet-defining. Since the separation problem of the
clique inequalities of even order is NP-hard, we get a polyhedral proof of the
NP-hardness of the Weighted Total Matching Problem.


Abstract:
  Recent approaches to data-to-text generation have adopted the very successful
encoder-decoder architecture or variants thereof. These models generate text
which is fluent (but often imprecise) and perform quite poorly at selecting
appropriate content and ordering it coherently. To overcome some of these
issues, we propose a neural model with a macro planning stage followed by a
generation stage reminiscent of traditional methods which embrace separate
modules for planning and surface realization. Macro plans represent high level
organization of important content such as entities, events and their
interactions; they are learnt from data and given as input to the generator.
Extensive experiments on two data-to-text benchmarks (RotoWire and MLB) show
that our approach outperforms competitive baselines in terms of automatic and
human evaluation.


Abstract:
  We establish the Krylov Safonov Harnack inequalities and Holder estimates for
fully nonlinear nonlocal operators of non-divergence form on Riemannian
manifolds with nonnegative sectional curvatures. To this end, we first define
the nonlocal Pucci operators on manifolds that give rise to the concept of
non-divergence form operators. We then provide the uniform regularity results
for these operators which recover the classical results for second order local
operators as limits.


Abstract:
  Understanding physical properties of quantum emitters strongly interacting
with quantized electromagnetic modes, both discrete and continuous spectra, is
one of the primary goals in the emergent field of waveguide quantum
electrodynamics (QED). When the light-matter coupling strength is comparable to
or even exceeds energies of elementary excitations, conventional approaches
based on perturbative treatment of light-matter interactions, two-level
description of matter excitations, and photon-number truncation are no longer
sufficient. Here we study in and out of equilibrium properties of waveguide QED
in such nonperturbative regimes on the basis of a comprehensive and rigorous
theoretical approach using an asymptotic decoupling unitary transformation. We
uncover several surprising features ranging from symmetry-protected many-body
bound states in the continuum to strong renormalization of the effective mass
and potential; the latter may explain recent experiments demonstrating
cavity-induced changes in chemical reactivity as well as enhancements of
ferromagnetism or superconductivity. To illustrate our general results with
concrete examples, we use our formalism to study a model of coupled cavity
arrays, which is relevant to experiments in superconducting qubits interacting
with microwave resonators or atoms coupled to photonic crystals. We examine the
relation between our results and delocalization-localization transition in the
spin-boson model; notably, we point out that one can find a quantum phase
transition akin to the superradiant transition in multi-emitter waveguide QED
systems with superlinear photonic dispersion. We also discuss applications of
our results to other problems in different fields, including quantum optics,
condensed matter physics, and quantum chemistry.


Abstract:
  Twisted bilayer graphene (TBG) realizes a highly tunable, strongly
interacting system featuring superconductivity and various correlated
insulating states. We establish gate-defined wires in TBG with
proximity-induced spin-orbit coupling as $(i)$ a tool for revealing the nature
of correlated insulators and $(ii)$ a platform for Majorana-based topological
qubits. In particular, we show that the band structure of a gate-defined wire
immersed in an `inter-valley coherent' correlated insulator inherits
electrically detectable fingerprints of symmetry breaking native to the latter.
Surrounding the wire by a superconducting TBG region on one side and an
inter-valley coherent correlated insulator on the other further enables the
formation of Majorana zero modes--possibly even at zero magnetic field
depending on the precise symmetry-breaking order present. Our proposal not only
introduces a highly gate-tunable topological qubit medium relying on internally
generated proximity effects, but can also shed light on the Cooper-pairing
mechanism in TBG.


Abstract:
  We study the concept of frame in tensor product of n-Hilbert spaces as tensor
product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of
the known results about bases to frames in this new Hilbert space. A
relationship between frame and bounded linear operator in tensor product of
n-Hilbert spaces is studied. Finally, the dual frame in tensor product of
n-Hilbert spaces is discussed.


Abstract:
  Using a holographic model, we study quantum field theories with a layer of
one CFT surrounded by another CFT, on either a periodic or an infinite
direction. We study the vacuum energy density in each CFT as a function of the
central charges, the thickness of the layer(s), and the properties of the
interfaces between the CFTs. The dual spacetimes in the holographic model
include two regions separated by a dynamical interface with some tension. For
two or more spatial dimensions, we find that a layer of CFT with more degrees
of freedom than the surrounding one can have an anomalously large negative
vacuum energy density for certain types of interfaces. The negative energy
density (or null-energy density in the direction perpendicular to the
interface) becomes arbitrarily large for fixed layer width when the tension of
the bulk interface approaches a lower critical value. We argue that in cases
where we have large negative energy density, we also have an anomalously high
transition temperature to the high-temperature thermal state.


Abstract:
  Spectral methods include a family of algorithms related to the eigenvectors
of certain data-generated matrices. In this work, we are interested in studying
the geometric landscape of the eigendecomposition problem in various spectral
methods. In particular, we first extend known results regarding the landscape
at critical points to larger regions near the critical points in a special case
of finding the leading eigenvector of a symmetric matrix. For a more general
eigendecomposition problem, inspired by recent findings on the connection
between the landscapes of empirical risk and population risk, we then build a
novel connection between the landscape of an eigendecomposition problem that
uses random measurements and the one that uses the true data matrix. We also
apply our theory to a variety of low-rank matrix optimization problems and
conduct a series of simulations to illustrate our theoretical findings.


Abstract:
  Control over plasmonic colors on the nanoscale is of great interest for
high-resolution display, imaging, and information encryption applications.
However, so far, very limited schemes have been attempted for dynamic plasmonic
color generation. In this paper, we demonstrate a scanning plasmonic color
generation scheme, in which subwavelength plasmonic pixels can be laterally
switched on/off through directional hydrogenation/dehydrogenation of a
magnesium screen. We show several dynamic plasmonic color displays with
different scanning functions by varying the number and geometries of the
palladium gates, where hydrogen enters the scanning screens. In particular, we
employ the scanning effects to create a dynamic plasmonic quick response code.
The information cannot be decrypted by varying the polarization states of light
or by accessing the physical features. Rather, it can only be read out using
hydrogen as a decoding key. Our work advances the established design concepts
for plasmonic color printing and provides insights into the development of
optical information storage and anticounterfeiting features.


Abstract:
  Large-radius excitons in polar crystals are considered. It is shown that
translation invariant description of excitons interacting with a phonon field
leads to a nonzero contribution of phonons into the exciton ground state energy
only in the case of weak or intermediate electron-phonon coupling. A conclusion
is made that self-trapped excitons cannot exist in the limit of strong
coupling. Peculiarities of the absorption and emission spectra of translation
invariant excitons in a phonon field are discussed. Conditions when the
hydrogen-like exciton model remains valid in the case of electron-phonon
interaction are found.


Abstract:
  The single ion properties of the zig-zag chain compound SrTm$_2$O$_4$ have
been investigated using heat capacity, magnetic susceptibility, magnetization,
inelastic neutron scattering, and polarized muon spectroscopy. Two crystal
field models are employed to estimate the single ion properties; a Density
Function Theory based model and an effective charge model based on the
Hutchings point charge model. The latter describes our experimental results
well. This model estimates an easy-axis anisotropy for one of the Tm$^{3+}$
sites and an easy-plane anisotropy for the second site. It also predicts a
mixed ground state with dominating $J = 0$ characteristics for both sites.
Additionally, muon spin rotation/relaxation ($\mu^+$SR) spectra reveal
oscillations, typically a sign of long-range magnetic order. However, the
temperature dependence of the precession frequency and the relaxation rates
indicate that the system is in an extended critical regime and the observed
relaxation is actually dynamic.


Abstract:
  Expanding laser plasmas, produced by high energy laser radiation, possess
both high thermal and magnetic field energy density. Characterization of such
plasma is challenging but needed for understanding of its physical behaviour.
Among all standard experimental techniques for plasma diagnostics, classical
interferometry is one of the most convenient, informative and accurate.
Attempts to extract more information from each single laser shot have led to
development of complex interferometry, which under certain processing allows to
reconstruct both plasma electron density and magnetic field strength
distributions using just one data object. However, the increase in complexity
and universality of the diagnostics requires a more detailed analysis of the
extracted values and their accuracy.This work focuses on axisymmetric
interaction geometry. We present general analysis, starting from the basic
principles and trace main error sources, finally ending up with plasma density
and magnetic field distributions with the derived error bars. Use of synthetic
profiles makes the analysis universal, though we present an example with real
experimental data in the Appendix.


Abstract:
  In this paper, we consider the portfolio optimization problem in a financial
market under a general utility function. Empirical results suggest that if a
significant market fluctuation occurs, invested wealth tends to have a notable
change from its current value. We consider an incomplete stochastic volatility
market model, that is driven by both a Brownian motion and a jump process. At
first, we obtain a closed-form formula for an approximation to the optimal
portfolio in a small-time horizon. This is obtained by finding the associated
Hamilton-Jacobi-Bellman integro-differential equation and then approximating
the value function by constructing appropriate super-solution and sub-solution.
It is shown that the true value function can be obtained by sandwiching the
constructed super-solution and sub-solution. We also prove the accuracy of the
approximation formulas. Finally, we provide a procedure for generating a
close-to-optimal portfolio for a finite time horizon.


Abstract:
  Multi-state survival analysis considers several potential events of interest
along a disease pathway. Such analyses are crucial to model complex patient
trajectories and are increasingly being used in epidemiological and health
economic settings. Multi-state models often make the Markov assumption, whereby
an individual's future trajectory is dependent only upon their present state,
not their past. In reality, there may be transitional dependence upon either
previous events and/or more than one timescale, for example time since entry to
the current or previous state(s). The aim of this study was to develop an
illness-death Weibull model allowing for multiple timescales to impact the
future risk of death. Following this, we evaluated the performance of the
multiple timescale model against a Markov illness-death model in a set of
plausible simulation scenarios when the Markov assumption was violated. Guided
by a study in breast cancer, data were simulated from Weibull baseline
distributions, with hazard functions dependent on single and multiple
timescales. Markov and non-Markov models were fitted to account for/ignore the
underlying data structure. Ignoring the presence of multiple timescales led to
bias in underlying transition rates between states and associated covariate
effects, while transition probabilities and lengths of stay were fairly
robustly estimated. Further work may be needed to evaluate different estimands
or more complex multi-state models. Software implementations in Stata are also
described for simulating and estimating multiple timescale multi-state models.


Abstract:
  The numerical solution of differential equations can be formulated as an
inference problem to which formal statistical approaches can be applied.
However, nonlinear partial differential equations (PDEs) pose substantial
challenges from an inferential perspective, most notably the absence of
explicit conditioning formula. This paper extends earlier work on linear PDEs
to a general class of initial value problems specified by nonlinear PDEs,
motivated by problems for which evaluations of the right-hand-side, initial
conditions, or boundary conditions of the PDE have a high computational cost.
The proposed method can be viewed as exact Bayesian inference under an
approximate likelihood, which is based on discretisation of the nonlinear
differential operator. Proof-of-concept experimental results demonstrate that
meaningful probabilistic uncertainty quantification for the unknown solution of
the PDE can be performed, while controlling the number of times the
right-hand-side, initial and boundary conditions are evaluated. A suitable
prior model for the solution of the PDE is identified using novel theoretical
analysis of the sample path properties of Mat\'{e}rn processes, which may be of
independent interest.


Abstract:
  The asset trading volume on blockchain-based exchanges (DEX) increased
substantially since the advent of Automated Market Makers (AMM). Yet, AMMs and
their forks compete on the same blockchain, incurring unnecessary network and
block-space overhead, by attracting sandwich attackers and arbitrage
competitions. Moreover, conceptually speaking, a blockchain is one database,
and we find little reason to partition this database into multiple competing
exchanges, which then necessarily require price synchronization through
arbitrage.
  This paper shows that DEX arbitrage and trade routing among similar AMMs can
be performed efficiently and atomically on-chain within smart contracts. These
insights lead us to create a new AMM design, an Automated Arbitrage Market
Maker, short A2MM DEX. A2MM aims to unite multiple AMMs to reduce overheads,
costs and increase blockchain security. With respect to Miner Extractable Value
(MEV), A2MM serves as a decentralized design for users to atomically collect
MEV, mitigating the dangers of centralized MEV relay services.
  We show that A2MM offers essential security benefits. First, A2MM strengthens
the blockchain consensus security by mitigating the competitive exploitation of
MEV, therefore reducing the risks of consensus forks. A2MM reduces the network
layer overhead of competitive transactions, improves network propagation,
leading to less stale blocks and better blockchain security. Through trade
routing, A2MM reduces the predatory risks of sandwich attacks by taking
advantage of the minimum profitable victim input. A2MM also offers financial
benefits to traders. Failed swap transactions from competitive trading occupy
valuable block space, implying an upward pressure on transaction fees. Our
evaluations shows that A2MM frees up 32.8% block-space of AMM-related
transactions. In expectation, A2MM's revenue allows to reduce swap fees by 90%.


Abstract:
  Some prokaryotes possess CRISPR-Cas systems that provide adaptive immunity to
viruses guided by DNA segments called spacers acquired from invading phage.
However, the patchy incidence and limited memory breadth of CRISPR-Cas systems
suggest that their fitness benefits are offset by costs. Here, we propose that
cross-reactive CRISPR targeting can lead to heterologous autoimmunity, whereby
foreign spacers guide self-targeting in a spacer-length dependent fashion.
Balancing antiviral defense against autoimmunity predicts a scaling relation
between spacer length and CRISPR repertoire size. We find evidence for this
scaling through comparative analysis of sequenced prokaryotic genomes, and show
that this association also holds at the level of CRISPR types. In contrast, the
scaling is absent in strains with nonfunctional CRISPR loci. Finally, we
demonstrate that stochastic spacer loss can explain variations around the
scaling relation, even between strains of the same species. Our results suggest
that heterologous autoimmunity is a selective factor shaping the evolution of
CRISPR-Cas systems.


Abstract:
  We consider computations over networks with multiple broadcast channels that
intersect at a single party. Each broadcast link suffers from random bit-flip
noise that affects the receivers independently. We design interactive coding
schemes that successfully perform any computation over these noisy networks and
strive to reduce their communication overhead with respect to the original
(noiseless) computation.
  A simple variant of a coding scheme by Rajagopalan and Schulman (STOC 1994)
shows that any (noiseless) protocol of $R$ rounds can be reliably simulated in
$O(R\log n)$ rounds over a network with $n=n_1n_2+1$ parties in which a single
party is connected to $n_2$ noisy broadcast channels, each of which connects
$n_1$ distinct parties. We design new coding schemes with improved overheads.
Our approach divides the network into four regimes according to the
relationship between $n_1$ and $n_2$. We employ a two-layer coding where the
inner code protects each broadcast channel and is tailored to the specific
conditions of the regime in consideration. The outer layer protects the
computation in the network and is generally based on the scheme of Rajagopalan
and Schulman, adapted to the case of broadcast channels. The overhead we obtain
ranges from $O(\log\log n_2)$ to $O(\log n_2 \frac{\log\log n_1}{\log n_1})$
and beats the trivial $O(\log n)$ overhead in all four regimes.


Abstract:
  EZ Cnc, or EPIC 212182292, is a non-Blazhko RRab variable star located in the
field of K2 Campaign 16. Its atmospheric parameters ($T_{\rm eff}$, $\log{g}$,
[M/H]) and radial velocities are measured from the 55 high-quality LAMOST
medium-resolution spectra. The fundamental frequency of pulsation is derived as
$f=1.8323(17)$ d$^{-1}$ from the K2 light curves. The amplitude ratios $R_{21}
= 0.5115(15), 0.490(8)$, $R_{31} = 0.3249(20), 0.279(7)$ and Fourier phase
differences $\varphi_{21}=2.7550(20), 2.764(16)$, $\varphi_{31}=5.7194(25),
5.719(31)$ are determined from the Fourier decomposition of K2 light curve and
LAMOST radial velocity curve, respectively. Through the constraints of the
parameters, four optimal models are obtained in a time-dependent turbulent
convection model survey for EPIC 212182292. The parameters of EPIC 212182292
are derived as $M=0.48\pm0.03$ M$_{\odot}$, $L = 42\pm2$ L$_{\odot}$, $T_{\rm
eff}=6846\pm50$ K, $\log{g}=2.79\pm0.01$ dex, and $Z = 0.006\pm0.002$,
respectively. The precisely determined parameters for RRab variable stars like
EPIC 212180092 might help to better understand the period-luminosity
relationship of RR Lyrae stars.


Abstract:
  The AGM postulates by Alchourr\'{o}n, G\"{a}rdenfors, and Makinson continue
to represent a cornerstone in research related to belief change. We generalize
the approach of Katsuno and Mendelzon (KM) for characterizing AGM base revision
from propositional logic to the setting of (multiple) base revision in
arbitrary monotonic logics. Our core result is a representation theorem using
the assignment of total - yet not transitive - "preference" relations to belief
bases. We also provide a characterization of all logics for which our result
can be strengthened to preorder assignments (as in KM's original work).


Abstract:
  Realizing complete observability in the three-phase distribution system
remains a challenge that hinders the implementation of classic state estimation
algorithms. In this paper, a new method, called the pruned physics-aware neural
network (P2N2), is developed to improve the voltage estimation accuracy in the
distribution system. The method relies on the physical grid topology, which is
used to design the connections between different hidden layers of a neural
network model. To verify the proposed method, a numerical simulation based on
one-year smart meter data of load consumptions for three-phase power flow is
developed to generate the measurement and voltage state data. The IEEE 123-node
system is selected as the test network to benchmark the proposed algorithm
against the classic weighted least squares (WLS). Numerical results show that
P2N2 outperforms WLS in terms of data redundancy and estimation accuracy.


Abstract:
  We show that one can enumerate the vertices of the convex hull of integer
points in polytopes whose constraint matrices have bounded and nonzero
subdeterminants, in time polynomial in the dimension and encoding size of the
polytope. This extends a previous result by Artmann et al. who showed that
integer linear optimization in such polytopes can be done in polynomial time.


Abstract:
  We study the structure of galactic halos within a scalar dark matter model,
endowed with a repulsive quartic self-interaction, capable of undergoing the
superfluid phase transition in high-density regions. We demonstrate that the
thermalized cores are prone to fragmentation into superfluid droplets due to
the Jeans instability. Furthermore, since cores of astrophysical size may be
generated only when most of the particles comprising the halo reside in a
highly degenerate phase-space, the well-known bound on the dark matter
self-interaction cross section inferred from the collision of clusters needs to
be revised, accounting for the enhancement of the interaction rate due to
degeneracy. As a result, generation of kpc-size superfluid solitons, within the
parameter subspace consistent with the Bullet Cluster bound, requires dark
matter particles to be ultra-light.


Abstract:
  The selection of a single molecular handedness, or homochirality across all
living matter, is a mystery in the origin of life. Frank's seminal model showed
in the fifties how chiral symmetry breaking can occur in non-equilibrium
chemical networks. However, an important shortcoming in this classic model is
that it considers a small number of species, while there is no reason for the
prebiotic system, in which homochirality first appeared, to have had such a
simple composition. Furthermore, this model does not provide information on
what could have been the size of the molecules involved in this homochiral
prebiotic system. Here, we show that large molecular systems are likely to
undergo a phase transition towards a homochiral state, as a consequence of the
fact that they contain a large number of chiral species. Using chemoinformatics
tools, we quantify how abundant are chiral species in the chemical universe of
all possible molecules of a given length. Then, we propose that Frank's model
should be extended to include a large number of species, in order to possess
the transition towards homochirality as confirmed by numerical simulations.
Finally, using random matrix theory, we prove that large non-equilibrium
reaction networks possess a generic and robust phase transition towards a
homochiral state.


Abstract:
  In machine learning for fluid mechanics, fully-connected neural network (FNN)
only uses the local features for modelling, while the convolutional neural
network (CNN) cannot be applied to data on structured/unstructured mesh. In
order to overcome the limitations of FNN and CNN, the unstructured
convolutional neural network (UCNN) is proposed, which aggregates and
effectively exploits the features of neighbour nodes through the weight
function. Adjoint vector modelling is taken as the task to study the
performance of UCNN. The mapping function from flow-field features to adjoint
vector is constructed through efficient parallel implementation on GPU. The
modelling capability of UCNN is compared with that of FNN on validation set and
in aerodynamic shape optimization at test case. The influence of mesh changing
on the modelling capability of UCNN is further studied. The results indicate
that UCNN is more accurate in modelling process.