Abstract:
  The Preconditioned Conjugate Gradient (PCG) method is widely used for solving
linear systems of equations with sparse matrices. A recent version of PCG,
Pipelined PCG, eliminates the dependencies in the computations of the PCG
algorithm so that the non-dependent computations can be overlapped with
communication. In this paper, we propose three methods for efficient execution
of the Pipelined PCG algorithm on GPU accelerated heterogeneous architectures.
  The first two methods achieve task-parallelism using asynchronous executions
of different tasks on CPU cores and GPU. The third method achieves data
parallelism by decomposing the workload between CPU and GPU based on a
performance model. The performance model takes into account the relative
performance of CPU cores and GPU using some initial executions and performs 2D
data decomposition. We also implement optimization strategies like kernel
fusion for GPU and merging vector operations for CPU. Our methods give up to 8x
speedup and on average 3x speedup over PCG CPU implementation of Paralution and
PETSc libraries. They also give up to 5x speedup and on average 1.45x speedup
over PCG GPU implementation of Paralution and PETSc libraries. The third method
also provides an efficient solution for solving problems that cannot be fit
into the GPU memory and gives up to 2.5x speedup for such problems.


Abstract:
  We develop Stratified Shortest Solution Imitation Learning (3SIL) to learn
equational theorem proving in a deep reinforcement learning (RL) setting. The
self-trained models achieve state-of-the-art performance in proving problems
generated by one of the top open conjectures in quasigroup theory, the Abelian
Inner Mapping (AIM) Conjecture. To develop the methods, we first use two
simpler arithmetic rewriting tasks that share tree-structured proof states and
sparse rewards with the AIM problems. On these tasks, 3SIL is shown to
significantly outperform several established RL and imitation learning methods.
The final system is then evaluated in a standalone and cooperative mode on the
AIM problems. The standalone 3SIL-trained system proves in 60 seconds more
theorems (70.2%) than the complex, hand-engineered Waldmeister system (65.5%).
In the cooperative mode, the final system is combined with the Prover9 system,
proving in 2 seconds what standalone Prover9 proves in 60 seconds.


Abstract:
  Semi-iNat is a challenging dataset for semi-supervised classification with a
long-tailed distribution of classes, fine-grained categories, and domain shifts
between labeled and unlabeled data. This dataset is behind the second iteration
of the semi-supervised recognition challenge to be held at the FGVC8 workshop
at CVPR 2021. Different from the previous one, this dataset (i) includes images
of species from different kingdoms in the natural taxonomy, (ii) is at a larger
scale -- with 810 in-class and 1629 out-of-class species for a total of 330k
images, and (iii) does not provide in/out-of-class labels, but provides coarse
taxonomic labels (kingdom and phylum) for the unlabeled images. This document
describes baseline results and the details of the dataset which is available
here: \url{https://github.com/cvl-umass/semi-inat-2021}.


Abstract:
  X-ray ptychography has revolutionised nanoscale phase contrast imaging at
large-scale synchrotron sources in recent years. We present here the first
successful demonstration of the technique in a small-scale laboratory setting.
We conducted an experiment with a liquid metal-jet X-ray source and a single
photon-counting detector with a high spectral resolution. The experiment used a
spot size of 5 microns to produce a ptychographic phase image of a Siemens star
test pattern with a sub-micron spatial resolution. The result and methodology
presented show how high-resolution phase contrast imaging can now be performed
at small-scale laboratory sources worldwide.


Abstract:
  We will prove that there are trajectories generated by the function at the
origin of the 5x+1 problem which are divergent. The iterative application of
this function on the set of positive integers allows us to determine that more
than 17% of all these integers start divergent trajectories. Regarding the 3x+1
problem, this percentage tends towards zero, suggesting that all positive
integers are part of converging trajectories. Despite this appearance, we
cannot conclude that all positive integers belong to convergent trajectories.
Nevertheless, the results obtained in this paper allow us to follow the
evolution of the distribution of trajectories and to understand why the values
of positive integers ending in the integer 1 are more and more large.


Abstract:
  In the last decade, companies adopted DevOps as a fast path to deliver
software products according to customer expectations, with well aligned teams
and in continuous cycles. As a basic practice, DevOps relies on pipelines that
simulate factory swim-lanes. The more automation in the pipeline, the shorter a
lead time is supposed to be. However, applying DevOps is challenging,
particularly for industrial control systems (ICS) that support critical
infrastructures and that must obey to rigorous requirements from security
regulations and standards. Current research on security compliant DevOps
presents open gaps for this particular domain and in general for systematic
application of security standards. In this paper, we present a systematic
approach to integrate standard-based security activities into DevOps pipelines
and highlight their automation potential. Our intention is to share our
experiences and help practitioners to overcome the trade-off between adding
security activities into the development process and keeping a short lead time.
We conducted an evaluation of our approach at a large industrial company
considering the IEC 62443-4-1 security standard that regulates ICS. The results
strengthen our confidence in the usefulness of our approach and artefacts, and
in that they can support practitioners to achieve security compliance while
preserving agility including short lead times.


Abstract:
  Approximation fixpoint theory (AFT) provides an algebraic framework for the
study of fixpoints of operators on bilattices and has found its applications in
characterizing semantics for various classes of logic programs and nonmonotonic
languages. In this paper, we show one more application of this kind: the
alternating fixpoint operator by Knorr et al. for the study of the well-founded
semantics for hybrid MKNF knowledge bases is in fact an approximator of AFT in
disguise, which, thanks to the power of abstraction of AFT, characterizes not
only the well-founded semantics but also two-valued as well as three-valued
semantics for hybrid MKNF knowledge bases. Furthermore, we show an improved
approximator for these knowledge bases, of which the least stable fixpoint is
information richer than the one formulated from Knorr et al.'s construction.
This leads to an improved computation for the well-founded semantics. This work
is built on an extension of AFT that supports consistent as well as
inconsistent pairs in the induced product bilattice, to deal with
inconsistencies that arise in the context of hybrid MKNF knowledge bases. This
part of the work can be considered generalizing the original AFT from symmetric
approximators to arbitrary approximators.


Abstract:
  Sparse inverse covariance estimation (i.e., edge de-tection) is an important
research problem in recent years, wherethe goal is to discover the direct
connections between a set ofnodes in a networked system based upon the observed
nodeactivities. Existing works mainly focus on unimodal distributions,where it
is usually assumed that the observed activities aregenerated from
asingleGaussian distribution (i.e., one graph).However, this assumption is too
strong for many real-worldapplications. In many real-world applications (e.g.,
brain net-works), the node activities usually exhibit much more complexpatterns
that are difficult to be captured by one single Gaussiandistribution. In this
work, we are inspired by Latent DirichletAllocation (LDA) [4] and consider
modeling the edge detectionproblem as estimating a mixture ofmultipleGaussian
distribu-tions, where each corresponds to a separate sub-network. Toaddress
this problem, we propose a novel model called GaussianMixture Graphical Lasso
(MGL). It learns the proportionsof signals generated by each mixture component
and theirparameters iteratively via an EM framework. To obtain
moreinterpretable networks, MGL imposes a special regularization,called Mutual
Exclusivity Regularization (MER), to minimize theoverlap between different
sub-networks. MER also addresses thecommon issues in read-world data sets,i.e.,
noisy observationsand small sample size. Through the extensive experiments
onsynthetic and real brain data sets, the results demonstrate thatMGL can
effectively discover multiple connectivity structuresfrom the observed node
activities


Abstract:
  The branching factor of a game is the average number of new states reachable
from a given state. It is a widely used metric in AI research on board games,
but less often computed or discussed for videogames. This paper provides
estimates for the branching factors of 103 Atari 2600 games, as implemented in
the Arcade Learning Environment (ALE). Depending on the game, ALE exposes
between 3 and 18 available actions per frame of gameplay, which is an upper
bound on branching factor. This paper shows, based on an enumeration of the
first 1 million distinct states reachable in each game, that the average
branching factor is usually much lower, in many games barely above 1. In
addition to reporting the branching factors, this paper aims to clarify what
constitutes a distinct state in ALE.


Abstract:
  A pure frequency domain method for the computation of periodic solutions of
nonlinear ordinary differential equations (ODEs) is proposed in this study. The
method is particularly suitable for the analysis of systems that feature
distinct states, i.e. where the ODEs involve piecewise defined functions. An
event-driven scheme is used which is based on the direct calculation of the
state transition time instants between these states. An analytical formulation
of the governing nonlinear algebraic system of equations is developed for the
case of piecewise polynomial systems. Moreover, it is shown that derivatives of
the solution of up to second order can be calculated analytically, making the
method especially attractive for design studies. The methodology is applied to
several structural dynamical systems with conservative and dissipative
nonlinearities in externally excited and autonomous configurations. Great
performance and robustness of the proposed procedure was ascertained.


Abstract:
  We introduce a gravitational waveform inversion strategy that discovers
mechanical models of binary black hole (BBH) systems. We show that only a
single time series of (possibly noisy) waveform data is necessary to construct
the equations of motion for a BBH system. Starting with a class of universal
differential equations parameterized by feed-forward neural networks, our
strategy involves the construction of a space of plausible mechanical models
and a physics-informed constrained optimization within that space to minimize
the waveform error. We apply our method to various BBH systems including
extreme and comparable mass ratio systems in eccentric and non-eccentric
orbits. We show the resulting differential equations apply to time durations
longer than the training interval, and relativistic effects, such as perihelion
precession, radiation reaction, and orbital plunge, are automatically accounted
for. The methods outlined here provide a new, data-driven approach to studying
the dynamics of binary black hole systems.


Abstract:
  Compressed sensing (CS) involves sampling signals at rates less than their
Nyquist rates and attempting to reconstruct them after sample acquisition. Most
such algorithms have parameters, for example the regularization parameter in
LASSO, which need to be chosen carefully for optimal performance. These
parameters can be chosen based on assumptions on the noise level or signal
sparsity, but this knowledge may often be unavailable. In such cases, cross
validation (CV) can be used to choose these parameters in a purely data-driven
fashion. Previous work analysing the use of CV in CS has been based on the
$\ell_2$ cross-validation error with Gaussian measurement noise. But it is well
known that the $\ell_2$ error is not robust to impulse noise and provides a
poor estimate of the recovery error, failing to choose the best parameter. Here
we propose using the $\ell_1$ CV error which provides substantial performance
benefits given impulse measurement noise. Most importantly, we provide a
detailed theoretical analysis and error bounds for the use of $\ell_1$ CV error
in CS reconstruction. We show that with high probability, choosing the
parameter that yields the minimum $\ell_1$ CV error is equivalent to choosing
the minimum recovery error (which is not observable in practice). To our best
knowledge, this is the first paper which theoretically analyzes $\ell_1$-based
CV in CS.


Abstract:
  In this work, we prove some trace theorems for function spaces with a
nonlocal character that contain the classical $W^{s,p}$ space as a subspace.
The result we obtain generalizes well known trace theorems for
$W^{s,p}(\Omega)$ functions which has a well-defined $W^{1-s/p, p}$ trace on
the boundary of a domain with sufficient regularity. The new generalized spaces
are associated with norms that are characterized by nonlocal interaction
kernels defined heterogeneously with a special localization feature on the
boundary. Intuitively speaking, the class contains functions that are as rough
as an $L^p$ function inside the domain of definition but as smooth as a
$W^{s,p}$ function near the boundary. Our result is that the $W^{1-s/p, p}$
norm of the trace on the boundary such functions is controlled by the nonlocal
norms that are weaker than the classical $W^{s, p}$ norm. These results are
improvement and refinement of the classical results since the boundary trace
can be attained without imposing regularity of the function in the interior of
the domain. They also extend earlier results in the case of $p=2$. In the
meantime, we prove Hardy-type inequalities for functions in the new generalized
spaces that vanish on the boundary, showing them having the same decay rate to
the boundary as functions in the smaller space $W^{s,p}(\Omega)$. A
Poincar\'e-type inequality is also derived. An application of the new theory
leads to the well-posedness of a nonlinear variational problem that allows
possible singular behavior in the interior with imposed smoother data on the
boundary.


Abstract:
  We propose a systematic and topological study of limits $\lim_{\nu\to
0^+}G_\mathbb{R}\cdot(\nu x)$ of continuous families of adjoint orbits for
non-compact simple Lie groups. This limit is always a finite union of nilpotent
orbits. We describe explicitly these nilpotent orbits in terms of Richardson
orbits in the case of hyperbolic semisimple elements. We also show that one can
approximate minimal nilpotent orbits or even nilpotent orbits by elliptic
semisimple orbits. The special cases of $\mathrm{SL}_n(\mathbb{R})$ and
$\mathrm{SU}(p,q)$ are computed in detail.


Abstract:
  The recent success of graph neural networks has significantly boosted
molecular property prediction, advancing activities such as drug discovery. The
existing deep neural network methods usually require large training dataset for
each property, impairing their performances in cases (especially for new
molecular properties) with a limited amount of experimental data, which are
common in real situations. To this end, we propose Meta-MGNN, a novel model for
few-shot molecular property prediction. Meta-MGNN applies molecular graph
neural network to learn molecular representation and builds a meta-learning
framework for model optimization. To exploit unlabeled molecular information
and address task heterogeneity of different molecular properties, Meta-MGNN
further incorporates molecular structure, attribute based self-supervised
modules and self-attentive task weights into the former framework,
strengthening the whole learning model. Extensive experiments on two public
multi-property datasets demonstrate that Meta-MGNN outperforms a variety of
state-of-the-art methods.


Abstract:
  An important challenge in reinforcement learning is training agents that can
solve a wide variety of tasks. If tasks depend on each other (e.g. needing to
learn to walk before learning to run), curriculum learning can speed up
learning by focusing on the next best task to learn. We explore curriculum
learning in a complex, visual domain with many hard exploration challenges:
Minecraft. We find that learning progress (defined as a change in success
probability of a task) is a reliable measure of learnability for automatically
constructing an effective curriculum. We introduce a learning-progress based
curriculum and test it on a complex reinforcement learning problem (called
"Simon Says") where an agent is instructed to obtain a desired goal item. Many
of the required skills depend on each other. Experiments demonstrate that: (1)
a within-episode exploration bonus for obtaining new items improves
performance, (2) dynamically adjusting this bonus across training such that it
only applies to items the agent cannot reliably obtain yet further increases
performance, (3) the learning-progress based curriculum elegantly follows the
learning curve of the agent, and (4) when the learning-progress based
curriculum is combined with the dynamic exploration bonus it learns much more
efficiently and obtains far higher performance than uniform baselines. These
results suggest that combining intra-episode and across-training exploration
bonuses with learning progress creates a promising method for automated
curriculum generation, which may substantially increase our ability to train
more capable, generally intelligent agents.


Abstract:
  We prove the unique existence of supersonic solutions of the Euler- Poisson
system for potential flow in a three-dimensional rectangular cylinder when
prescribing the velocity and the strength of electric field at the entrance.
Overall, the main framework is similar to [1], but there are several technical
differences to be taken care of vary carefully. And, it is our main goal to
treat all the technical differences occurring when one considers a three
dimensional supersonic solution of the steady Euler-Poisson system.


Abstract:
  We try to obtain meromorphic solution of Time dependent Schroedinger equation
which partially satisfies Painleve Integrable property. Our study and analysis
exhibits meromorphic behavior of classical particle trajectory. In other words,
particle is confined in punctured complex domain in singular fundamental
domain. . We have explicitly developed solution from Jacobi Elliptic function
and pole expansion approach in which solution remains meromorphic . Branch
point analysis also shows solution branches out near such singular point.
Meromorphic behavior is significant for a classical particle within quantum
limit.


Abstract:
  We consider the spin boson model with external magnetic field. We prove a
path integral formula for the heat kernel, known as Feynman-Kac-Nelson (FKN)
formula. We use this path integral representation to express the ground state
energy as a stochastic integral. Using this connection, we determine the
expansion coefficients of the ground state energy with respect to the magnetic
field strength and express them in terms of correlation functions of a
continuous Ising model. We then use a recently proven correlation inequality to
prove that the second order derivative is finite. As an application, we show
existence of ground states in infrared-singular situations.


Abstract:
  Federated learning aims to learn a global model that performs well on client
devices with limited cross-client communication. Personalized federated
learning (PFL) further extends this setup to handle data heterogeneity between
clients by learning personalized models. A key challenge in this setting is to
learn effectively across clients even though each client has unique data that
is often limited in size. Here we present pFedGP, a solution to PFL that is
based on Gaussian processes (GPs) with deep kernel learning. GPs are highly
expressive models that work well in the low data regime due to their Bayesian
nature. However, applying GPs to PFL raises multiple challenges. Mainly, GPs
performance depends heavily on access to a good kernel function, and learning a
kernel requires a large training set. Therefore, we propose learning a shared
kernel function across all clients, parameterized by a neural network, with a
personal GP classifier for each client. We further extend pFedGP to include
inducing points using two novel methods, the first helps to improve
generalization in the low data regime and the second reduces the computational
cost. We derive a PAC-Bayes generalization bound on novel clients and
empirically show that it gives non-vacuous guarantees. Extensive experiments on
standard PFL benchmarks with CIFAR-10, CIFAR-100, and CINIC-10, and on a new
setup of learning under input noise show that pFedGP achieves well-calibrated
predictions while significantly outperforming baseline methods, reaching up to
21% in accuracy gain.


Abstract:
  The nature of trions and their interaction with light has remained a puzzle.
The composition and dispersion of polaritons involving trions provide insights
into this puzzle. Trions and excitons in doped two-dimensional (2D) materials
are not independent excitations but are strongly coupled as a result of Coulomb
interactions. When excitons in doped 2D materials are also strongly coupled
with light inside an optical waveguide, the resulting polariton states are
coherent superpositions of exciton, trion, and photon states. We realize these
exciton-trion-polaritons by coupling an electron-doped monolayer of
two-dimensional material MoSe2 to the optical mode in a photonic crystal
waveguide. Our theoretical model, based on a many-body description of these
polaritons, reproduces the measured polariton energy band dispersion and Rabi
splittings with excellent accuracy. Our work sheds light on the structure of
trion states in 2D matrials and also on the indirect mechanism by which they
interact with light.


Abstract:
  The Time Dependent Boltzmann equation (TDBE) is a viable option to study
strongly out-of-equilibrium thermalization dynamics which are becoming
increasingly critical for many novel physical applications like Ultrafast
thermalization, Terahertz radiation etc. However its applicability is greatly
limited by the impractical scaling of the solution to its scattering integral
term. In our previous work\cite{Michael} we had proposed a numerical solver to
calculate the scattering integral term in the TDBE and then improved on
it\cite{1DPaper} to include second degree momentum discretisation and adaptive
time stepping. Our solver requires no close-to-equilibrium assumptions and can
work with realistic band structures and scattering amplitudes. Moreover, it is
numerically efficient and extremely robust against inherent numerical
instabilities. While in our previous work \cite{1DPaper} we showcased the
application of our solver to 1D materials, here we showcase its applications to
a simple 2D system and analyse thermalisations of the introduced
out-of-equilibrium excitations. The excitations added at higher energies were
found to thermalise faster than those introduced at relatively lower energies.
Also, we conclude that the thermalisation of the out-of-equilibrium population
to equilibrium values is not a simple exponential decay but rather a
non-trivial function of time. Nonetheless, by fitting a double exponential
function to the decay of the out-of-equilibrium population with time we were
able to generate quantitative insights into the time scales involved in the
thermalisations.


Abstract:
  Defined by Borel, a real number is normal to an integer base $b$, greater
than or equal to $2$, if in its base-$b$ expansion every block of digits occurs
with the same limiting frequency as every other block of the same length. We
consider the problem of insertion in constructed base-$b$ normal expansions to
obtain normality to base $(b+1)$.


Abstract:
  We investigate the quality of space approximation of a class of stochastic
integral equations of convolution type with Gaussian noise. Such equations
arise, for example, when considering mild solutions of stochastic fractional
order partial differential equations but also when considering mild solutions
of classical stochastic partial differential equations. The key requirement for
the equations is a smoothing property of the deterministic evolution operator
which is typical in parabolic type problems. We show that if one has access to
nonsmooth data estimates for the deterministic error operator together with its
derivative of a space discretization procedure, then one obtains error
estimates in pathwise H\"older norms with rates that can be read off the
deterministic error rates. We illustrate the main result by considering a class
of stochastic fractional order partial differential equations and space
approximations performed by spectral Galerkin methods and finite elements. We
also improve an existing result on the stochastic heat equation.


Abstract:
  Consider the random graph~\(G(n,p)\) obtained by allowing each edge in the
complete graph on~\(n\) vertices to be present with probability~\(p\)
independent of the other edges. In this paper, we study the minimum number of
edge edit operations needed to convert~\(G(n,p)\) into an Eulerian graph. We
obtain deviation estimates for three types Eulerian edit numbers based on
whether we perform only edge additions or only edge deletions or a combination
of both and show that with high probability, roughly~\(\frac{n}{4}\) operations
suffice in all three cases.


Abstract:
  We consider bond and site Bernoulli Percolation in both the oriented and the
non-oriented cases on $\mathbb{Z}^d$ and obtain rigorous upper bounds for the
critical points in those models for every dimension $d \geq 3$.


Abstract:
  This paper presents a novel multi-axis force-sensing approach in robotic
minimally invasive surgery with no modification to the surgical instrument.
Thus, it is adaptable to different surgical instruments. A novel 6-axis optical
force sensor, with local signal conditioning and digital electronics, was
mounted onto the proximal shaft of a da Vinci EndoWrist instrument. A new
cannula design comprising an inner tube and an outer tube was proposed. The
inner tube is attached to the cannula interface to the robot base through a
compliant leaf spring with adjustable stiffness. It allows bending of the
instrument shaft due to the tip forces. The outer tube mechanically filters out
the body forces from affecting the instrument bending behavior. A mathematical
model of the sensing principle was developed and used for model-based
calibration. A data-driven calibration based on a shallow neural network
architecture comprising a single 5-nodes hidden layer and a 5x1 output layer is
discussed. Extensive testing was conducted to validate that the sensor can
successfully measure the lateral forces and moments and the axial torque
applied to the instruments distal end within the desired resolution, accuracy,
and range requirements.


Abstract:
  We prove the conjectured first order expansion of the Levy-Lieb functional in
the semiclassical limit, arising from Density Functional Theory (DFT). This is
accomplished by interpreting the problem as the singular perturbation of an
Optimal Transport problem via a Dirichlet penalization.


Abstract:
  Domain generalization (DG) methods aim to achieve generalizability to an
unseen target domain by using only training data from the source domains.
Although a variety of DG methods have been proposed, a recent study shows that
under a fair evaluation protocol, called DomainBed, the simple empirical risk
minimization (ERM) approach works comparable to or even outperforms previous
methods. Unfortunately, simply solving ERM on a complex, non-convex loss
function can easily lead to sub-optimal generalizability by seeking sharp
minima. In this paper, we theoretically show that finding flat minima results
in a smaller domain generalization gap. We also propose a simple yet effective
method, named Stochastic Weight Averaging Densely (SWAD), to find flat minima.
SWAD finds flatter minima and suffers less from overfitting than does the
vanilla SWA by a dense and overfit-aware stochastic weight sampling strategy.
SWAD shows state-of-the-art performances on five DG benchmarks, namely PACS,
VLCS, OfficeHome, TerraIncognita, and DomainNet, with consistent and large
margins of +1.6% averagely on out-of-domain accuracy. We also compare SWAD with
conventional generalization methods, such as data augmentation and consistency
regularization methods, to verify that the remarkable performance improvements
are originated from by seeking flat minima, not from better in-domain
generalizability. Last but not least, SWAD is readily adaptable to existing DG
methods without modification; the combination of SWAD and an existing DG method
further improves DG performances. Source code is available at
https://github.com/khanrc/swad.


Abstract:
  Text generation has become one of the most important yet challenging tasks in
natural language processing (NLP). The resurgence of deep learning has greatly
advanced this field by neural generation models, especially the paradigm of
pretrained language models (PLMs). In this paper, we present an overview of the
major advances achieved in the topic of PLMs for text generation. As the
preliminaries, we present the general task definition and briefly describe the
mainstream architectures of PLMs for text generation. As the core content, we
discuss how to adapt existing PLMs to model different input data and satisfy
special properties in the generated text. We further summarize several
important fine-tuning strategies for text generation. Finally, we present
several future directions and conclude this paper. Our survey aims to provide
text generation researchers a synthesis and pointer to related research.


Abstract:
  While synthetic bilingual corpora have demonstrated their effectiveness in
low-resource neural machine translation (NMT), adding more synthetic data often
deteriorates translation performance. In this work, we propose alternated
training with synthetic and authentic data for NMT. The basic idea is to
alternate synthetic and authentic corpora iteratively during training. Compared
with previous work, we introduce authentic data as guidance to prevent the
training of NMT models from being disturbed by noisy synthetic data.
Experiments on Chinese-English and German-English translation tasks show that
our approach improves the performance over several strong baselines. We
visualize the BLEU landscape to further investigate the role of authentic and
synthetic data during alternated training. From the visualization, we find that
authentic data helps to direct the NMT model parameters towards points with
higher BLEU scores and leads to consistent translation performance improvement.


Abstract:
  We give algorithms to compute decompositions of a given polynomial, or more
generally mixed tensor, as sum of rank one tensors, and to establish whether
such a decomposition is unique. In particular, we present methods to compute
the decomposition of a general plane quintic in seven powers, and of a general
space cubic in five powers; the two decompositions of a general plane sextic of
rank nine, and the five decompositions of a general plane septic. Furthermore,
we give Magma implementations of all our algorithms.


Abstract:
  In order to treat the multiple time scales of ocean dynamics in an efficient
manner, the baroclinic-barotropic splitting technique has been widely used for
solving the primitive equations for ocean modeling. Based on the framework of
strong stability-preserving Runge-Kutta approach, we propose two high-order
multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the
resulting split system in this paper. The proposed schemes allow for a large
time step to be used for the three-dimensional baroclinic (slow) mode and a
small time step for the two-dimensional barotropic (fast) mode, in which each
of the two mode solves just need to satisfy their respective CFL conditions for
numerical stability. Specifically, at each time step, the baroclinic velocity
is first computed by advancing the baroclinic mode and fluid thickness of the
system with the large time-step \textcolor{black}{and the assistance of some
intermediate approximations of the baroctropic mode obtained by substepping
with the small-time step}; then the barotropic velocity is corrected by using
the small time step to re-advance the barotropic mode under an improved
barotropic forcing produced by interpolation of the forcing terms from the
preceding baroclinic mode solves; lastly, the fluid thickness is updated by
coupling the baroclinic and barotropic velocities. Additionally, numerical
inconsistencies on the discretized sea surface height caused by the mode
splitting are relieved via a reconciliation process with carefully calculated
flux deficits. Two benchmark tests from the "MPAS-Ocean" platform are carried
out to numerically demonstrate the performance and parallel scalability of the
proposed SSPRK-SE schemes.


Abstract:
  The performance of neural network models is often limited by the availability
of big data sets. To treat this problem, we survey and develop novel synthetic
data generation and augmentation techniques for enhancing low/zero-sample
learning in satellite imagery. In addition to extending synthetic data
generation approaches, we propose a hierarchical detection approach to improve
the utility of synthetic training samples. We consider existing techniques for
producing synthetic imagery--3D models and neural style transfer--as well as
introducing our own adversarially trained reskinning network, the
GAN-Reskinner, to blend 3D models. Additionally, we test the value of synthetic
data in a two-stage, hierarchical detection/classification model of our own
construction. To test the effectiveness of synthetic imagery, we employ it in
the training of detection models and our two stage model, and evaluate the
resulting models on real satellite images. All modalities of synthetic data are
tested extensively on practical, geospatial analysis problems. Our experiments
show that synthetic data developed using our approach can often enhance
detection performance, particularly when combined with some real training
images. When the only source of data is synthetic, our GAN-Reskinner often
boosts performance over conventionally rendered 3D models and in all cases the
hierarchical model outperforms the baseline end-to-end detection architecture.


Abstract:
  The introduction of transient learning degrees of freedom into a system can
lead to novel material design and training protocols that guide a system into a
desired metastable state. In this approach, some degrees of freedom, which were
not initially included in the system dynamics, are first introduced and
subsequently removed from the energy minimization process once the desired
state is reached. Using this conceptual framework, we create stable jammed
packings that exist in exceptionally deep energy minima marked by the absence
of low-frequency quasilocalized modes; this added stability persists in the
thermodynamic limit. The inclusion of particle radii as transient degrees of
freedom leads to deeper and much more stable minima than does the inclusion of
particle stiffnesses. This is because particle radii couple to the jamming
transition whereas stiffnesses do not. Thus different choices for the added
degrees of freedom can lead to very different training outcomes.


Abstract:
  A Non-Binary Snow Index for Multi-Component Surfaces (NBSI-MS) is proposed to
map snow/ice cover. The NBSI-MS is based on the spectral characteristics of
different Land Cover Types (LCTs) such as snow, water, vegetation, bare land,
impervious, and shadow surfaces. This index can increase the separability
between NBSI-MS values corresponding to snow from other LCTs and accurately
delineate the snow/ice cover in non-binary maps. To test the robustness of the
NBSI-MS, Greenland and France-Italy regions were examined where snow interacts
with highly diversified geographical ecosystem. Data recorded by Landsat 5 TM,
Landsat 8 OLI, and Sentinel-2A MSI satellites have been used. The NBSI-MS
performance was also compared against the well-known NDSI, NDSII-1, S3, and SWI
methods and evaluated based on Ground Reference Test Pixels (GRTPs) over
non-binarized results. The results show that the NBSI-MS achieves overall
accuracy (OA) ranging from 0.99 to 1 with kappa coefficient values in the same
range as OA. The precision assessment confirms the performance superiority of
the proposed NBSI-MS method for removing water and shadow surfaces over the
compared relevant indices.


Abstract:
  Xova is a software package that implements baseline-dependent time and
channel averaging on Measurement Set data. The uv-samples along a baseline
track are aggregated into a bin until a specified decorrelation tolerance is
exceeded. The degree of decorrelation in the bin correspondingly determines the
amount of channel and timeslot averaging that is suitable for samples in the
bin. This necessarily implies that the number of channels and timeslots varies
per bin and the output data loses the rectilinear input shape of the input
data.


Abstract:
  We consider the combination of uplink code-domain non-orthogonal multiple
access (NOMA) with massive multiple-input multiple-output (MIMO) and
reconfigurable intelligent surfaces (RISs). We assume a setup in which the base
station (BS) is capable of forming beams towards the RISs under line-of-sight
conditions, and where each RIS is covering a cluster of users. In order to
support multi-user transmissions within a cluster, code-domain NOMA via
spreading is utilized. We investigate the optimization of the RIS phase-shifts
such that a large number of users is supported. As it turns out, it is a
coupled optimization problem that depends on the detection order under
interference cancellation and the applied filtering at the BS. We propose to
decouple those variables by using sum-rate optimized phase-shifts as the
initial solution, allowing us to obtain a decoupled estimate of those
variables. Then, in order to determine the final phase-shifts, the problem is
relaxed into a semidefinite program that can be solved efficiently via convex
optimization algorithms. Simulation results show the effectiveness of our
approach in improving the detectability of the users.


Abstract:
  The development of thermal energy storage materials is the most attractive
strategy to harvest the solar energy and increase the energy utilization
efficiency. Phase change materials (PCMs) have received much attention in this
research field for several decades. Herein, we reported a new kind of PCM micro
topological structure, design direction, and the ultra-flexible, form-stable
and smart PCMs, polyrotaxane. The structure of polyrotaxane was fully confirmed
by 1H nuclear magnetic resonance,attenuated total reflection-fourier transform
infrared and X-ray diffraction. Then the tensile properties,thermal stability
in the air, phase change energy storage and shape memory properties of the
films were systematically analyzed. The results showed that all the mechanical
performance, thermal stability in air and shape memory properties of
polyrotaxanes were enhanced significantly compared to those of polyethylene
oxide (PEO). The form stability at temperatures above the melting point of PEO
significantly increased with the {\alpha}-CD addition. Further with the high
phase transition enthalpy and excellent cycle performance, the polyrotaxane
films are therefore promising sustainable and advanced form-stable phase change
materials for thermal energy storage. Notably, its ultra-high flexibility,
remolding ability and excellent shape memory properties provide a convenient
way for the intelligent heat treatment packaging of complex and flexible
electronic devices. In addition, this is a totally novel insight for
polyrotaxane application and new design method for form-stable PCMs.


Abstract:
  The scaleup of quantum computers operating in the microwave domain requires
advanced control electronics, and the use of integrated components that operate
at the temperature of the quantum devices is potentially beneficial. However,
such an approach requires ultra-low power dissipation and high signal quality
in order to ensure quantum-coherent operations. Here, we report an on-chip
device that is based on a Josephson junction coupled to a spiral resonator and
is capable of coherent continuous-wave microwave emission. We show that
characteristics of the device accurately follow a theory based on a
perturbative treatment of the capacitively shunted Josephson junction as a gain
element. The infidelity of typical quantum gate operations due to the phase
noise of this cryogenic 25-pW microwave source is less than 0.1% up to 10-ms
evolution times, which is below the infidelity caused by dephasing in
state-of-the-art superconducting qubits. Together with future cryogenic
amplitude and phase modulation techniques, our approach may lead to scalable
cryogenic control systems for quantum processors.


Abstract:
  We study space-pass tradeoffs in graph streaming algorithms for parameter
estimation and property testing problems such as estimating the size of maximum
matchings and maximum cuts, weight of minimum spanning trees, or testing if a
graph is connected or cycle-free versus being far from these properties. We
develop a new lower bound technique that proves that for many problems of
interest, including all the above, obtaining a $(1+\epsilon)$-approximation
requires either $n^{\Omega(1)}$ space or $\Omega(1/\epsilon)$ passes, even on
highly restricted families of graphs such as bounded-degree planar graphs. For
multiple of these problems, this bound matches those of existing algorithms and
is thus (asymptotically) optimal.
  Our results considerably strengthen prior lower bounds even for arbitrary
graphs: starting from the influential work of [Verbin, Yu; SODA 2011], there
has been a plethora of lower bounds for single-pass algorithms for these
problems; however, the only multi-pass lower bounds proven very recently in
[Assadi, Kol, Saxena, Yu; FOCS 2020] rules out sublinear-space algorithms with
exponentially smaller $o(\log{(1/\epsilon)})$ passes for these problems.
  One key ingredient of our proofs is a simple streaming XOR Lemma, a generic
hardness amplification result, that we prove: informally speaking, if a
$p$-pass $s$-space streaming algorithm can only solve a decision problem with
advantage $\delta > 0$ over random guessing, then it cannot solve XOR of $\ell$
independent copies of the problem with advantage much better than
$\delta^{\ell}$. This result can be of independent interest and useful for
other streaming lower bounds as well.


Abstract:
  We propose a novel algorithm for multi-player multi-armed bandits without
collision sensing information. Our algorithm circumvents two problems shared by
all state-of-the-art algorithms: it does not need as an input a lower bound on
the minimal expected reward of an arm, and its performance does not scale
inversely proportionally to the minimal expected reward. We prove a theoretical
regret upper bound to justify these claims. We complement our theoretical
results with numerical experiments, showing that the proposed algorithm
outperforms state-of-the-art in practice as well.


Abstract:
  Here it is proposed a three-dimensional plasmonic nonvolatile memory crossbar
arrays that can ensure a dual-mode operation in electrical and optical domains.
This can be realized through plasmonics that serves as a bridge between
photonics and electronics as the metal electrode is part of the waveguide. The
proposed arrangement is based on low-loss long-range dielectric-loaded surface
plasmon polariton waveguide where a metal stripe is placed between a buffer
layer and ridge. To achieve a dual-mode operation the materials were defined
that can provide both electrical and optical modulation functionality.


Abstract:
  Harnessing the potential wide-ranging quantum science applications of
molecules will require control of their interactions. Here, we use microwave
radiation to directly engineer and tune the interaction potentials between
ultracold calcium monofluoride (CaF) molecules. By merging two optical
tweezers, each containing a single molecule, we probe collisions in three
dimensions. The correct combination of microwave frequency and power creates an
effective repulsive shield, which suppresses the inelastic loss rate by a
factor of six, in agreement with theoretical calculations. The demonstrated
microwave shielding shows a general route to the creation of long-lived, dense
samples of ultracold molecules and evaporative cooling.


Abstract:
  We provide an explicit characterization of the covariant isotropy group of
any Grothendieck topos, i.e. the group of (extended) inner automorphisms of any
sheaf over a small site. As a consequence, we obtain an explicit
characterization of the centre of a Grothendieck topos, i.e. the automorphism
group of its identity functor.


Abstract:
  One of the fundamental task in graph data mining is to find a planted
community(dense subgraph), which has wide application in biology, finance, spam
detection and so on. For a real network data, the existence of a dense subgraph
is generally unknown. Statistical tests have been devised to testing the
existence of dense subgraph in a homogeneous random graph. However, many
networks present extreme heterogeneity, that is, the degrees of nodes or
vertexes don't concentrate on a typical value. The existing tests designed for
homogeneous random graph are not straightforwardly applicable to the
heterogeneous case. Recently, scan test was proposed for detecting a dense
subgraph in heterogeneous(inhomogeneous) graph(\cite{BCHV19}). However, the
computational complexity of the scan test is generally not polynomial in the
graph size, which makes the test impractical for large or moderate networks. In
this paper, we propose a polynomial-time test that has the standard normal
distribution as the null limiting distribution. The power of the test is
theoretically investigated and we evaluate the performance of the test by
simulation and real data example.


Abstract:
  Domain experts often need to extract structured information from large
corpora. We advocate for a search paradigm called ``extractive search'', in
which a search query is enriched with capture-slots, to allow for such rapid
extraction. Such an extractive search system can be built around syntactic
structures, resulting in high-precision, low-recall results. We show how the
recall can be improved using neural retrieval and alignment. The goals of this
paper are to concisely introduce the extractive-search paradigm; and to
demonstrate a prototype neural retrieval system for extractive search and its
benefits and potential. Our prototype is available at
\url{https://spike.neural-sim.apps.allenai.org/} and a video demonstration is
available at \url{https://vimeo.com/559586687}.


Abstract:
  We study the Symmetric Rendezvous Search Problem for a multi-robot system.
There are $n>2$ robots arbitrarily located on a line. Their goal is to meet
somewhere on the line as quickly as possible. The robots do not know the
initial location of any of the other robots or their own positions on the line.
The symmetric version of the problem requires the robots to execute the same
search strategy to achieve rendezvous. Therefore, we solve the problem in an
online fashion with a randomized strategy. In this paper, we present a
symmetric rendezvous algorithm which achieves a constant competitive ratio for
the total distance traveled by the robots. We validate our theoretical results
through simulations.


Abstract:
  External knowledge (a.k.a. side information) plays a critical role in
zero-shot learning (ZSL) which aims to predict with unseen classes that have
never appeared in training data. Several kinds of external knowledge, such as
text and attribute, have been widely investigated, but they alone are limited
with incomplete semantics. Some very recent studies thus propose to use
Knowledge Graph (KG) due to its high expressivity and compatibility for
representing kinds of knowledge. However, the ZSL community is still in short
of standard benchmarks for studying and comparing different external knowledge
settings and different KG-based ZSL methods. In this paper, we proposed six
resources covering three tasks, i.e., zero-shot image classification (ZS-IMGC),
zero-shot relation extraction (ZS-RE), and zero-shot KG completion (ZS-KGC).
Each resource has a normal ZSL benchmark and a KG containing semantics ranging
from text to attribute, from relational knowledge to logical expressions. We
have clearly presented these resources including their construction,
statistics, data formats and usage cases w.r.t. different ZSL methods. More
importantly, we have conducted a comprehensive benchmarking study, with two
general and state-of-the-art methods, two setting-specific methods and one
interpretable method. We discussed and compared different ZSL paradigms w.r.t.
different external knowledge settings, and found that our resources have great
potential for developing more advanced ZSL methods and more solutions for
applying KGs for augmenting machine learning. All the resources are available
at https://github.com/China-UK-ZSL/Resources_for_KZSL.


Abstract:
  We define a model of interactive communication where two agents with private
types can exchange information before a game is played. The model contains
Bayesian persuasion as a special case of a one-round communication protocol. We
define message complexity corresponding to the minimum number of interactive
rounds necessary to achieve the best possible outcome. Our main result is that
for bilateral trade, agents don't stop talking until they reach an efficient
outcome: Either agents achieve an efficient allocation in finitely many rounds
of communication; or the optimal communication protocol has infinite number of
rounds. We show an important class of bilateral trade settings where efficient
allocation is achievable with a small number of rounds of communication.


Abstract:
  The Earth's N2-dominated atmosphere is a very special feature. Firstly, N2 as
main gas is unique on the terrestrial planets in the inner solar system and
gives a hint for tectonic activity. Studying the origins of atmospheric
nitrogen and its stability provides insights into the uniqueness of the Earth's
habitat. Secondly, the coexistence of N2 and O2 within an atmosphere is
unequaled in the entire solar system. Such a combination is strongly linked to
the existence of aerobic lifeforms. The availability of nitrogen on the
surface, in the ocean, and within the atmosphere can enable or prevent the
habitability of a terrestrial planet, since nitrogen is vitally required by all
known lifeforms. In the present work, the different origins of atmospheric
nitrogen, the stability of nitrogen dominated atmospheres, and the development
of early Earth's atmospheric N2 are discussed. We show why N2-O2-atmospheres
constitute a biomarker not only for any lifeforms but for aerobic lifeforms,
which was the first major step that led to higher developed life on Earth.


Abstract:
  Risk capital allocations (RCAs) are an important tool in quantitative risk
management, where they are utilized to, e.g., gauge the profitability of
distinct business units, determine the price of a new product, and conduct the
marginal economic capital analysis. Nevertheless, the notion of RCA has been
living in the shadow of another, closely related notion, of risk measure (RM)
in the sense that the latter notion often shapes the fashion in which the
former notion is implemented. In fact, as the majority of the RCAs known
nowadays are induced by RMs, the popularity of the two are apparently very much
correlated. As a result, it is the RCA that is induced by the Conditional Tail
Expectation (CTE) RM that has arguably prevailed in scholarly literature and
applications. Admittedly, the CTE RM is a sound mathematical object and an
important regulatory RM, but its appropriateness is controversial in, e.g.,
profitability analysis and pricing. In this paper, we address the question as
to whether or not the RCA induced by the CTE RM may concur with alternatives
that arise from the context of profit maximization. More specifically, we
provide exhaustive description of all those probabilistic model settings, in
which the mathematical and regulatory CTE RM may also reflect the risk
perception of a profit-maximizing insurer.


Abstract:
  According to Skolem's conjecture, if an exponential Diophantine equation is
not solvable, then it is not solvable modulo an appropriately chosen modulus.
Besides several concrete equations, the conjecture has only been proved for
rather special cases. In this paper we prove the conjecture for equations of
the form $x^n-by_1^{k_1}\dots y_\ell^{k_\ell}=\pm 1$, where
$b,x,y_1,\dots,y_\ell$ are fixed integers and $n,k_1,\dots,k_\ell$ are
non-negative integral unknowns. This result extends a recent theorem of Hajdu
and Tijdeman.


Abstract:
  The COVID-19 pandemic has impacted lives and economies across the globe,
leading to many deaths. While vaccination is an important intervention, its
roll-out is slow and unequal across the globe. Therefore, extensive testing
still remains one of the key methods to monitor and contain the virus. Testing
on a large scale is expensive and arduous. Hence, we need alternate methods to
estimate the number of cases. Online surveys have been shown to be an effective
method for data collection amidst the pandemic. In this work, we develop
machine learning models to estimate the prevalence of COVID-19 using
self-reported symptoms. Our best model predicts the daily cases with a mean
absolute error (MAE) of 226.30 (normalized MAE of 27.09%) per state, which
demonstrates the possibility of predicting the actual number of confirmed cases
by utilizing self-reported symptoms. The models are developed at two levels of
data granularity - local models, which are trained at the state level, and a
single global model which is trained on the combined data aggregated across all
states. Our results indicate a lower error on the local models as opposed to
the global model. In addition, we also show that the most important symptoms
(features) vary considerably from state to state. This work demonstrates that
the models developed on crowd-sourced data, curated via online platforms, can
complement the existing epidemiological surveillance infrastructure in a
cost-effective manner. The code is publicly available at
https://github.com/parthpatwa/Can-Self-Reported-Symptoms-Predict-Daily-COVID-19-Cases.


Abstract:
  The current manuscript highlights the preparation of NiFe2O4 nanoparticles by
adopting sol-gel auto combustion route. The prime focus of this study is to
investigate the impact of gamma irradiation on the microstructural,
morphological, functional, optical and magnetic characteristics. The resulted
NiFe2O4 products have been characterized employing numerous instrumental
equipments such as FESEM, XRD, UV visible spectroscopy, FTIR and PPMS for a
variety of gamma ray doses (0 kGy, 25 kGy and 100 kGy). FESEM micrographs
illustrate the aggregation of ferrite nanoparticles in pristine NiFe2O4 product
having an average particle size of 168 nm and the surface morphology is altered
after exposure to gamma-irradiation. XRD spectra have been analyzed employing
Rietveld method and the results of the XRD investigation reveal the desired
phases (cubic spinel phases) of NiFe2O4 with observing other transitional
phases. Several microstructural parameters such as bond length, bond angle,
hopping length etc. have been determined from the analysis of Rietveld method.
This study reports that the gamma irradiations demonstrate a great influence on
optical bandgap energy and it varies from 1.80 and 1.89 eV evaluated via K M
function. FTIR measurement depicts a proof for the persistence of Ni-O and Fe-O
stretching vibrations within the respective products and thus indicating the
successful development of NiFe2O4. The saturation magnetization (MS) of
pristine Ni ferrite product is noticed to be 28.08 emug-1. A considerable
increase in MS is observed in case of low gamma-dose (25 kGy) and a decrement
nature is disclosed after the result of high dose of gamma irradiation
(100kGy).


Abstract:
  This paper extends the concept of informative selection, population
distribution and sample distribution to a spatial process context. These
notions were first defined in a context where the output of the random process
of interest consists of independent and identically distributed realisations
for each individual of a population. It has been showed that informative
selection was inducing a stochastic dependence among realisations on the
selected units. In the context of spatial processes, the "population" is a
continuous space and realisations for two different elements of the population
are not independent. We show how informative selection may induce a different
dependence among selected units and how the sample distribution differs from
the population distribution.


Abstract:
  Fueled by the call for formative assessments, diagnostic classification
models (DCMs) have recently gained popularity in psychometrics. Despite their
potential for providing diagnostic information that aids in classroom
instruction and students' learning, empirical applications of DCMs to classroom
assessments have been highly limited. This is partly because how DCMs with
different estimation methods perform in small sample contexts is not yet
well-explored. Hence, this study aims to investigate the performance of
respondent classification and item parameter estimation with a comprehensive
simulation design that resembles classroom assessments using different
estimation methods. The key findings are the following: (1) although the marked
difference in respondent classification accuracy was not observed among the
maximum likelihood (ML), Bayesian, and nonparametric methods, the Bayesian
method provided slightly more accurate respondent classification in
parsimonious DCMs than the ML method, and in complex DCMs, the ML method
yielded the slightly better result than the Bayesian method; (2) while item
parameter recovery was poor in both Bayesian and ML methods, the Bayesian
method exhibited unstable slip values owing to the multimodality of their
posteriors under complex DCMs, and the ML method produced irregular estimates
that appear to be well-estimated due to a boundary problem under parsimonious
DCMs.


Abstract:
  We study the constant term functor for $\mathbb{F}_p$-sheaves on the affine
Grassmannian in characteristic $p$ with respect to a Levi subgroup. Our main
result is that the constant term functor induces a tensor functor between
categories of equivariant perverse $\mathbb{F}_p$-sheaves. We apply this fact
to get information about the Tannakian monoids of the corresponding categories
of perverse sheaves. As a byproduct we also obtain geometric proofs of several
results due to Herzig on the mod $p$ Satake transform and the structure of the
space of mod $p$ Satake parameters.


Abstract:
  This paper studies the expressive power of artificial neural networks (NNs)
with rectified linear units. To study them as a model of real-valued
computation, we introduce the concept of Max-Affine Arithmetic Programs and
show equivalence between them and NNs concerning natural complexity measures.
We then use this result to show that two fundamental combinatorial optimization
problems can be solved with polynomial-size NNs, which is equivalent to the
existence of very special strongly polynomial time algorithms. First, we show
that for any undirected graph with $n$ nodes, there is an NN of size
$\mathcal{O}(n^3)$ that takes the edge weights as input and computes the value
of a minimum spanning tree of the graph. Second, we show that for any directed
graph with $n$ nodes and $m$ arcs, there is an NN of size $\mathcal{O}(m^2n^2)$
that takes the arc capacities as input and computes a maximum flow. These
results imply in particular that the solutions of the corresponding parametric
optimization problems where all edge weights or arc capacities are free
parameters can be encoded in polynomial space and evaluated in polynomial time,
and that such an encoding is provided by an NN.


Abstract:
  We present SMURF, a method for unsupervised learning of optical flow that
improves state of the art on all benchmarks by $36\%$ to $40\%$ (over the prior
best method UFlow) and even outperforms several supervised approaches such as
PWC-Net and FlowNet2. Our method integrates architecture improvements from
supervised optical flow, i.e. the RAFT model, with new ideas for unsupervised
learning that include a sequence-aware self-supervision loss, a technique for
handling out-of-frame motion, and an approach for learning effectively from
multi-frame video data while still only requiring two frames for inference.


Abstract:
  This work describes and demonstrates the operation of a virtual X-ray
algorithm operating on finite-element post-processing results which allows for
higher polynomial orders in geometry representation as well as density
distribution. A nested hierarchy of oriented bounding boxes is used for
preselecting candidate elements undergoing a ray-casting procedure. The exact
intersection points of the ray with the finite element are not computed,
instead the ray is discretized by a sequence of points. The element-local
coordinates of each discretized point are determined using a local
Newton-iteration and the resulting densities are accumulated. This procedure
results in highly accurate virtual X-ray images of finite element models.


Abstract:
  As the Data Science field continues to mature, and we collect more data, the
demand to store and analyze them will continue to increase. This increase in
data availability and demand for analytics will put a strain on data centers
and compute clusters-with implications for both energy costs and emissions. As
the world battles a climate crisis, it is prudent for organizations with data
centers to have a framework for combating increasing energy costs and emissions
to meet demand for analytics work. In this paper, I present a generalized
framework for organizations to audit data centers energy efficiency to
understand the resources required to operate a given data center and effective
steps organizations can take to improve data center efficiency and lower the
environmental impact.


Abstract:
  We study the bar instability in collisionless, rotating, anisotropic, stellar
systems, using N-body simulations and also the matrix technique for calculation
of modes with the perturbed collisionless Boltzmann equation. These methods are
applied to spherical systems with an initial Plummer density distribution, but
modified kinematically in two ways: the velocity distribution is tangentially
anisotropic, using results of Dejonghe, and the system is set in rotation by
reversing the velocities of a fraction of stars in various regions of phase
space, a la Lynden-Bell. The aim of the N-body simulations is first to survey
the parameter space, and, using those results, to identify regions of phase
space (by radius and orbital inclination) which have the most important
influence on the bar instability. The matrix method is then used to identify
the resonant interactions in the system which have the greatest effect on the
growth rate of a bar. Complementary series of N-body simulations examine these
processes in relation to the evolving frequency distribution and the pattern
speed. Finally, the results are synthesised with an existing theoretical
framework, and used to consider the old question of constructing a stability
criterion.


Abstract:
  Polygonal billiards are an example of pseudo-chaotic dynamics, a combination
of integrable evolution and sudden jumps due to conical singular points that
arise from the corners of the polygons. Such pseudo-chaotic behaviour, often
characterised by an algebraic separation of nearby trajectories, is believed to
be linked to the wild dependence that particle transport has on the fine
details of the billiard table. Here we address this relation through a detailed
numerical study of the statistics of displacement in a family of polygonal
channel billiards with parallel walls. We show that transport is characterised
by strong anomalous diffusion, with a mean square displacement that scales in
time faster than linear, and with a probability density of the displacement
exhibiting exponential tails and ballistic fronts. In channels of finite length
the distribution of first-passage times is characterised by fat tails, with a
mean first-passage time that diverges when the aperture angle is rational.
These findings have non trivial consequences for a variety of experiments.


Abstract:
  A set of vertices $S\subseteq V(G)$ is a basis or resolving set of a graph
$G$ if for each $x,y\in V(G)$ there is a vertex $u\in S$ such that $d(x,u)\neq
d(y,u)$. A basis $S$ is a fault-tolerant basis if $S\setminus \{x\}$ is a basis
for every $x \in S$. The fault-tolerant metric dimension (FTMD) $\beta'(G)$ of
$G$ is the minimum cardinality of a fault-tolerant basis. It is shown that each
twin vertex of $G$ belongs to every fault-tolerant basis of $G$. As a
consequence, $\beta'(G) = n(G)$ iff each vertex of $G$ is a twin vertex, which
corrects a wrong characterization of graphs $G$ with $\beta'(G) = n(G)$ from
[Mathematics 7(1) (2019) 78]. This FTMD problem is reinvestigated for Butterfly
networks, Benes networks, and silicate networks. This extends partial results
from [IEEE Access 8 (2020) 145435--145445], and at the same time, disproves
related conjectures from the same paper.


Abstract:
  Within the framework of the flux formulation of Double Field Theory (DFT) we
employ a generalised Scherk-Schwarz ansatz and discuss the classification of
the twists that in the presence of the strong constraint give rise to constant
generalised fluxes interpreted as gaugings. We analyse the various
possibilities of turning on the fluxes $H_{ijk}, F_{ij}{}^k, Q_i{}^{jk}$ and
$R^{ijk}$, and the solutions for the twists allowed in each case. While we do
not impose the DFT (or equivalently supergravity) equations of motion, our
results provide solution-generating techniques in supergravity when applied to
a background that does solve the DFT equations. At the same time, our results
give rise also to canonical transformations of 2-dimensional $\sigma$-models, a
fact which is interesting especially because these are integrability-preserving
transformations on the worldsheet. Both the solution-generating techniques of
supergravity and the canonical transformations of 2-dimensional $\sigma$-models
arise as maps that leave the generalised fluxes of DFT and their flat
derivatives invariant. These maps include the known
abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter
deformations, as well as novel generalisations of them.


Abstract:
  A didactical survey of the foundations of Algorithmic Information Theory.
These notes are short on motivation, history and background but introduce some
of the main techniques and concepts of the field.
  The "manuscript" has been evolving over the years. Please, look at "Version
history" below to see what has changed when.


Abstract:
  In multicentric calculus one takes a polynomial $p$ with distinct roots as a
new variable and represents complex valued functions by $\mathbb C^d$-valued
functions, where $d$ is the degree of $p$. An application is e.g. the
possibility to represent a piecewise constant holomorphic function as a
convergent power series, simultaneously in all components of $|p(z)| \le \rho$.
In this paper we study the necessary modifications needed, if we take a
rational function $r=p/q$ as the new variable instead. This allows to consider
functions defined in neighborhoods of any compact set as opposed to the
polynomial case where the domains $|p(z)| \le \rho$ are always polynomially
convex. Two applications are formulated. One giving a convergent power series
expression for Sylvester equations $AX-XB =C$ in the general case of $A,B$
being bounded operators in Banach spaces with distinct spectra. The other
application formulates a K-spectral result for bounded operators in Hilbert
spaces.


Abstract:
  Image-only and pseudo-LiDAR representations are commonly used for monocular
3D object detection. However, methods based on them have shortcomings of either
not well capturing the spatial relationships in neighbored image pixels or
being hard to handle the noisy nature of the monocular pseudo-LiDAR point
cloud. To overcome these issues, in this paper we propose a novel
object-centric voxel representation tailored for monocular 3D object detection.
Specifically, voxels are built on each object proposal, and their sizes are
adaptively determined by the 3D spatial distribution of the points, allowing
the noisy point cloud to be organized effectively within a voxel grid. This
representation is proved to be able to locate the object in 3D space
accurately. Furthermore, prior works would like to estimate the orientation via
deep features extracted from an entire image or a noisy point cloud. By
contrast, we argue that the local RoI information from the object image patch
alone with a proper resizing scheme is a better input as it provides complete
semantic clues meanwhile excludes irrelevant interferences. Besides, we
decompose the confidence mechanism in monocular 3D object detection by
considering the relationship between 3D objects and the associated 2D boxes.
Evaluated on KITTI, our method outperforms state-of-the-art methods by a large
margin. The code will be made publicly available soon.


Abstract:
  Optical atomic clocks have already overcome the eighteenth decimal digit of
instability and uncertainty demonstrating incredible control over external
perturbations of the clock transition frequency. At the same time there is an
increasing demand for atomic and ionic transitions with minimal sensitivity to
external fields, with practical operational wavelengths and robust readout
protocols. One of the goals is to simplify clock's operation maintaining its
relative uncertainty at low 10-18 level. It is especially important for
transportable and envisioned space-based optical clocks. We proved earlier that
the 1.14um inner-shell magnetic dipole transition in neutral thulium possesses
very low blackbody radiation shift compared to other neutrals. Here we
demonstrate operation of a bi-colour thulium optical clock with extraordinary
low sensitivity to the Zeeman shift due to a simultaneous interrogation of two
clock transitions and data processing. Our experiment shows suppression of the
quadratic Zeeman shift by at least three orders of magnitude. The effect of
tensor lattice Stark shift can be also reduced to below 10-18 in fractional
frequency units. All these features make thulium optical clock almost free from
hard-to-control systematic shifts. Together with convenient cooling and
trapping laser wavelengths, it provides great perspectives for thulium lattice
clock as a high-performance transportable system.


Abstract:
  In the past decades, great progress has been made in the field of optical and
particle-based measurement techniques for experimental analysis of fluid flows.
Particle Image Velocimetry (PIV) technique is widely used to identify flow
parameters from time-consecutive snapshots of particles injected into the
fluid. The computation is performed as post-processing of the experimental data
via proximity measure between particles in frames of reference. However, the
post-processing step becomes problematic as the motility and density of the
particles increases, since the data emerges in extreme rates and volumes.
Moreover, existing algorithms for PIV either provide sparse estimations of the
flow or require large computational time frame preventing from on-line use. The
goal of this manuscript is therefore to develop an accurate on-line algorithm
for estimation of the fine-grained velocity field from PIV data. As the data
constitutes a pair of images, we employ computer vision methods to solve the
problem. In this work, we introduce a convolutional neural network adapted to
the problem, namely Volumetric Correspondence Network (VCN) which was recently
proposed for the end-to-end optical flow estimation in computer vision. The
network is thoroughly trained and tested on a dataset containing both synthetic
and real flow data. Experimental results are analyzed and compared to that of
conventional methods as well as other recently introduced methods based on
neural networks. Our analysis indicates that the proposed approach provides
improved efficiency also keeping accuracy on par with other state-of-the-art
methods in the field. We also verify through a-posteriori tests that our newly
constructed VCN schemes are reproducing well physically relevant statistics of
velocity and velocity gradients.


Abstract:
  We study a predictive model for explaining the apparent deviation of the muon
anomalous magnetic moment from the Standard Model expectation. There are no new
scalars and hence no new hierarchy puzzles beyond those associated with the
Higgs; the only new particles at the TeV scale are vector-like singlet and
doublet leptons. Interestingly, this simple model provides a calculable example
violating the Wilsonian notion of naturalness: despite the absence of any
symmetries prohibiting its generation, the coefficient of the naively leading
dimension-six operator for $(g-2)$ vanishes at one-loop. While effective field
theorists interpret this either as a surprising UV cancellation of power
divergences, or as a delicate cancellation between matching UV and calculable
IR corrections to $(g-2)$ from parametrically separated scales, there is a
simple explanation in the full theory: the loop integrand is a total derivative
of a function vanishing in both the deep UV and IR. The leading contribution to
$(g-2)$ arises from dimension-eight operators, and thus the required masses of
new fermions are lower than naively expected, with a sizeable portion of
parameter space already covered by direct searches at the LHC. The viable
parameter space free of fine-tuning for the muon mass will be fully covered by
future direct LHC searches, and {\it all} of the parameter space can be probed
by precision measurements at planned future lepton colliders.


Abstract:
  We introduce the problem of optimal congestion control in cache networks,
whereby \emph{both} rate allocations and content placements are optimized
\emph{jointly}. We formulate this as a maximization problem with non-convex
constraints, and propose solving this problem via (a) a Lagrangian barrier
algorithm and (b) a convex relaxation. We prove different optimality guarantees
for each of these two algorithms; our proofs exploit the fact that the
non-convex constraints of our problem involve DR-submodular functions.


Abstract:
  In context of the Wolfram Physics Project, a certain class of abstract
rewrite systems known as "multiway systems" have played an important role in
discrete models of spacetime and quantum mechanics. However, as abstract
mathematical entities, these rewrite systems are interesting in their own
right. This paper undertakes the effort to establish computational properties
of multiway systems. Specifically, we investigate growth rates and growth
classes of string-based multiway systems. After introducing the concepts of
"growth functions", "growth rates" and "growth classes" to quantify a system's
state-space growth over "time" (successive steps of evolution) on different
levels of precision, we use them to show that multiway systems can, in a
specific sense, grow slower than all computable functions while never exceeding
the growth rate of exponential functions. In addition, we start developing a
classification scheme for multiway systems based on their growth class.
Furthermore, we find that multiway growth functions are not trivially regular
but instead "computationally diverse", meaning that they are capable of
computing or approximating various commonly encountered mathematical functions.
We discuss several implications of these properties as well as their physical
relevance. Apart from that, we present and exemplify methods for explicitly
constructing multiway systems to yield desired growth functions.


Abstract:
  The metastable helium line at 1083 nm can be used to probe the extended upper
atmospheres of close-in exoplanets and thus provide insight into their
atmospheric mass loss, which is likely to be significant in sculpting their
population. We used an ultranarrowband filter centered on this line to observe
two transits of the low-density gas giant HAT-P-18b, using the 200" Hale
Telescope at Palomar Observatory, and report the detection of its extended
upper atmosphere. We constrain the excess absorption to be $0.46\pm0.12\%$ in
our 0.635 nm bandpass, exceeding the transit depth from the Transiting
Exoplanet Survey Satellite (TESS) by $3.9\sigma$. If we fit this signal with a
1D Parker wind model, we find that it corresponds to an atmospheric mass loss
rate between $8.3^{+2.8}_{-1.9} \times 10^{-5}$ $M_\mathrm{J}$/Gyr and
$2.63^{+0.46}_{-0.64} \times 10^{-3}$ $M_\mathrm{J}$/Gyr for thermosphere
temperatures ranging from 4000 K to 13000 K, respectively. With a J magnitude
of 10.8, this is the faintest system for which such a measurement has been made
to date, demonstrating the effectiveness of this approach for surveying mass
loss on a diverse sample of close-in gas giant planets.


Abstract:
  In recent years, artificial neural networks (ANNs) have won numerous contests
in pattern recognition and machine learning. ANNS have been applied to problems
ranging from speech recognition to prediction of protein secondary structure,
classification of cancers, and gene prediction. Here, we intend to maximize the
chances of finding the Higgs boson decays to two $\tau$ leptons in the pseudo
dataset using a Machine Learning technique to classify the recorded events as
signal or background.


Abstract:
  We combine infectious disease transmission and the non-pharmaceutical
intervention (NPI) response to disease incidence into one closed model
consisting of two coupled delay differential equations for the incidence rate
and the time-dependent reproduction number. The model contains three free
parameters, the initial reproduction number, the intervention strength, and the
response delay relative to the time of infection. The NPI response is modeled
by assuming that the rate of change of the reproduction number is proportional
to the negative deviation of the incidence rate from an intervention threshold.
This delay dynamical system exhibits damped oscillations in one part of the
parameter space, and growing oscillations in another, and these are separated
by a surface where the solution is a strictly periodic nonlinear oscillation.
For parameters relevant for the COVID-19 pandemic, the tipping transition from
damped to growing oscillations occurs for response delays of the order of one
week, and suggests that effective control and mitigation of successive epidemic
waves cannot be achieved unless NPIs are implemented in a precautionary manner,
rather than merely as a response to the present incidence rate.


Abstract:
  Goal Recognition is the task of discerning the correct intended goal that an
agent aims to achieve, given a set of possible goals, a domain model, and a
sequence of observations as a sample of the plan being executed in the
environment. Existing approaches assume that the possible goals are formalized
as a conjunction in deterministic settings. In this paper, we develop a novel
approach that is capable of recognizing temporally extended goals in Fully
Observable Non-Deterministic (FOND) planning domain models, focusing on goals
on finite traces expressed in Linear Temporal Logic (LTLf) and (Pure) Past
Linear Temporal Logic (PLTLf). We empirically evaluate our goal recognition
approach using different LTLf and PLTLf goals over six common FOND planning
domain models, and show that our approach is accurate to recognize temporally
extended goals at several levels of observability.


Abstract:
  Additive Manufacturing (AM) processes intended for large scale components
deposit large volumes of material to shorten process duration. This reduces the
resolution of the AM process, which is typically defined by the size of the
deposition nozzle. If the resolution limitation is not considered when
designing for Large-Scale Additive Manufacturing (LSAM), difficulties can arise
in the manufacturing process, which may require the adaptation of the
deposition parameters. This work incorporates the nozzle size constraint into
Topology Optimization (TO) in order to generate optimized designs suitable to
the process resolution. This article proposes and compares two methods, which
are based on existing TO techniques that enable control of minimum and maximum
member size, and of minimum cavity size. The first method requires the minimum
and maximum member size to be equal to the deposition nozzle size, thus design
features of uniform width are obtained in the optimized design. The second
method defines the size of the solid members sufficiently small for the
resulting structure to resemble a structural skeleton, which can be interpreted
as the deposition path. Through filtering and projection techniques, the thin
structures are thickened according to the chosen nozzle size. Thus, a topology
tailored to the size of the deposition nozzle is obtained along with a
deposition proposal. The methods are demonstrated and assessed using 2D and 3D
benchmark problems.


Abstract:
  We reobserved in the $R_C$ and $i'_{Sloan}$ bands, during the years
2020-2021, seven Mira variables in Cassiopeia, for which historical
$i'_{Sloan}$ light curves were available from Asiago Observatory plates taken
in the years 1967-84. The aim was to check if any of them had undergone a
substantial change in the period or in the light curve shape. Very recent
public data form ZTF-DR5 were also used to expand our time base window. A
marked color change was detected for all the stars along their variability
cycle. The star V890 Cas showed a significant period decrease of 12\% from 483
to 428 days, one of the largest known to date. All the stars, save AV Cas,
showed a smaller variation amplitude in the recent CCD data, possibly due to a
photometric accuracy higher than that of the photographic plates.


Abstract:
  Furstenberg--Zimmer structure theory refers to the extension of the dichotomy
between the compact and weakly mixing parts of a measure preserving dynamical
system and the algebraic and geometric descriptions of such parts to a
conditional setting, where such dichotomy is established relative to a factor
and conditional analogues of those algebraic and geometric descriptions are
sought. Although the unconditional dichotomy and the characterizations are
known for arbitrary systems, the relative situation is understood under certain
countability and separability hypotheses on the underlying groups and spaces.
The aim of this article is to remove these restrictions in the relative
situation and establish a Furstenberg--Zimmer structure theory in full
generality. To achieve this generalization we had to change our perspective
from systems defined on concrete probability spaces to systems defined on
abstract probability algebras, and we had to introduce novel tools to analyze
systems relative to a factor. However, the change of perspective and the new
tools lead to some simplifications in the arguments and the presentation which
we arrange in a self-contained manner. As an independent byproduct, we
establish a connection between the relative analysis of systems in ergodic
theory and the internal logic in certain Boolean topoi.


Abstract:
  Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic
response by virtue of their dominant bending modes. Their behavior is even
richer at finite temperature. Here we use molecular dynamics (MD) to study the
vibrations of a thermally fluctuating two-dimensional elastic sheet with one
end clamped at its zero-temperature length. We uncover a tilt phase in which
the sheet fluctuates about a mean plane inclined with respect to the
horizontal, thus breaking reflection symmetry. We determine the phase behavior
as a function of the aspect ratio of the sheet and the temperature. We show
that tilt may be viewed as a type of transverse buckling instability induced by
clamping coupled to thermal fluctuations and develop an analytic model that
predicts the tilted and untilted regions of the phase diagram. Qualitative
agreement is found with the MD simulations. Unusual response driven by control
of purely geometric quantities like the aspect ratio, as opposed to external
fields, offers a very rich playground for two-dimensional mechanical
metamaterials.


Abstract:
  We constructs a new network by superposition of hexahedron , which are
scale-free, highly sparse,disassortative ,and maximal planar graphs. The
network degree distribution, agglomeration coefficient and degree of
correlation are computed separately using the iterative method, and these
characteristics are found to be very rich. The method of network characteristic
analysis can be applied to some actual systems, so as to study the complexity
of real network system under the framework of complex network theory.


Abstract:
  In this paper we explore conditions on variable symbols with respect to Haar
systems, defining Calder\'on-Zygmund type operators with respect to the dyadic
metrics associated to the Haar bases.We show that Petermichl's dyadic kernel
can be seen as a variable kernel singular integral and we extend it to dyadic
systems built on spaces of homogeneous type.


Abstract:
  We consider the problem of statistical inference for a class of
partially-observed diffusion processes, with discretely-observed data and
finite-dimensional parameters. We construct unbiased estimators of the score
function, i.e. the gradient of the log-likelihood function with respect to
parameters, with no time-discretization bias. These estimators can be
straightforwardly employed within stochastic gradient methods to perform
maximum likelihood estimation or Bayesian inference. As our proposed
methodology only requires access to a time-discretization scheme such as the
Euler-Maruyama method, it is applicable to a wide class of diffusion processes
and observation models. Our approach is based on a representation of the score
as a smoothing expectation using Girsanov theorem, and a novel adaptation of
the randomization schemes developed in Mcleish [2011], Rhee and Glynn [2015],
Jacob et al. [2020a]. This allows one to remove the time-discretization bias
and burn-in bias when computing smoothing expectations using the conditional
particle filter of Andrieu et al. [2010]. Central to our approach is the
development of new couplings of multiple conditional particle filters. We prove
under assumptions that our estimators are unbiased and have finite variance.
The methodology is illustrated on several challenging applications from
population ecology and neuroscience.


Abstract:
  Chronological age of healthy people is able to be predicted accurately using
deep neural networks from neuroimaging data, and the predicted brain age could
serve as a biomarker for detecting aging-related diseases. In this paper, a
novel 3D convolutional network, called two-stage-age-network (TSAN), is
proposed to estimate brain age from T1-weighted MRI data. Compared with
existing methods, TSAN has the following improvements. First, TSAN uses a
two-stage cascade network architecture, where the first-stage network estimates
a rough brain age, then the second-stage network estimates the brain age more
accurately from the discretized brain age by the first-stage network. Second,
to our knowledge, TSAN is the first work to apply novel ranking losses in brain
age estimation, together with the traditional mean square error (MSE) loss.
Third, densely connected paths are used to combine feature maps with different
scales. The experiments with $6586$ MRIs showed that TSAN could provide
accurate brain age estimation, yielding mean absolute error (MAE) of $2.428$
and Pearson's correlation coefficient (PCC) of $0.985$, between the estimated
and chronological ages. Furthermore, using the brain age gap between brain age
and chronological age as a biomarker, Alzheimer's disease (AD) and Mild
Cognitive Impairment (MCI) can be distinguished from healthy control (HC)
subjects by support vector machine (SVM). Classification AUC in AD/HC and
MCI/HC was $0.904$ and $0.823$, respectively. It showed that brain age gap is
an effective biomarker associated with risk of dementia, and has potential for
early-stage dementia risk screening. The codes and trained models have been
released on GitHub: https://github.com/Milan-BUAA/TSAN-brain-age-estimation.


Abstract:
  This paper investigates task-oriented communication for edge inference, where
a low-end edge device transmits the extracted feature vector of a local data
sample to a powerful edge server for processing. It is critical to encode the
data into an informative and compact representation for low-latency inference
given the limited bandwidth. We propose a learning-based communication scheme
that jointly optimizes feature extraction, source coding, and channel coding in
a task-oriented manner, i.e., targeting the downstream inference task rather
than data reconstruction. Specifically, we leverage an information bottleneck
(IB) framework to formalize a rate-distortion tradeoff between the
informativeness of the encoded feature and the inference performance. As the IB
optimization is computationally prohibitive for the high-dimensional data, we
adopt a variational approximation, namely the variational information
bottleneck (VIB), to build a tractable upper bound. To reduce the communication
overhead, we leverage a sparsity-inducing distribution as the variational prior
for the VIB framework to sparsify the encoded feature vector. Furthermore,
considering dynamic channel conditions in practical communication systems, we
propose a variable-length feature encoding scheme based on dynamic neural
networks to adaptively adjust the activated dimensions of the encoded feature
to different channel conditions. Extensive experiments evidence that the
proposed task-oriented communication system achieves a better rate-distortion
tradeoff than baseline methods and significantly reduces the feature
transmission latency in dynamic channel conditions.


Abstract:
  In this manuscript, we consider a scenario in which a spin-1/2 quanton goes
through a superposition of co-rotating and counter-rotating geodetic circular
paths, which play the role of the paths of a Mach-Zehnder interferometer in a
stationary and axisymmetric spacetime. Since the spin of the particle plays the
role of a quantum clock, as the quanton moves in a superposed path it gets
entangled with the momentum (or the path), and this will cause the
interferometric visibility (or the internal quantum coherence) to drop, since,
in stationary axisymmetric spacetimes there is a difference in proper time
elapsed along the two trajectories. However, as we show here, the proper time
of each path will couple to the corresponding local Wigner rotation, and the
effect in the spin of the superposed particle will be a combination of both.
Besides, we discuss a general framework to study the local Wigner rotations of
spin-1/2 particles in general stationary axisymmetric spacetimes for circular
orbits.


Abstract:
  The apparent clustering in longitude of perihelion $\varpi$ and ascending
node $\Omega$ of extreme trans-Neptunian objects (ETNOs) has been attributed to
the gravitational effects of an unseen 5-10 Earth-mass planet in the outer
solar system. To investigate how selection bias may contribute to this
clustering, we consider 14 ETNOs discovered by the Dark Energy Survey, the
Outer Solar System Origins Survey, and the survey of Sheppard and Trujillo.
Using each survey's published pointing history, depth, and TNO tracking
selections, we calculate the joint probability that these objects are
consistent with an underlying parent population with uniform distributions in
$\varpi$ and $\Omega$. We find that the mean scaled longitude of perihelion and
orbital poles of the detected ETNOs are consistent with a uniform population at
a level between $17\%$ and $94\%$, and thus conclude that this sample provides
no evidence for angular clustering.


Abstract:
  This paper presents DLL, a fast direct map-based localization technique using
3D LIDAR for its application to aerial robots. DLL implements a point cloud to
map registration based on non-linear optimization of the distance of the points
and the map, thus not requiring features, neither point correspondences. Given
an initial pose, the method is able to track the pose of the robot by refining
the predicted pose from odometry. Through benchmarks using real datasets and
simulations, we show how the method performs much better than Monte-Carlo
localization methods and achieves comparable precision to other
optimization-based approaches but running one order of magnitude faster. The
method is also robust under odometric errors. The approach has been implemented
under the Robot Operating System (ROS), and it is publicly available.


Abstract:
  Considering an example of the long-range Kitaev model, we are looking for a
correlation length in a model with long range interactions whose correlation
functions away from a critical point have power-law tails instead of the usual
exponential decay. It turns out that quasiparticle spectrum depends on a
distance from the critical point in a way that allows to identify the standard
correlation length exponent, $\nu$. The exponent implicitly defines a
correlation length $\xi$ that diverges when the critical point is approached.
We show that the correlation length manifests itself also in the correlation
function but not in its exponential tail because there is none. Instead $\xi$
is a distance that marks a crossover between two different algebraic decays
with different exponents. At distances shorter than $\xi$ the correlator decays
with the same power law as at the critical point while at distances longer than
$\xi$ it decays faster, with a steeper power law. For this correlator it is
possible to formulate the usual scaling hypothesis with $\xi$ playing the role
of the scaling distance. The correlation length also leaves its mark on the
subleading anomalous fermionic correlator but, interestingly, there is a regime
of long range interactions where its short distance critical power-law decay is
steeper than its long distance power law tail.


Abstract:
  We present a numerical study on a disordered artificial spin-ice system which
interpolates between the long-range ordered square ice and the fully degenerate
shakti ice. Starting from the square-ice geometry, disorder is implemented by
adding vertical/horizontal magnetic islands to the center of some randomly
chosen square plaquettes of the array, at different densities. When no island
is added we have ordered square ice. When all square plaquettes have been
modified we obtain shakti ice, which is disordered yet in a topological phase
corresponding to the Rys F-model. In between, geometrical frustration due to
these additional center spins disrupts the long-range Ising order of
square-ice, giving rise to a spin-glass regime at low temperatures. The
artificial spin system proposed in our work provides an experimental platform
to study the interplay between quenched disorder and geometrical frustration.


Abstract:
  Low power spintronic devices based on the propagation of pure magnonic spin
currents in antiferromagnetic insulator materials offer several distinct
advantages over ferromagnetic components including higher frequency magnons and
a stability against disturbing external magnetic fields. In this work, we make
use of the insulating antiferromagnetic phase of iron oxide, the mineral
hematite $\alpha$-Fe$_2$O$_3$ to investigate the long distance transport of
thermally generated magnonic spin currents. We report on the excitation of
magnons generated by the spin Seebeck effect, transported both parallel and
perpendicular to the antiferromagnetic easy-axis under an applied magnetic
field. Making use of an atomistic hematite toy model, we calculate the
transport characteristics from the deviation of the antiferromagnetic ordering
from equilibrium under an applied field. We resolve the role of the magnetic
order parameters in the transport, and experimentally we find significant
thermal spin transport without the need for a net magnetization.


Abstract:
  We study the finite convergence of iterative methods for solving convex
feasibility problems. Our key assumptions are that the interior of the solution
set is nonempty and that certain overrelaxation parameters converge to zero,
but with a rate slower than any geometric sequence. Unlike other works in this
area, which require divergent series of overrelaxations, our approach allows us
to consider some summable series. By employing quasi-Fej\'{e}rian analysis in
the latter case, we obtain additional asymptotic convergence guarantees, even
when the interior of the solution set is empty.