Abstract:
  In recent years, deep neural networks (DNNs) achieved state-of-the-art
performance on several computer vision tasks. However, the one typical drawback
of these DNNs is the requirement of massive labeled data. Even though few-shot
learning methods address this problem, they often use techniques such as
meta-learning and metric-learning on top of the existing methods. In this work,
we address this problem from a neuroscience perspective by proposing a
hypothesis named Ikshana, which is supported by several findings in
neuroscience. Our hypothesis approximates the refining process of conceptual
gist in the human brain while understanding a natural scene/image. While our
hypothesis holds no particular novelty in neuroscience, it provides a novel
perspective for designing DNNs for vision tasks. By following the Ikshana
hypothesis, we design a novel neural-inspired CNN architecture named
IkshanaNet. The empirical results demonstrate the effectiveness of our method
by outperforming several baselines on the entire and subsets of the Cityscapes
and the CamVid semantic segmentation benchmarks.


Abstract:
  Deep learning (DL) has gained much attention and become increasingly popular
in modern data science. Computer scientists led the way in developing deep
learning techniques, so the ideas and perspectives can seem alien to
statisticians. Nonetheless, it is important that statisticians become involved
-- many of our students need this expertise for their careers. In this paper,
developed as part of a program on DL held at the Statistical and Applied
Mathematical Sciences Institute, we address this culture gap and provide tips
on how to teach deep learning to statistics graduate students. After some
background, we list ways in which DL and statistical perspectives differ,
provide a recommended syllabus that evolved from teaching two iterations of a
DL graduate course, offer examples of suggested homework assignments, give an
annotated list of teaching resources, and discuss DL in the context of two
research areas.


Abstract:
  The problem of finding near-stationary points in convex optimization has not
been adequately studied yet, unlike other optimality measures such as
minimizing function value. Even in the deterministic case, the optimal method
(OGM-G, due to Kim and Fessler (2021)) has just been discovered recently. In
this work, we conduct a systematic study of the algorithmic techniques in
finding near-stationary points of convex finite-sums. Our main contributions
are several algorithmic discoveries: (1) we discover a memory-saving variant of
OGM-G based on the performance estimation problem approach (Drori and Teboulle,
2014); (2) we design a new accelerated SVRG variant that can simultaneously
achieve fast rates for both minimizing gradient norm and function value; (3) we
propose an adaptively regularized accelerated SVRG variant, which does not
require the knowledge of some unknown initial constants and achieves
near-optimal complexities. We put an emphasis on the simplicity and
practicality of the new schemes, which could facilitate future developments.


Abstract:
  Digital pathology tasks have benefited greatly from modern deep learning
algorithms. However, their need for large quantities of annotated data has been
identified as a key challenge. This need for data can be countered by using
unsupervised learning in situations where data are abundant but access to
annotations is limited. Feature representations learned from unannotated data
using contrastive predictive coding (CPC) have been shown to enable classifiers
to obtain state of the art performance from relatively small amounts of
annotated computer vision data. We present a modification to the CPC framework
for use with digital pathology patches. This is achieved by introducing an
alternative mask for building the latent context and using a multi-directional
PixelCNN autoregressor. To demonstrate our proposed method we learn feature
representations from the Patch Camelyon histology dataset. We show that our
proposed modification can yield improved deep classification of histology
patches.


Abstract:
  Exotic high-rank multipolar order parameters have been found to be
unexpectedly active in more and more correlated materials in recent years. Such
multipoles are usually dubbed as "Hidden Orders" since they are insensitive to
common experimental probes. Theoretically, it is also difficult to predict
multipolar orders via \textit{ab initio} calculations in real materials. Here,
we present an efficient method to predict possible multipoles in materials
based on linear response theory under random phase approximation. Using this
method, we successfully predict two pure meta-stable magnetic octupolar states
in monolayer $\alpha$-\ce{RuCl3}, which is confirmed by self-consistent
unrestricted Hartree-Fock calculations. We then demonstrate that these
octupolar states can be stabilized in monolayer $\alpha$-\ce{RuI3}, one of
which becomes the octupolar ground state. Furthermore, we also predict a
fingerprint of orthogonal magnetization pattern produced by the octupole
moment, which can be easily detected by experiment. The method and the example
presented in this work serve as a guidance for searching multipolar order
parameters in other correlated materials.


Abstract:
  With sequentially stacked self-attention, (optional) encoder-decoder
attention, and feed-forward layers, Transformer achieves big success in natural
language processing (NLP), and many variants have been proposed. Currently,
almost all these models assume that the layer order is fixed and kept the same
across data samples. We observe that different data samples actually favor
different orders of the layers. Based on this observation, in this work, we
break the assumption of the fixed layer order in the Transformer and introduce
instance-wise layer reordering into the model structure. Our Instance-wise
Ordered Transformer (IOT) can model variant functions by reordered layers,
which enables each sample to select the better one to improve the model
performance under the constraint of almost the same number of parameters. To
achieve this, we introduce a light predictor with negligible parameter and
inference cost to decide the most capable and favorable layer order for any
input sequence. Experiments on 3 tasks (neural machine translation, abstractive
summarization, and code generation) and 9 datasets demonstrate consistent
improvements of our method. We further show that our method can also be applied
to other architectures beyond Transformer. Our code is released at Github.


Abstract:
  This article shows that achieving capacity region of a 2-users weak Gaussian
Interference Channel (GIC) is equivalent to enlarging the core in a nested set
of Polymatroids (each equivalent to capacity region of a multiple-access
channel) through maximizing a minimum rate, then projecting along its
orthogonal span and continuing recursively. This formulation relies on defining
dummy private messages to capture the effect of interference in GIC. It follows
that relying on independent Gaussian random code-books is optimum, and the
corresponding solution corresponds to achieving the boundary in HK constraints.


Abstract:
  In this paper, we represent the problem of selecting miners within a
blockchain-based system as a subset selection problem. We formulate the problem
of minimising blockchain energy consumption as an optimisation problem with two
conflicting objectives: energy consumption and trust. The proposed model is
compared across different algorithms to demonstrate its performance.


Abstract:
  Edge computing offers the distinct advantage of harnessing compute
capabilities on resources located at the edge of the network to run workloads
of relatively weak user devices. This is achieved by offloading computationally
intensive workloads, such as deep learning from user devices to the edge. Using
the edge reduces the overall communication latency of applications as workloads
can be processed closer to where data is generated on user devices rather than
sending them to geographically distant clouds. Specialised hardware
accelerators, such as Graphics Processing Units (GPUs) available in the
cloud-edge network can enhance the performance of computationally intensive
workloads that are offloaded from devices on to the edge. The underlying
approach required to facilitate this is virtualization of GPUs. This paper
therefore sets out to investigate the potential of GPU accelerator
virtualization to improve the performance of deep learning workloads in a
cloud-edge environment. The AVEC accelerator virtualization framework is
proposed that incurs minimum overheads and requires no source-code modification
of the workload. AVEC intercepts local calls to a GPU on a device and forwards
them to an edge resource seamlessly. The feasibility of AVEC is demonstrated on
a real-world application, namely OpenPose using the Caffe deep learning
library. It is observed that on a lab-based experimental test-bed AVEC delivers
up to 7.48x speedup despite communication overheads incurred due to data
transfers.


Abstract:
  As herd size on dairy farms continues to increase, automatic health
monitoring of cows is gaining in interest. Lameness, a prevalent health
disorder in dairy cows, is commonly detected by analyzing the gait of cows. A
cow's gait can be tracked in videos using pose estimation models because models
learn to automatically localize anatomical landmarks in images and videos. Most
animal pose estimation models are static, that is, videos are processed frame
by frame and do not use any temporal information. In this work, a static
deep-learning model for animal-pose-estimation was extended to a temporal model
that includes information from past frames. We compared the performance of the
static and temporal pose estimation models. The data consisted of 1059 samples
of 4 consecutive frames extracted from videos (30 fps) of 30 different dairy
cows walking through an outdoor passageway. As farm environments are prone to
occlusions, we tested the robustness of the static and temporal models by
adding artificial occlusions to the videos.The experiments showed that, on
non-occluded data, both static and temporal approaches achieved a Percentage of
Correct Keypoints (PCKh@0.2) of 99%. On occluded data, our temporal approach
outperformed the static one by up to 32.9%, suggesting that using temporal data
was beneficial for pose estimation in environments prone to occlusions, such as
dairy farms. The generalization capabilities of the temporal model was
evaluated by testing it on data containing unknown cows (cows not present in
the training set). The results showed that the average PCKh@0.2 was of 93.8% on
known cows and 87.6% on unknown cows, indicating that the model was capable of
generalizing well to new cows and that they could be easily fine-tuned to new
herds. Finally, we showed that with harder tasks, such as occlusions and
unknown cows, a deeper architecture was more beneficial.


Abstract:
  Document-level machine translation conditions on surrounding sentences to
produce coherent translations. There has been much recent work in this area
with the introduction of custom model architectures and decoding algorithms.
This paper presents a systematic comparison of selected approaches from the
literature on two benchmarks for which document-level phenomena evaluation
suites exist. We find that a simple method based purely on back-translating
monolingual document-level data performs as well as much more elaborate
alternatives, both in terms of document-level metrics as well as human
evaluation.


Abstract:
  The possibility that rotating black holes could be natural particle
accelerators has been subject of intense debate. While it appears that for
extremal Kerr black holes arbitrarily high center of mass energies could be
achieved, several works pointed out that both theoretical as well as
astrophysical arguments would severely dampen the attainable energies. In this
work we study particle collisions near Kerr--Newman black holes, by reviewing
and extending previously proposed scenarios. Most importantly, we implement the
hoop conjecture for all cases and we discuss the astrophysical relevance of
these collisional Penrose processes. The outcome of this investigation is that
scenarios involving near-horizon target particles are in principle able to
attain, sub-Planckian, but still ultra high, center of mass energies of the
order of $10^{21}-10^{23}$ eV. Thus, these target particle collisional Penrose
processes could contribute to the observed spectrum of ultra high-energy cosmic
rays, even if the hoop conjecture is taken into account, and as such deserve
further scrutiny in realistic settings.


Abstract:
  In this paper, we describe a method to tackle data sparsity and create
recommendations in domains with limited knowledge about user preferences. We
expand the variational autoencoder collaborative filtering from a single-domain
to a multi-domain setting. The intuition is that user-item interactions in a
source domain can augment the recommendation quality in a target domain. The
intuition can be taken to its extreme, where, in a cross-domain setup, the user
history in a source domain is enough to generate high-quality recommendations
in a target one. We thus create a Product-of-Experts (POE) architecture for
recommendations that jointly models user-item interactions across multiple
domains. The method is resilient to missing data for one or more of the
domains, which is a situation often found in real life. We present results on
two widely-used datasets - Amazon and Yelp, which support the claim that
holistic user preference knowledge leads to better recommendations.
Surprisingly, we find that in some cases, a POE recommender that does not
access the target domain user representation can surpass a strong VAE
recommender baseline trained on the target domain.


Abstract:
  The KATRIN experiment is designed for a direct and model-independent
determination of the effective electron anti-neutrino mass via a high-precision
measurement of the tritium $\beta$-decay endpoint region with a sensitivity on
$m_\nu$ of 0.2$\,$eV/c$^2$ (90% CL). For this purpose, the $\beta$-electrons
from a high-luminosity windowless gaseous tritium source traversing an
electrostatic retarding spectrometer are counted to obtain an integral spectrum
around the endpoint energy of 18.6$\,$keV. A dominant systematic effect of the
response of the experimental setup is the energy loss of $\beta$-electrons from
elastic and inelastic scattering off tritium molecules within the source. We
determined the \linebreak energy-loss function in-situ with a pulsed
angular-selective and monoenergetic photoelectron source at various
tritium-source densities. The data was recorded in integral and differential
modes; the latter was achieved by using a novel time-of-flight technique.
  We developed a semi-empirical parametrization for the energy-loss function
for the scattering of 18.6-keV electrons from hydrogen isotopologs. This model
was fit to measurement data with a 95% T$_2$ gas mixture at 30$\,$K, as used in
the first KATRIN neutrino mass analyses, as well as a D$_2$ gas mixture of 96%
purity used in KATRIN commissioning runs. The achieved precision on the
energy-loss function has abated the corresponding uncertainty of
$\sigma(m_\nu^2)<10^{-2}\,\mathrm{eV}^2$ [arXiv:2101.05253] in the KATRIN
neutrino-mass measurement to a subdominant level.


Abstract:
  We present the results from a new search for candidate galaxies at z ~ 8.5-11
discovered over the 850 arcmin^2 area probed by the Cosmic Assembly
Near-Infrared Deep Extragalactic Legacy Survey (CANDELS). We use a photometric
redshift selection including both Hubble and Spitzer Space Telescope photometry
to robustly identify galaxies in this epoch at F160W < 26.6. We use a detailed
vetting procedure, including screening for persistence, stellar contamination,
inclusion of ground-based imaging, and followup space-based imaging to build a
robust sample of 11 candidate galaxies, three presented here for the first
time. The inclusion of Spitzer/IRAC photometry in the selection process reduces
contamination, and yields more robust redshift estimates than Hubble alone. We
constrain the evolution of the rest-frame ultraviolet luminosity function via a
new method of calculating the observed number densities without choosing a
prior magnitude bin size. We find that the abundance at our brightest probed
luminosities (M_UV=-22.3) is consistent with predictions from simulations which
assume that galaxies in this epoch have gas depletion times at least as short
as those in nearby starburst galaxies. Due to large Poisson and cosmic variance
uncertainties we cannot conclusively rule out either a smooth evolution of the
luminosity function continued from z=4-8, or an accelerate decline at z > 8. We
calculate that the presence of seven galaxies in a single field (EGS) is an
outlier at the 2-sigma significance level, implying the discovery of a
significant overdensity. These scenarios will be imminently testable to high
confidence within the first year of observations of the James Webb Space
Telescope.


Abstract:
  This paper investigates the stability properties of the spectrum of the
classical Steklov problem under domain perturbation. We find conditions which
guarantee the spectral stability and we show their optimality. We emphasize the
fact that our spectral stability results also involve convergence of
eigenfunctions in a suitable sense according with the definition of connecting
system by \cite{Vainikko}. The convergence of eigenfunctions can be expressed
in terms of the $H^1$ strong convergence. The arguments used in our proofs are
based on an appropriate definition of compact convergence of the resolvent
operators associated with the Steklov problems on varying domains. In order to
show the optimality of our conditions we present alternative assumptions which
give rise to a degeneration of the spectrum or to a discontinuity of the
spectrum in the sense that the eigenvalues converge to the eigenvalues of a
limit problem which does not coincide with the Steklov problem on the limiting
domain.


Abstract:
  In recent years, pi-conjugated polymers are attracting considerable interest
in view of their light-dependent torsional reorganization around the
pi-conjugated backbone, which determines peculiar light-emitting properties.
Motivated by the interest in designing conjugated polymers with tunable
photoswitchable pathways, we devised a computational framework to enhance the
sampling of the torsional conformational space and at the same time estimate
ground to excited-state free-energy differences. This scheme is based on a
combination of Hamiltonian Replica Exchange (REM), Parallel Bias metadynamics,
and free-energy perturbation theory. In our scheme, each REM replica samples an
intermediate unphysical state between the ground and the first two excited
states, which are characterized by TD-DFT simulations at the B3LYP/6-31G* level
of theory. We applied the method to a 5-mer of 9,9-dioctylfluorene and found
that upon irradiation this system can undergo a dihedral inversion from 155 to
-155 degrees crossing a barrier that decreases from 0.1 eV in the ground state
(S0) to 0.05 eV and 0.04 eV in the first (S1) and second (S2) excited states.
Furthermore, S1 and even more S2 were predicted to stabilize coplanar
dihedrals, with a local free-energy minimum located at +-44 degrees. The
presence of a free-energy barrier of 0.08 eV for the S1 and 0.12 eV for the S2
state can trap this conformation in a basin far from the global free-energy
minimum located at 155 degrees. The simulation results were compared with the
experimental emission spectrum, showing a quantitative agreement with the
predictions provided by our framework.


Abstract:
  We explore variants of Erd\H os' unit distance problem concerning dot
products between successive pairs of points chosen from a large finite subset
of either $\mathbb F_q^d$ or $\mathbb Z_q^d,$ where $q$ is a power of an odd
prime. Specifically, given a large finite set of points $E$, and a sequence of
elements of the base field (or ring) $(\alpha_1,\ldots,\alpha_k)$, we give
conditions guaranteeing the expected number of $(k+1)$-tuples of distinct
points $(x_1,\dots, x_{k+1})\in E^{k+1}$ satisfying $x_j \cdot
x_{j+1}=\alpha_j$ for every $1\leq j \leq k$.


Abstract:
  The generation of high-order harmonics in finite, hexagonal nanoribbons is
simulated. Ribbons with armchair and zig-zag edges are investigated by using a
tight-binding approach with only nearest neighbor hopping. By turning an
alternating on-site potential off or on, the system describes for example
graphene or hexagonal boron nitride, respectively. The incoming laser pulse is
linearly polarized along the ribbons. The emitted light has a polarization
component parallel to the polarization of the incoming field. The presence or
absence of a polarization component perpendicular to the polarization of the
incoming field can be explained by the symmetry of the ribbons. Characteristic
features in the harmonic spectra for the finite ribbons are analyzed with the
help of the band structure for the corresponding periodic systems.


Abstract:
  Pions constitute nearly $70\%$ of final state particles in ultra high energy
collisions. They act as a probe to understand the statistical properties of
Quantum Chromodynamics (QCD) matter i.e. Quark Gluon Plasma (QGP) created in
such relativistic heavy ion collisions (HIC). Apart from this, direct photons
are the most versatile tools to study relativistic HIC. They are produced, by
various mechanisms, during the entire space-time history of the strongly
interacting system. Direct photons provide measure of jet-quenching when
compared with other quark or gluon jets. The $\pi^{0}$ decay into two photons
make the identification of non-correlated gamma coming from another process
cumbersome in the Electromagnetic Calorimeter. We investigate the use of deep
learning architecture for reconstruction and identification of single as well
as multi particles showers produced in calorimeter by particles created in high
energy collisions. We utilize the data of electromagnetic shower at calorimeter
cell-level to train the network and show improvements for identification and
characterization. These networks are fast and computationally inexpensive for
particle shower identification and reconstruction for current and future
experiments at particle colliders.


Abstract:
  We propose a three-terminal structure to probe robust signatures of Majorana
zero modes. This structure consists of a quantum dot coupled to the normal
metal, s-wave superconducting and Majorana Y-junction leads. The zero-bias
differential conductance at zero temperature of the normal-metal lead peaks at
$2e^{2}/h$, which will be deflected after Majorana braiding. This quantized
conductance can entirely arise from the Majorana-induced crossed Andreev
reflection, protected by the energy gap of the superconducting lead. We find
that the effect of thermal broadening is significantly suppressed when the dot
is on resonance. In the case that the energy level of the quantum dot is much
larger than the superconducting gap, tunneling processes are dominated by
Majorana-induced crossed Andreev reflection. Particularly, a novel kind of
crossed Andreev reflection equivalent to the splitting of charge quanta $3e$
occurs after Majorana braiding.


Abstract:
  Fuzzing is becoming more and more popular in the field of vulnerability
detection. In the process of fuzzing, seed selection strategy plays an
important role in guiding the evolution direction of fuzzing. However, the SOTA
fuzzers only focus on individual uncertainty, neglecting the multi-factor
uncertainty caused by both randomization and evolution. In this paper, we
consider seed selection in fuzzing as a large-scale online planning problem
under uncertainty. We propose \mytool which is a new intelligent seed selection
strategy. In Alpha-Fuzz, we leverage the MCTS algorithm to deal with the
effects of the uncertainty of randomization and evolution of fuzzing.
Especially, we analyze the role of the evolutionary relationship between seeds
in the process of fuzzing, and propose a new tree policy and a new default
policy to make the MCTS algorithm better adapt to the fuzzing. We compared
\mytool with four state-of-the-art fuzzers in 12 real-world applications and
LAVA-M data set. The experimental results show that \mytool could find more
bugs on lava-M and outperforms other tools in terms of code coverage and number
of bugs discovered in the real-world applications. In addition, we tested the
compatibility of \mytool, and the results showed that \mytool could improve the
performance of existing tools such as MOPT and QSYM.


Abstract:
  The Baikal Gigaton Volume Detector (Baikal-GVD) is a km$^3$-scale neutrino
detector currently under construction in Lake Baikal, Russia. The detector
consists of several thousand optical sensors arranged on vertical strings, with
36 sensors per string. The strings are grouped into clusters of 8 strings each.
Each cluster can operate as a stand-alone neutrino detector. The detector
layout is optimized for the measurement of astrophysical neutrinos with
energies of $\sim$ 100 TeV and above. Events resulting from charged current
interactions of muon (anti-)neutrinos will have a track-like topology in
Baikal-GVD. A fast $\chi^2$-based reconstruction algorithm has been developed
to reconstruct such track-like events. The algorithm has been applied to data
collected in 2019 from the first five operational clusters of Baikal-GVD,
resulting in observations of both downgoing atmospheric muons and upgoing
atmospheric neutrinos. This serves as an important milestone towards
experimental validation of the Baikal-GVD design. The analysis is limited to
single-cluster data, favoring nearly-vertical tracks.


Abstract:
  Using a three-dimensional active vertex model, we numerically study the
shapes of strained unsupported epithelial monolayers subject to active
junctional noise due to stochastic binding and unbinding of myosin. We find
that while uniaxial, biaxial, and isotropic in-plane compressive strains do
lead to the formation of longitudinal, herringbone-pattern, and labyrinthine
folds, respectively, the villus morphology characteristic of, e.g., the small
intestine appears only if junctional tension fluctuations are strong enough to
fluidize the tissue. Moreover, the fluidized epithelium features villi even in
absence of compressive strain provided that the apico-basal differential
tension is large enough. We analyze several details of the different epithelial
forms including the role of strain rate and the modulation of tissue thickness
across folds. Our results show that nontrivial morphologies can form even in
unsupported, non-patterned epithelia.


Abstract:
  In this paper we study the magnetic charges of the free massless
Rarita-Schwinger field in four dimensional asymptotically flat space-time. This
is the first step towards extending the study of the dual BMS charges to
supergravity. The magnetic charges appear due to the addition of a boundary
term in the action. This term is similar to the theta term in Yang-Mills
theory. At null-infinity an infinite dimensional algebra is discovered, both
for the electric and magnetic charge.


Abstract:
  Graded modal types systems and coeffects are becoming a standard formalism to
deal with context-dependent computations where code usage plays a central role.
The theory of program equivalence for modal and coeffectful languages, however,
is considerably underdeveloped if compared to the denotational and operational
semantics of such languages. This raises the question of how much of the theory
of ordinary program equivalence can be given in a modal scenario. In this work,
we show that coinductive equivalences can be extended to a modal setting, and
we do so by generalising Abramsky's applicative bisimilarity to coeffectful
behaviours. To achieve this goal, we develop a general theory of ternary
program relations based on the novel notion of a comonadic lax extension, on
top of which we define a modal extension of Abramsky's applicative bisimilarity
(which we dub modal applicative bisimilarity). We prove such a relation to be a
congruence, this way obtaining a compositional technique for reasoning about
modal and coeffectful behaviours. But this is not the end of the story: we also
establish a correspondence between modal program relations and program
distances. This correspondence shows that modal applicative bisimilarity and (a
properly extended) applicative bisimilarity distance coincide, this way
revealing that modal program equivalences and program distances are just two
sides of the same coin.


Abstract:
  We study multivariate approximation in the average case setting with the
error measured in the weighted $L_2$ norm. We consider algorithms that use
standard information $\Lambda^{\rm std}$ consisting of function values or
general linear information $\Lambda^{\rm all}$ consisting of arbitrary
continuous linear functionals. We investigate the equivalences of various
notions of algebraic and exponential tractability for $\Lambda^{\rm std}$ and
$\Lambda^{\rm all}$ for the absolute error criterion, and show that the power
of $\Lambda^{\rm std}$ is the same as that of $\Lambda^{\rm all}$ for all
notions of algebraic and exponential tractability without any condition.
Specifically, we solve Open Problems 116-118 and almost solve Open Problem 115
as posed by E.Novak and H.Wo\'zniakowski in the book: Tractability of
Multivariate Problems, Volume III: Standard Information for Operators, EMS
Tracts in Mathematics, Z\"urich, 2012.


Abstract:
  A topological pump enables robust transport of quantized particles when the
system parameters are varied in a cyclic process. In previous studies,
topological pump was achieved inhomogeneous systems guaranteed by a topological
invariant of the bulk band structure when time is included as an additional
synthetic dimension. Recently, bulk-boundary correspondence has been
generalized to the bulk-disclination correspondence, describing the emergence
of topological bounded states in the crystallographic defects protected by the
bulk topology. Here we show the topological pumping can happen between
different disclination states with different chiralities in an inhomogeneous
structure. Based on a generalized understanding of the charge pumping process,
we explain the topological disclination pump by tracing the motion of Wannier
centers in each unit cell. Besides, by constructing two disclination structures
and introducing a symmetry-breaking perturbation, we achieve a topological
pumping between different dislocation cores. Our result opens a route to study
the topological pumping in inhomogeneous topological crystalline systems and
provides a flexible platform for robust energy transport.


Abstract:
  Person images captured by surveillance cameras are often occluded by various
obstacles, which lead to defective feature representation and harm person
re-identification (Re-ID) performance. To tackle this challenge, we propose to
reconstruct the feature representation of occluded parts by fully exploiting
the information of its neighborhood in a gallery image set. Specifically, we
first introduce a visible part-based feature by body mask for each person
image. Then we identify its neighboring samples using the visible features and
reconstruct the representation of the full body by an outlier-removable graph
neural network with all the neighboring samples as input. Extensive experiments
show that the proposed approach obtains significant improvements. In the
large-scale Occluded-DukeMTMC benchmark, our approach achieves 64.2% mAP and
67.6% rank-1 accuracy which outperforms the state-of-the-art approaches by
large margins, i.e.,20.4% and 12.5%, respectively, indicating the effectiveness
of our method on occluded Re-ID problem.


Abstract:
  This paper studies system theoretic properties of the class of difference
inclusions of convex processes. We will develop a framework considering
eigenvalues and eigenvectors, weakly and strongly invariant cones, and a
decomposition of convex processes. This will allow us to characterize
reachability, stabilizability and (null-)controllability of nonstrict convex
processes in terms of spectral properties. These characterizations generalize
all previously known results regarding for instance linear processes and
specific classes of nonstrict convex processes.


Abstract:
  In the international oil trade network (iOTN), trade shocks triggered by
extreme events may spread over the entire network along the trade links of the
central economies and even lead to the collapse of the whole system. In this
study, we focus on the concept of "too central to fail" and use traditional
centrality indicators as strategic indicators for simulating attacks on
economic nodes, and simulates various situations in which the structure and
function of the global oil trade network are lost when the economies suffer
extreme trade shocks. The simulation results show that the global oil trade
system has become more vulnerable in recent years. The regional aggregation of
oil trade is an essential source of iOTN's vulnerability. Maintaining global
oil trade stability and security requires a focus on economies with greater
influence within the network module of the iOTN. International organizations
such as OPEC and OECD established more trade links around the world, but their
influence on the iOTN is declining. We improve the framework of oil security
and trade risk assessment based on the topological index of iOTN, and provide a
reference for finding methods to maintain network robustness and trade
stability.


Abstract:
  Audio-visual speech enhancement system is regarded to be one of promising
solutions for isolating and enhancing speech of desired speaker. Conventional
methods focus on predicting clean speech spectrum via a naive convolution
neural network based encoder-decoder architecture, and these methods a) not
adequate to use data fully and effectively, b) cannot process features
selectively. The proposed model addresses these drawbacks, by a) applying a
model that fuses audio and visual features layer by layer in encoding phase,
and that feeds fused audio-visual features to each corresponding decoder layer,
and more importantly, b) introducing soft threshold attention into the model to
select the informative modality softly. This paper proposes attentional
audio-visual multi-layer feature fusion model, in which soft threshold
attention unit are applied on feature mapping at every layer of decoder. The
proposed model demonstrates the superior performance of the network against the
state-of-the-art models.


Abstract:
  In this article we propose a shooting algorithm for partially-affine optimal
control problems, this is, systems in which the controls appear both linearly
and nonlinearly in the dynamics. Since the shooting system generally has more
equations than unknowns, the algorithm relies on the Gauss-Newton method. As a
consequence, the convergence is locally quadratic provided that the derivative
of the shooting function is injective and Lipschitz continuous at the optimal
solution. We provide a proof of the convergence for the proposed algorithm
using recently developed second order sufficient conditions for weak optimality
of partially-affine problems. We illustrate the applicability of the algorithm
by solving an optimal treatment-vaccination epidemiological problem.


Abstract:
  We optimize a selection of eigenvalues of the Laplace operator with Dirichlet
or Neumann boundary conditions by adjusting the shape of the domain on which
the eigenvalue problem is considered. Here, a phase-field function is used to
represent the shapes over which we minimize. The idea behind this method is to
modify the Laplace operator by introducing phase-field dependent coefficients
in order to extend the eigenvalue problem on a fixed design domain containing
all admissible shapes. The resulting shape and topology optimization problem
can then be formulated as an optimal control problem with PDE constraints in
which the phase-field function acts as the control. For this optimal control
problem, we establish first-order necessary optimality conditions and we
rigorously derive its sharp interface limit. Eventually, we present and discuss
several numerical simulations for our optimization problem.


Abstract:
  Numerous early warning systems based on rainfall measurements have been
designed over the last decades to forecast the onset of rainfall-induced
shallow landslides. However, their use over large areas poses challenges due to
uncertainties related with the interaction among various controlling factors.
We propose a hybrid stochastic-mechanical approach to quantify the role of the
hydro-mechanical factors influencing slope stability and rank their importance.
The proposed methodology relies on a physically-based model of landslide
triggering, and a stochastic approach treating selected model parameters as
correlated aleatory variables. The features of the methodology are illustrated
by referencing data for Campania, an Italian region characterized by
landslide-prone volcanic deposits. Synthetic intensity-duration (ID) thresholds
are computed through Monte Carlo simulations. Several key variables are treated
as aleatoric, constraining their statistical properties through available
measurements. The variabilities of topographic features (e.g., slope angle),
physical and hydrological properties (e.g., porosity, dry unit weight
${\gamma}_d$, and saturated hydraulic conductivity, $K_s$), and pre-rainstorm
suction is evaluated to inspect its role on the resulting scatter of ID
thresholds. We find that: i) $K_s$ is most significant for high-intensity
storms; ii) in steep slopes, changes in pressure head greatly reduce the
timescale of landslide triggering, making the system heavily reliant on initial
conditions; iii) for events occurring at long failure times (gentle slopes
and/or low intensity storms), the significance of the evolving stress level
(through ${\gamma}_d$) is highest. The proposed approach can be translated to
other regions, expanded to encompass new aleatory variables, and combined with
other hydro-mechanical triggering models.


Abstract:
  The design and performance of the inner detector trigger for the high level
trigger of the ATLAS experiment at the Large Hadron Collider during the 2016-18
data taking period is discussed. In 2016, 2017, and 2018 the ATLAS detector
recorded 35.6 fb$^{-1}$, 46.9 fb$^{-1}$, and 60.6 fb$^{-1}$ respectively of
proton-proton collision data at a centre-of-mass energy of 13 TeV. In order to
deal with the very high interaction multiplicities per bunch crossing expected
with the 13 TeV collisions the inner detector trigger was redesigned during the
long shutdown of the Large Hadron Collider from 2013 until 2015. An overview of
these developments is provided and the performance of the tracking in the
trigger for the muon, electron, tau and $b$-jet signatures is discussed. The
high performance of the inner detector trigger with these extreme interaction
multiplicities demonstrates how the inner detector tracking continues to lie at
the heart of the trigger performance and is essential in enabling the ATLAS
physics programme.


Abstract:
  Two-dimensional (2D) semiconductors are promising candidates for scaled
transistors because they are immune to mobility degradation at the monolayer
limit. However, sub-10 nm scaling of 2D semiconductors, such as MoS2, is
limited by the contact resistance. In this work, we show for the first time a
statistical study of Au contacts to chemical vapor deposited monolayer MoS2
using transmission line model (TLM) structures, before and after dielectric
encapsulation. We report contact resistance values as low as 330 ohm-um, which
is the lowest value reported to date. We further study the effect of Al2O3
encapsulation on variability in contact resistance and other device metrics.
Finally, we note some deviations in the TLM model for short-channel devices in
the back-gated configuration and discuss possible modifications to improve the
model accuracy.


Abstract:
  In an unpublished work of Fasel-Rao-Swan the notion of the relative Witt
group $W_E(R,I)$ is defined. In this article we will give the details of this
construction. Then we studied the injectivity of the relative Vaserstein symbol
$V_{R,I}: Um_3(R,I)/E_3(R,I)\rightarrow W_E(R,I)$. We established injectivity
of this symbol if $R$ is an affine non-singular algebra of dimension $3$ over a
perfect $C_1$-field and $I$ is a local complete intersection ideal of $R$. It
is believed that for a $3$-dimensional affine algebra non-singularity is not
necessary for establishing injectivity of the Vaserstein symbol . At the end of
the article we will give an example of a singular $3$-dimensional algebra over
a perfect $C_1$-field for which the Vaserstein symbol is injective.


Abstract:
  Using a variant of Caccioppoli's inequality involving small weights, i.e.
weights of the form $(1+|\nabla u|^2)^{-\alpha/2}$ for some $\alpha > 0$, we
establish several Liouville-type theorems under general non-standard growth
conditions.


Abstract:
  As the COVID-19 virus spread over the world, governments restricted mobility
to slow transmission. Public health measures had different intensities across
European countries but all had significant impact on peoples daily lives and
economic activities, causing a drop of CO2 emissions of about 10% for the whole
year 2020. Here, we analyze changes in natural gas use in the industry and
built environment sectors during the first half of year 2020 with daily gas
flows data from pipeline and storage facilities in Europe. We find that
reductions of industrial gas use reflect decreases in industrial production
across most countries. Surprisingly, natural gas use in buildings also
decreased despite most people being confined at home and cold spells in March
2020. Those reductions that we attribute to the impacts of COVID-19 remain of
comparable magnitude to previous variations induced by cold or warm climate
anomalies in the cold season. We conclude that climate variations played a
larger role than COVID-19 induced stay-home orders in natural gas consumption
across Europe.


Abstract:
  We demonstrate the stability of ferromagnetic order of one unit cell thick
optimally doped manganite (La0.7Ba0.3MnO3, LBMO) epitaxially grown between two
layers of SrRuO3 (SRO) by using x-ray magnetic circular dichroism. At low
temperature LBMO shows an inverted hysteresis loop due to the strong
antiferromagnetic coupling to SRO. Moreover, above SRO TC the manganite still
exhibits magnetic remanence. Density Functional Theory calculations show that
coherent interfaces of LBMO with SRO hinder electronic confinement and the
strong magnetic coupling enables the increase of the LBMO TC. From the
structural point of view, interfacing with SRO enables LBMO to have octahedral
rotations similar to bulk. All these factors jointly contribute for stable
ferromagnetism up to 130 K for a one unit cell LBMO film.


Abstract:
  We tackle the long-tailed visual recognition problem from the knowledge
distillation perspective by proposing a Distill the Virtual Examples (DiVE)
method. Specifically, by treating the predictions of a teacher model as virtual
examples, we prove that distilling from these virtual examples is equivalent to
label distribution learning under certain constraints. We show that when the
virtual example distribution becomes flatter than the original input
distribution, the under-represented tail classes will receive significant
improvements, which is crucial in long-tailed recognition. The proposed DiVE
method can explicitly tune the virtual example distribution to become flat.
Extensive experiments on three benchmark datasets, including the large-scale
iNaturalist ones, justify that the proposed DiVE method can significantly
outperform state-of-the-art methods. Furthermore, additional analyses and
experiments verify the virtual example interpretation, and demonstrate the
effectiveness of tailored designs in DiVE for long-tailed problems.


Abstract:
  We prove several statements about arithmetic hyperbolicity of certain blow-up
varieties. As a corollary we obtain multiple examples of simply connected
quasi-projective varieties that are pseudo-arithmetically hyperbolic. This
generalizes results of Corvaja and Zannier obtained in dimension 2 to arbitrary
dimension. The key input is an application of the Ru-Vojta's strategy. We also
obtain the analogue results for function fields and Nevanlinna theory with the
goal to apply them in a future paper in the context of Campana's conjectures.


Abstract:
  We show how one may classify all semisimple algebras containing the
$\mathfrak{su}(3)\oplus \mathfrak{su}(2) \oplus \mathfrak{u}(1)$ symmetry of
the Standard Model and acting on some given matter sector, enabling theories
beyond the Standard Model with unification (partial or total) of symmetries
(gauge or global) to be catalogued. With just a single generation of Standard
Model fermions plus a singlet neutrino, the only {gauge} symmetries correspond
to the well-known algebras $\mathfrak{su}(5),\mathfrak{so}(10),$ and
$\mathfrak{su}(4)\oplus \mathfrak{su}(2) \oplus \mathfrak{su}(2)$, but with two
or more generations a limited number of exotic symmetries mixing flavour,
colour, and electroweak degrees of freedom become possible. We provide a
complete catalogue in the case of 3 generations or fewer and outline how our
method generalizes to cases with additional matter.


Abstract:
  With the rapid development of Internet of Things (IoT), massive machine-type
communication has become a promising application scenario, where a large number
of devices transmit sporadically to a base station (BS). Reconfigurable
intelligent surface (RIS) has been recently proposed as an innovative new
technology to achieve energy efficiency and coverage enhancement by
establishing favorable signal propagation environments, thereby improving data
transmission in massive connectivity. Nevertheless, the BS needs to detect
active devices and estimate channels to support data transmission in
RIS-assisted massive access systems, which yields unique challenges. This paper
shall consider an RIS-assisted uplink IoT network and aims to solve the
RIS-related activity detection and channel estimation problem, where the BS
detects the active devices and estimates the separated channels of the
RIS-to-device link and the RIS-to-BS link. Due to limited scattering between
the RIS and the BS, we model the RIS-to-BS channel as a sparse channel. As a
result, by simultaneously exploiting both the sparsity of sporadic transmission
in massive connectivity and the RIS-to-BS channels, we formulate the
RIS-related activity detection and channel estimation problem as a sparse
matrix factorization problem. Furthermore, we develop an approximate message
passing (AMP) based algorithm to solve the problem based on Bayesian inference
framework and reduce the computational complexity by approximating the
algorithm with the central limit theorem and Taylor series arguments. Finally,
extensive numerical experiments are conducted to verify the effectiveness and
improvements of the proposed algorithm.


Abstract:
  Time series forecasting is a relevant task that is performed in several
real-world scenarios such as product sales analysis and prediction of energy
demand. Given their accuracy performance, currently, Recurrent Neural Networks
(RNNs) are the models of choice for this task. Despite their success in time
series forecasting, less attention has been paid to make the RNNs trustworthy.
For example, RNNs can not naturally provide an uncertainty measure to their
predictions. This could be extremely useful in practice in several cases e.g.
to detect when a prediction might be completely wrong due to an unusual pattern
in the time series. Whittle Sum-Product Networks (WSPNs), prominent deep
tractable probabilistic circuits (PCs) for time series, can assist an RNN with
providing meaningful probabilities as uncertainty measure. With this aim, we
propose RECOWN, a novel architecture that employs RNNs and a discriminant
variant of WSPNs called Conditional WSPNs (CWSPNs). We also formulate a
Log-Likelihood Ratio Score as better estimation of uncertainty that is tailored
to time series and Whittle likelihoods. In our experiments, we show that
RECOWNs are accurate and trustworthy time series predictors, able to "know when
they do not know".


Abstract:
  We present a new model-based interpolation procedure for satisfiability
modulo theories (SMT). The procedure uses a new mode of interaction with the
SMT solver that we call solving modulo a model. This either extends a given
partial model into a full model for a set of assertions or returns an
explanation (a model interpolant) when no solution exists. This mode of
interaction fits well into the model-constructing satisfiability (MCSAT)
framework of SMT. We use it to develop an interpolation procedure for any
MCSAT-supported theory. In particular, this method leads to an effective
interpolation procedure for nonlinear real arithmetic. We evaluate the new
procedure by integrating it into a model checker and comparing it with
state-of-art model-checking tools for nonlinear arithmetic.


Abstract:
  The Cox construction presents a toric variety as a quotient of affine space
by a torus. The category of coherent sheaves on the corresponding stack thus
has an evident description as invariants in a quotient of the category of
modules over a polynomial ring. Here we give the mirror to this description,
and in particular, a clean new proof of mirror symmetry for smooth toric
stacks.


Abstract:
  This literature review focuses on the use of Natural Language Generation
(NLG) to automatically detect and generate persuasive texts. Extending previous
research on automatic identification of persuasion in text, we concentrate on
generative aspects through conceptualizing determinants of persuasion in five
business-focused categories: benevolence, linguistic appropriacy, logical
argumentation, trustworthiness, tools and datasets. These allow NLG to increase
an existing message's persuasiveness. Previous research illustrates key aspects
in each of the above mentioned five categories. A research agenda to further
study persuasive NLG is developed. The review includes analysis of
seventy-seven articles, outlining the existing body of knowledge and showing
the steady progress in this research field.


Abstract:
  If one proposes to use the theory of Eisenstein cohomology to prove
algebraicity results for the special values of automorphic L-functions as in my
work with Harder for Rankin-Selberg L-functions, or its generalizations as in
my work with Bhagwat for L-functions for orthogonal groups and independently
with Krishnamurthy on Asai L-functions, then in a key step, one needs to prove
that the normalised standard intertwining operator between induced
representations for p-adic groups has a certain arithmetic property. The
principal aim of this article is to address this particular local problem in
the generality of the Langlands-Shahidi machinery. The main result of this
article is invoked in some of the works mentioned above, and I expect that it
will be useful in future investigations on the arithmetic properties of
automorphic L-functions.


Abstract:
  In 2007, Grytczuk conjecture that for any sequence $(\ell_i)_{i\ge1}$ of
alphabets of size $3$ there exists a square-free infinite word $w$ such that
for all $i$, the $i$-th letter of $w$ belongs to $\ell_i$. The result of Thue
of 1906 implies that there is an infinite square-free word if all the $\ell_i$
are identical. On the other, hand Grytczuk, Przyby{\l}o and Zhu showed in 2011
that it also holds if the $\ell_i$ are of size $4$ instead of $3$.
  In this article, we first show that if the lists are of size $4$, the number
of square-free words is at least $2.45^n$ (the previous similar bound was
$2^n$). We then show our main result: we can construct such a square-free word
if the lists are subsets of size $3$ of the same alphabet of size $4$. Our
proof also implies that there are at least $1.25^n$ square-free words of length
$n$ for any such list assignment. This proof relies on the existence of a set
of coefficients verified with a computer. We suspect that the full conjecture
could be resolved by this method with a much more powerful computer (but we
might need to wait a few decades for such a computer to be available).


Abstract:
  In recent years, Quantum Computing witnessed massive improvements both in
terms of resources availability and algorithms development. The ability to
harness quantum phenomena to solve computational problems is a long-standing
dream that has drawn the scientific community's interest since the late '80s.
In such a context, we pose our contribution. First, we introduce basic concepts
related to quantum computations, and then we explain the core functionalities
of technologies that implement the Gate Model and Adiabatic Quantum Computing
paradigms. Finally, we gather, compare and analyze the current state-of-the-art
concerning Quantum Perceptrons and Quantum Neural Networks implementations.


Abstract:
  Force chains, which are quasi-linear self-organised structures carrying large
stresses, are ubiquitous in jammed amorphous materials, such as granular
materials, foams, emulsions or even assemblies of cells. Predicting where they
will form upon mechanical deformation is crucial in order to describe the
physical properties of such materials, but remains an open question. Here we
demonstrate that graph neural networks (GNN) can accurately infer the location
of these force chains in frictionless materials from the local structure prior
to deformation, without receiving any information about the inter-particle
forces. Once trained on a prototypical system, the GNN prediction accuracy
proves to be robust to changes in packing fraction, mixture composition, amount
of deformation, and the form of the interaction potential. The GNN is also
scalable, as it can make predictions for systems much larger than those it was
trained on. Our results and methodology will be of interest for experimental
realizations of granular matter and jammed disordered systems, e.g. in cases
where direct visualisation of force chains is not possible or contact forces
cannot be measured.


Abstract:
  In a recent paper published in PNAS authors prove that locality and free
choice are equivalent resources which need to be relaxed in order to fully
reproduce some statistics in Bell experiments (while always maintaining
realism). We explain that their assumption of free choice is simply
counterfactual definiteness or noncontextuality. Therefore the resource in Bell
experiments is contextuality and not the violations of locality and/or of free
choice. It is definitely less mind boggling conclusion because experimenters`
freedom of choice is a prerequisite of science,


Abstract:
  We present a solution to multi-robot distributed semantic mapping of novel
and unfamiliar environments. Most state-of-the-art semantic mapping systems are
based on supervised learning algorithms that cannot classify novel observations
online. While unsupervised learning algorithms can invent labels for novel
observations, approaches to detect when multiple robots have independently
developed their own labels for the same new class are prone to erroneous or
inconsistent matches. These issues worsen as the number of robots in the system
increases and prevent fusing the local maps produced by each robot into a
consistent global map, which is crucial for cooperative planning and joint
mission summarization. Our proposed solution overcomes these obstacles by
having each robot learn an unsupervised semantic scene model online and use a
multiway matching algorithm to identify consistent sets of matches between
learned semantic labels belonging to different robots. Compared to the state of
the art, the proposed solution produces 20-60% higher quality global maps that
do not degrade even as many more local maps are fused.


Abstract:
  Fashion is intertwined with external cultural factors, but identifying these
links remains a manual process limited to only the most salient phenomena. We
propose a data-driven approach to identify specific cultural factors affecting
the clothes people wear. Using large-scale datasets of news articles and
vintage photos spanning a century, we present a multi-modal statistical model
to detect influence relationships between happenings in the world and people's
choice of clothing. Furthermore, on two image datasets we apply our model to
improve the concrete vision tasks of visual style forecasting and photo
timestamping. Our work is a first step towards a computational, scalable, and
easily refreshable approach to link culture to clothing.


Abstract:
  We calculate the response of a lead-based detector, such as the Helium and
Lead Observatory (HALO) or its planned upgrade HALO-1kt to a galactic
core-collapse supernova. We pay particular attention to the time dependence of
the reaction rates. All reaction rates decrease as the neutrino luminosity
exponentially drops during the cooling period but the ratio of one-neutron (1n)
to two-neutron (2n) event rates in HALO is independent of this overall
decrease. Nevertheless, we find that this ratio still changes with time due to
the changing character of neutrino flavor transformations with the evolving
conditions in the supernova. In the case of inverted hierarchy, this is caused
by the fact that the spectral splits become less and less sharp with the
decreasing luminosity. In the case of normal hierarchy, it is caused by the
passage of the shock wave through the Mikheyev-Smirnov-Wolfenstein resonance
region. However, in both cases, we find that the change in the ratio of 1n to
2n event rates is limited to a few percent.


Abstract:
  In this study, a variational method for the inverse problem of self-assembly,
i.e., a reconstruction of the interparticle interaction potential of a given
structure, is applied to three-dimensional crystals. According to the method,
the interaction potential is derived as a function that maximizes the
free-energy functional of the one- and two-particle density distribution
functions. The interaction potentials of the target crystals, including those
with face-centered cubic (fcc), body-centered cubic (bcc), and simple hexagonal
(shx) lattices, are obtained by numerical maximization of the functional. Monte
Carlo simulations for the systems of particles with these interactions were
carried out, and the self-assembly of the target crystals was confirmed for the
bcc and shx cases. However, in the many-particle system with the predicted
interaction for the fcc lattice, the fcc lattice did not spontaneously form and
was metastable.


Abstract:
  A formalisation of G\"odel's incompleteness theorems using the Isabelle proof
assistant is described. This is apparently the first mechanical verification of
the second incompleteness theorem. The work closely follows {\'S}wierczkowski
(2003), who gave a detailed proof using hereditarily finite set theory. The
adoption of this theory is generally beneficial, but it poses certain technical
issues that do not arise for Peano arithmetic. The formalisation itself should
be useful to logicians, particularly concerning the second incompleteness
theorem, where existing proofs are lacking in detail.


Abstract:
  We investigate experimentally the behavior of self-propelled water-in-oil
droplets, confined in capillaries of different square and circular
cross-sections. The droplet's activity comes from the formation of swollen
micelles at its interface. In straight capillaries the velocity of the droplet
decreases with increasing confinement. However at very high confinement, the
velocity converges toward a non-zero value, so that even very long droplets
swim. Stretched circular capillaries are then used to explore even higher
confinement. The lubrication layer around the droplet then takes a non-uniform
thickness which constitutes a significant difference with usual flow-driven
passive droplets. A neck forms at the rear of the droplet, deepens with
increasing confinement, and eventually undergoes successive spontaneous
splitting events for large enough confinement. Such observations stress the
critical role of the activity of the droplet interface on the droplet's
behavior under confinement. We then propose an analytical formulation by
integrating the interface activity and the swollen micelles transport problem
into the classical Bretherton approach. The model accounts for the convergence
of the droplet's velocity to a finite value for large confinement, and for the
non-classical shape of the lubrication layer. We further discuss on the
saturation of the micelles concentration along the interface, which would
explain the divergence of the lubrication layer thickness for long enough
droplets, eventually leading to the spontaneous droplet division.


Abstract:
  In this methodological paper, we first review the classic cubic Diophantine
equation $a^3 + b^3 + c^3 = d^3$, and consider the specific class of solutions
$q_1^3 + q_2^3 + q_3^3 = q_4^3$ with each $q_i$ being a binary quadratic form.
Next we turn our attention to the familiar sums of powers of the first $n$
positive integers, $S_k = 1^k + 2^k + \cdots + n^k$, and express the squares
$S_k^2$, $S_m^2$, and the product $S_k S_m$ as a linear combination of power
sums. These expressions, along with the above quadratic-form solution for the
cubic equation, allows one to generate an infinite number of relations of the
form $Q_1^3 + Q_2^3 + Q_3^3 = Q_4^3$, with each $Q_i$ being a linear
combination of power sums. Also, we briefly consider the quadratic Diophantine
equations $a^2 + b^2 + c^2 = d^2$ and $a^2 + b^2 = c^2$, and give a family of
corresponding solutions $Q_1^2 + Q_2^2 + Q_3^2 = Q_4^2$ and $Q_1^2 + Q_2^2 =
Q_3^2$ in terms of sums of powers of integers.


Abstract:
  While reinforcement learning (RL) has proven to be the approach of choice for
tackling many complex problems, it remains challenging to develop and deploy RL
agents in real-life scenarios successfully. This paper presents pH-RL
(personalization in e-Health with RL) a general RL architecture for
personalization to bring RL to health practice. pH-RL allows for various levels
of personalization in health applications and allows for online and batch
learning. Furthermore, we provide a general-purpose implementation framework
that can be integrated with various healthcare applications. We describe a
step-by-step guideline for the successful deployment of RL policies in a mobile
application. We implemented our open-source RL architecture and integrated it
with the MoodBuster mobile application for mental health to provide messages to
increase daily adherence to the online therapeutic modules. We then performed a
comprehensive study with human participants over a sustained period. Our
experimental results show that the developed policies learn to select
appropriate actions consistently using only a few days' worth of data.
Furthermore, we empirically demonstrate the stability of the learned policies
during the study.


Abstract:
  In this paper we discuss the optimal control of a quasilinear parabolic state
equation. Its form is leaned on the kind of problems arising for example when
controlling the anisotropic Allen-Cahn equation as a model for crystal growth.
Motivated by this application we consider the state equation as a result of a
gradient flow of an energy functional. The quasilinear term is strongly
monotone and obeys a certain growth condition and the lower order term is
non-monotone. The state equation is discretized implicitly in time with
piecewise constant functions. The existence of the control-to-state operator
and its Lipschitz-continuity is shown for the time discretized as well as for
the time continuous problem. Latter is based on the convergence proof of the
discretized solutions. Finally we present for both the existence of global
minimizers. Also convergence of a subsequence of time discrete optimal controls
to a global minimizer of the time continuous problem can be shown. Our results
hold in arbitrary space dimensions.


Abstract:
  We show that general time-local quantum master equations admit an unravelling
in quantum trajectories with jumps. The sufficient condition is to weigh state
vector Monte Carlo averages by a probability pseudo-measure which we call the
"influence martingale". The influence martingale satisfies a $ 1d $ stochastic
differential equation enslaved to the ones governing the quantum trajectories.
Our interpretation is that the influence martingale models interference effects
between distinct realizations of the quantum trajectories at strong
system-environment coupling.
  If the master equation generates a completely positive dynamical map, there
is no interference. In such a case the influence martingale becomes positive
definite and the Monte Carlo average straightforwardly reduces to the well
known unravelling of completely positive divisible dynamical maps.


Abstract:
  Sustainable urban design or planning is not a LEGO-like assembly of
prefabricated elements, but an embryo-like growth with persistent
differentiation and adaptation towards a coherent whole. The coherent whole has
a striking character - called living structure - that consists of far more
small substructures than large ones. To detect the living structure, natural
streets or axial lines have been previously adopted to be topologically
represent an urban environment as a coherent whole. This paper develops a new
approach to detecting the underlying living structure of urban environments.
The approach takes an urban environment as a whole and recursively decomposes
it into meaningful subwholes at different levels of hierarchy or scale ranging
from the largest to the smallest. We compared the new approach to natural
street and axial line approaches and demonstrated, through four case studies,
that the new approach is better and more powerful. Based on the study, we
further discuss how the new approach can be used not only for understanding,
but also for effectively designing or planning the living structure of an urban
environment to be more living or more livable. Keywords: Urban design or
planning, structural beauty, space syntax, natural streets, life, wholeness


Abstract:
  Tree-based models are among the most efficient machine learning techniques
for data mining nowadays due to their accuracy, interpretability, and
simplicity. The recent orthogonal needs for more data and privacy protection
call for collaborative privacy-preserving solutions. In this work, we survey
the literature on distributed and privacy-preserving training of tree-based
models and we systematize its knowledge based on four axes: the learning
algorithm, the collaborative model, the protection mechanism, and the threat
model. We use this to identify the strengths and limitations of these works and
provide for the first time a framework analyzing the information leakage
occurring in distributed tree-based model learning.


Abstract:
  Let $\K$ be a finite field and $X$ be a complete simplicial toric variety
over $\K$. We give an algorithm relying on elimination theory for finding
generators of the vanishing ideal of a subgroup $Y_Q$ parameterized by a matrix
$Q$ which can be used to study algebraic geometric codes arising from $Y_Q$. We
give a method to compute the lattice $L$ whose ideal $I_L$ is exactly $I(Y_Q)$
under a mild condition. As applications, we give precise descriptions for the
lattices corresponding to some special subgroups. We also prove a
Nullstellensatz type theorem valid over finite fields, and share
\verb|Macaulay2| codes for our algorithms.


Abstract:
  Vanadium oxides have been highly attractive for over half a century since the
discovery of the metal insulator transition near room temperatures. Here NaxVO2
is studied through a systematic comparison with other layered sodium metal
oxides with early 3d transition metals, first disclosing a unified evolution
pattern of Na density waves through in situ XRD analysis. Combining ab-initio
simulations and theoretical modelings, a sodium-modulated Peierls-like
transition mechanism is then proposed for the bonding formation of metal ion
dimers. More importantly, the unique trimer structure in NaxVO2 is shown to be
very sensitive to the onsite Coulomb repulsion value, suggesting a delicate
balance between strong electronic correlations and orbital effects that can be
precisely modulated by both Na compositions and atomic stackings. This unveils
a unique opportunity to design strongly correlated materials with tailored
electronic transitions through electrochemical modulations and crystallographic
designs, to elegantly balance various competition effects. We think the
understanding will also help further elucidate complicated electronic behaviors
in other vanadium oxide systems.


Abstract:
  In Europe, 20% of road crashes occur at intersections. In recent years,
evolving communication technologies are making V2V and V2I faster and more
reliable; with such advancements, these crashes, as well as their economic
cost, can be partially reduced. In this work, we concentrate on straight path
intersection collisions. Connectivity-based algorithms relying on 5G technology
and smart sensors are presented and compared to a commercial radar AEB logic in
order to evaluate performances and effectiveness in collision avoidance or
mitigation. The aforementioned novel safety systems are tested in a blind
intersection and low adherence scenario. The first algorithm proposed is
obtained by incorporating connectivity information to the original control
scheme, while the second algorithm proposed is a novel control logic fully
capable of utilizing also adherence estimation provided by smart sensors. Test
results show an improvement in terms of safety for both the architecture and
high prospects for future developments.


Abstract:
  This paper deals with the generalized spectrum of continuously invertible
linear operators defined on infinite dimensional Hilbert spaces. More
precisely, we consider two bounded, coercive, and self-adjoint operators
$\bc{A, B}: V\mapsto V^{\#}$, where $V^{\#}$ denotes the dual of $V$, and
investigate the conditions under which the whole spectrum of
$\bc{B}^{-1}\bc{A}:V\mapsto V$ can be approximated to an arbitrary accuracy by
the eigenvalues of the finite dimensional discretization
$\bc{B}_n^{-1}\bc{A}_n$. Since $\bc{B}^{-1}\bc{A}$ is continuously invertible,
such an investigation cannot use the concept of uniform (normwise) convergence,
and it relies instead on the pointwise (strong) convergence of
$\bc{B}_n^{-1}\bc{A}_n$ to $\bc{B}^{-1}\bc{A}$.
  The paper is motivated by operator preconditioning which is employed in the
numerical solution of boundary value problems. In this context, $\bc{A},
\bc{B}: H_0^1(\Omega) \mapsto H^{-1}(\Omega)$ are the standard
integral/functional representations of the differential operators $ -\nabla
\cdot (k(x)\nabla u)$ and $-\nabla \cdot (g(x)\nabla u)$, respectively, and
$k(x)$ and $g(x)$ are scalar coefficient functions. The investigated question
differs from the eigenvalue problem studied in the numerical PDE literature
which is based on the approximation of the eigenvalues within the framework of
compact operators.
  This work follows the path started by the two recent papers published in
[SIAM J. Numer. Anal., 57 (2019), pp.~1369-1394 and 58 (2020), pp.~2193-2211]
and addresses one of the open questions formulated at the end of the second
paper.


Abstract:
  We prove that if there are $\mathfrak c$ incomparable selective ultrafilters
then, for every infinite cardinal $\kappa$ such that $\kappa^\omega=\kappa$,
there exists a group topology on the free Abelian group of cardinality $\kappa$
without nontrivial convergent sequences and such that every finite power is
countably compact. In particular, there are arbitrarily large countably compact
groups. This answers a 1992 question of D. Dikranjan and D. Shakhmatov.


Abstract:
  For fixed $q\in\{3,7,11,19, 43,67,163\}$, we consider the density of primes
$p$ congruent to $1$ modulo $4$ such that the class group of the number field
$\mathbb{Q}(\sqrt{-qp})$ has order divisible by $16$. We show that this density
is equal to $1/8$, in line with a more general conjecture of Gerth.
Vinogradov's method is the key analytic tool for our work.


Abstract:
  The recent proposal of antidoping scheme breaks new ground in conceiving
conversely functional materials and devices, yet the few available examples
belong to the correlated electron systems. Here we demonstrate both
theoretically and experimentally that the main group oxide BaBiO$_3$ is a model
system for antidoping using oxygen vacancies. The first principles calculations
show that the band gap systematically increases due to the strongly enhanced
BiO breathing distortions away from the vacancies and the annihilation of Bi 6s
and O 2p hybridized conduction bands near the vacancies. The spectroscopic
experiments confirm the band gap increasing systematically with electron
doping, with a maximal gap enhancement of 75% when the film's stoichiometry is
reduced to BaBiO$_{2.75}$. The Raman and diffraction experiments show the
suppression of the overall breathing distortion. The study unambiguously
demonstrates the remarkable antidoping effect in a material without strong
electron correlations and underscores the importance of bond disproportionation
in realizing such an effect.


Abstract:
  We provide a tight result for a fundamental problem arising from packing
squares into a circular container: The critical density of packing squares into
a disk is $\delta=\frac{8}{5\pi}\approx 0.509$. This implies that any set of
(not necessarily equal) squares of total area $A \leq \frac{8}{5}$ can always
be packed into a disk with radius 1; in contrast, for any $\varepsilon>0$ there
are sets of squares of total area $\frac{8}{5}+\varepsilon$ that cannot be
packed, even if squares may be rotated. This settles the last (and arguably,
most elusive) case of packing circular or square objects into a circular or
square container: The critical densities for squares in a square
$\left(\frac{1}{2}\right)$, circles in a square
$\left(\frac{\pi}{(3+2\sqrt{2})}\approx 0.539\right)$ and circles in a circle
$\left(\frac{1}{2}\right)$ have already been established, making use of
recursive subdivisions of a square container into pieces bounded by straight
lines, or the ability to use recursive arguments based on similarity of objects
and container; neither of these approaches can be applied when packing squares
into a circular container. Our proof uses a careful manual analysis,
complemented by a computer-assisted part that is based on interval arithmetic.
Beyond the basic mathematical importance, our result is also useful as a
blackbox lemma for the analysis of recursive packing algorithms. At the same
time, our approach showcases the power of a general framework for
computer-assisted proofs, based on interval arithmetic.


Abstract:
  It is shown that the dipole moment of polar (water, methanol, formamide,
acetone and acetonitrile) molecules in the neighborhood of a cation is
increased primarily by polarization from the bare electrostatic charge of the
cation, although the effective value of the latter is somewhat reduced by "back
donation" of electrons from neighbouring polar molecules. In other words, the
classical picture may be viewed as if a point charge slightly smaller than the
nominal charge of the cation would be placed at the cation site. It was found
that the geometrical arrangement of the polar molecules in the first solvation
shell is such that their mutual polarization reduces the dipole moments of
individual molecules, so that in some cases they become smaller than the dipole
moment of the free protic or aprotic molecule. We conjecture that this behavior
is essentially a manifestation of the Le Chatellier-Braun principle.


Abstract:
  It was recently discovered that atoms subject to a time-periodic drive can
give rise to a crystal structure in phase space. In this work, we point out the
atom-atom interactions give rise to collective phonon excitations of
phase-space crystal via a pairing interaction with intrinsically complex phases
that can lead to a phonon Chern insulator, accompanied by topologically robust
chiral transport along the edge of the phase-space crystal. This topological
phase is realized even in scenarios where the time-reversal transformation is a
symmetry, which is surprising because the breaking of time-reversal symmetry is
a strict precondition for topological chiral transport in the standard setting
of real-space crystals. Our work has also important implications for the
dynamics of 2D charged particles in a strong magnetic field.


Abstract:
  Background: For its simplicity, the eikonal method is the tool of choice to
analyze nuclear reactions at high energies ($E>100$ MeV/nucleon), including
knockout reactions. However, so far, the effective interactions used in this
method are assumed to be fully local.
  Purpose: Given the recent studies on non-local optical potentials, in this
work we assess whether non-locality in the optical potentials is expected to
impact reactions at high energies and then explore different avenues for
extending the eikonal method to include non-local interactions.
  Method: We compare angular distributions obtained for non-local interactions
(using the exact R-matrix approach for elastic scattering and the adiabatic
distorted wave approximation for transfer) with those obtained using their
local-equivalent interactions.
  Results: Our results show that transfer observables are significantly
impacted by non-locality in the high-energy regime. Because knockout reactions
are dominated by stripping (transfer to inelastic channels), non-locality is
expected to have a large effect on knockout observables too. Three approaches
are explored for extending the eikonal method to non-local interactions,
including an iterative method and a perturbation theory.
  Conclusions: None of the derived extensions of the eikonal model provide a
good description of elastic scattering. This work suggests that non-locality
removes the formal simplicity associated with the eikonal model.


Abstract:
  Over the past decade the in-medium similarity renormalization group (IMSRG)
approach has proven to be a powerful and versatile ab initio many-body method
for studying medium-mass nuclei. So far, the IMSRG was limited to the
approximation in which only up to two-body operators are incorporated in the
renormalization group flow, referred to as the IMSRG(2). In this work, we
extend the IMSRG(2) approach to fully include three-body operators yielding the
IMSRG(3) approximation. We use a perturbative scaling analysis to estimate the
importance of individual terms in this approximation and introduce truncations
that aim to approximate the IMSRG(3) at a lower computational cost. The
IMSRG(3) is systematically benchmarked for different nuclear Hamiltonians for
${}^{4}\text{He}$ and ${}^{16}\text{O}$ in small model spaces. The IMSRG(3)
systematically improves over the IMSRG(2) relative to exact results.
Approximate IMSRG(3) truncations constructed based on computational cost are
able to reproduce much of the systematic improvement offered by the full
IMSRG(3). We also find that the approximate IMSRG(3) truncations behave
consistently with expectations from our perturbative analysis, indicating that
this strategy may also be used to systematically approximate the IMSRG(3).


Abstract:
  We demonstrate that the reduced Hartree-Fock equation (REHF) with an Anderson
type background charge distribution has an unique stationary solution by
explicitly computing a screening mass at positive temperature.


Abstract:
  A* search is an informed search algorithm that uses a heuristic function to
guide the order in which nodes are expanded. Since the computation required to
expand a node and compute the heuristic values for all of its generated
children grows linearly with the size of the action space, A* search can become
impractical for problems with large action spaces. This computational burden
becomes even more apparent when heuristic functions are learned by general, but
computationally expensive, deep neural networks. To address this problem, we
introduce DeepCubeAQ, a deep reinforcement learning and search algorithm that
builds on the DeepCubeA algorithm and deep Q-networks. DeepCubeAQ learns a
heuristic function that, with a single forward pass through a deep neural
network, computes the sum of the transition cost and the heuristic value of all
of the children of a node without explicitly generating any of the children,
eliminating the need for node expansions. DeepCubeAQ then uses a novel variant
of A* search, called AQ* search, that uses the deep Q-network to guide search.
We use DeepCubeAQ to solve the Rubik's cube when formulated with a large action
space that includes 1872 meta-actions and show that this 157-fold increase in
the size of the action space incurs less than a 4-fold increase in computation
time when performing AQ* search and that AQ* search is orders of magnitude
faster than A* search.


Abstract:
  The resolution of $4$-dimensional massless field operators of higher spins
was constructed by Eastwood-Penrose-Wells by using the twistor method. Recently
physicists are interested in $6$-dimensional physics including the massless
field operators of higher spins on Lorentzian space $\Bbb R^{5,1}$. Its
Euclidean version $\mathscr{D}_0$ and their function theory are discussed in
\cite{wangkang3}. In this paper, we construct an exact sequence of Hilbert
spaces as weighted $L^2$ spaces resolving $\mathscr{D}_0$: $$L^2_\varphi(\Bbb
R^6, \mathscr{V}_0)\overset{\mathscr{D}_0}\longrightarrow L^2_\varphi(\Bbb
R^6,\mathscr{V}_1)\overset{\mathscr{D}_1}\longrightarrow L^2_\varphi(\Bbb R^6,
\mathscr{V}_2)\overset{\mathscr{D}_2}\longrightarrow L^2_\varphi(\Bbb R^6,
\mathscr{V}_3)\longrightarrow 0,$$ with suitable operators $\mathscr{D}_l$ and
vector spaces $\mathscr{V}_l$. Namely, we can solve $\mathscr{D}_{l}u=f$ in
$L^2_\varphi(\Bbb R^6, \mathscr{V}_{l})$ when $\mathscr{D}_{l+1} f=0$ for $f\in
L^2_{\varphi}(\Bbb R^6, \mathscr{V}_{l+1})$. This is proved by using the $L^2$
method in the theory of several complex variables, which is a general framework
to solve overdetermined PDEs under the compatibility condition. To apply this
method here, it is necessary to consider weighted $L^2$ spaces, an advantage of
which is that any polynomial is $L^2_{\varphi}$ integrable. As a corollary, we
prove that $$ P(\Bbb R^6, \mathscr{V}_0)\overset{\mathscr{D}_0}\longrightarrow
P(\Bbb R^6,\mathscr{V}_1)\overset{\mathscr{D}_1}\longrightarrow P(\Bbb R^6,
\mathscr{V}_2)\overset{\mathscr{D}_2}\longrightarrow P(\Bbb R^6,
\mathscr{V}_3)\longrightarrow 0$$ is a resolution, where $P(\Bbb R^6,
\mathscr{V}_l)$ is the space of all $\mathscr{V}_l$-valued polynomials. This
provides an analytic way to construct a resolution of a differential operator
acting on vector valued polynomials.


Abstract:
  Angular momentum plays a central role in a multitude of phenomena in quantum
mechanics, recurring in every length scale from the microscopic interactions of
light and matter to the macroscopic behavior of superfluids. Vortex beams,
carrying intrinsic orbital angular momentum (OAM), are now regularly generated
with elementary particles such as photons and electrons, and harnessed for
numerous applications including microscopy and communication. Untapped
possibilities remain hidden in vortices of non-elementary particles, as their
composite structure can lead to coupling of OAM with internal degrees of
freedom. However, thus far, the creation of a vortex beam of a non-elementary
particle has never been demonstrated experimentally. We present the first
vortex beams of atoms and molecules, formed by diffracting supersonic beams of
helium atoms and dimers, respectively, off binary masks made from transmission
gratings. By achieving large particle coherence lengths and nanometric grating
features, we observe a series of vortex rings corresponding to different OAM
states in the accumulated images of particles impacting a detector. This method
is general and can be applied to most atomic and molecular gases. Our results
may open new frontiers in atomic physics, utilizing the additional degree of
freedom of OAM to probe collisions and alter fundamental interactions.


Abstract:
  Using a tight-biding model, we elaborate that the previously discovered
out-of-plane polarized helical edge spin current caused by Rashba spin-orbit
coupling can be attributed to the fact that in a strip geometry, a positive
momentum eigenstate does not always have the same spin polarization at the edge
as the corresponding negative momentum eigenstate. In addition, in the presence
of a magnetization pointing perpendicular to the edge, an edge charge current
is produced, which can be chiral or nonchiral depending on whether the
magnetization lies in-plane or out-of-plane. The spin polarization near the
edge develops a transverse component orthogonal to the magnetization, which is
antisymmetric between the two edges and tends to cause a noncollinear magnetic
order between the two edges. If the magnetization only occupies a region near
one edge, or in an irregular shaped quantum dot, this transverse component has
a nonzero average, rendering a gate voltage-induced magnetoelectric torque
without the need of a bias voltage. We also argue that other types of
spin-orbit coupling that can be obtained from the Rashba type through a unitary
transformation, such as the Dresselhaus spin-orbit coupling, will have similar
effects too.


Abstract:
  Hydrodynamics is a general theoretical framework for describing the long-time
large-distance behaviors of various macroscopic physical systems, with its
equations based on conservation laws such as energy-momentum conservation and
charge conservation. Recently there has been significant interest in
understanding the implications of angular momentum conservation for a
corresponding hydrodynamic theory. In this work, we examine the key conceptual
issues for such a theory in the relativistic regime where the orbital and spin
components get entangled. We derive the equations for relativistic viscous
hydrodynamics with angular momentum through Navier-Stokes type of gradient
expansion analysis.


Abstract:
  Split-learning (SL) has recently gained popularity due to its inherent
privacy-preserving capabilities and ability to enable collaborative inference
for devices with limited computational power. Standard SL algorithms assume an
ideal underlying digital communication system and ignore the problem of scarce
communication bandwidth. However, for a large number of agents, limited
bandwidth resources, and time-varying communication channels, the communication
bandwidth can become the bottleneck. To address this challenge, in this work,
we propose a novel SL framework to solve the remote inference problem that
introduces an additional layer at the agent side and constrains the choices of
the weights and the biases to ensure over the air aggregation. Hence, the
proposed approach maintains constant communication cost with respect to the
number of agents enabling remote inference under limited bandwidth. Numerical
results show that our proposed algorithm significantly outperforms the digital
implementation in terms of communication-efficiency, especially as the number
of agents grows large.


Abstract:
  Time series analysis is quickly proceeding towards long and complex tasks. In
recent years, fast approximate algorithms for discord search have been proposed
in order to compensate for the increasing size of the time series. It is more
interesting, however, to find quick exact solutions. In this research, we
improved HOT SAX by exploiting two main ideas: the warm-up process, and the
similarity between sequences close in time. The resulting algorithm, called HOT
SAX Time (HST), has been validated with real and synthetic time series, and
successfully compared with HOT SAX, RRA, SCAMP, and DADD. The complexity of a
discord search has been evaluated with a new indicator, the cost per sequence
(cps), which allows one to compare searches on time series of different
lengths. Numerical evidence suggests that two conditions are involved in
determining the complexity of a discord search in a non-trivial way: the length
of the discords, and the noise/signal ratio. In the case of complex searches,
HST can be more than 100 times faster than HOT SAX, thus being at the forefront
of the exact discord search.


Abstract:
  In this work, we revisit the adaptive L1 time-stepping scheme for solving the
time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit
scheme is shown to preserve a variational energy dissipation law on arbitrary
nonuniform time meshes by using the recent discrete analysis tools, i.e., the
discrete orthogonal convolution kernels and discrete complementary convolution
kernels. Then the discrete embedding techniques and the fractional Gr\"onwall
inequality were applied to establish an $L^2$ norm error estimate on nonuniform
time meshes. An adaptive time-stepping strategy according to the dynamical
feature of the system is presented to capture the multi-scale behaviors and to
improve the computational performance.


Abstract:
  Extended decorations on naturally decorated trees were introduced in the work
of Bruned, Hairer and Zambotti on algebraic renormalization of regularity
structures to provide a convenient framework for the renormalization of systems
of singular stochastic PDEs within that setting. This non-dynamical feature of
the trees complicated the analysis of the dynamical counterpart of the
renormalization process. We provide a new proof of the renormalized system
by-passing the use of extended decorations and working for a large class of
renormalization maps, with the BPHZ renormalization as a special case. The
proof reveals important algebraic properties connected to preparation maps.


Abstract:
  PYROBOCOP is a lightweight Python-based package for control and optimization
of robotic systems described by nonlinear Differential Algebraic Equations
(DAEs). In particular, the package can handle systems with contacts that are
described by complementarity constraints and provides a general framework for
specifying obstacle avoidance constraints. The package performs direct
transcription of the DAEs into a set of nonlinear equations by performing
orthogonal collocation on finite elements. The resulting optimization problem
belongs to the class of Mathematical Programs with Complementarity Constraints
(MPCCs). MPCCs fail to satisfy commonly assumed constraint qualifications and
require special handling of the complementarity constraints in order for
NonLinear Program (NLP) solvers to solve them effectively. PYROBOCOP provides
automatic reformulation of the complementarity constraints that enables NLP
solvers to perform optimization of robotic systems. The package is interfaced
with ADOLC for obtaining sparse derivatives by automatic differentiation and
IPOPT for performing optimization. We demonstrate the effectiveness of our
approach in terms of speed and flexibility. We provide several numerical
examples for several robotic systems with collision avoidance as well as
contact constraints represented using complementarity constraints. We provide
comparisons with other open source optimization packages like CasADi and Pyomo .


Abstract:
  Demand response (DR) programs engage distributed demand-side resources, e.g.,
controllable residential and commercial loads, in providing ancillary services
for electric power systems. Ensembles of these resources can help reducing
system load peaks and meeting operational limits by adjusting their electric
power consumption. To equip utilities or load aggregators with adequate
decision-support tools for ensemble dispatch, we develop a Markov Decision
Process (MDP) approach to optimally control load ensembles in a
privacy-preserving manner. To this end, the concept of differential privacy is
internalized into the MDP routine to protect transition probabilities and,
thus, privacy of DR participants. The proposed approach also provides a
trade-off between solution optimality and privacy guarantees, and is analyzed
using real-world data from DR events in the New York University microgrid in
New York, NY.


Abstract:
  A 3D unit cell model containing eight different spherical particles embedded
in a homogeneous strain gradient plasticity (SGP) matrix material is presented.
The interaction between particles and matrix is controlled by an interface
model formulated within the higher order SGP theory used. Strengthening of the
particle reinforced material is investigated in terms of the increase in
macroscopic yield stress. The results are used to validate a closed form
strengthening relation proposed by the authors, which suggests that the
increase in macroscopic yield stress is governed by the interface strength
times the total surface area of particles in the material volume.


Abstract:
  The Higgs boson decay modes to $b$ and $c$ quarks are crucial for many Higgs
precision measurements. The presence of semileptonic decays in the jets
originating from $b$ and $c$ quarks causes missing energy due to the
undetectable neutrinos. A correction for the missing neutrino momenta can be
derived from the kinematics of the decay up to a two-fold ambiguity. The
correct solution can be identified by a kinematic fit, which exploits the
well-known initial state at an $e^{+}e^{-}$ collider by adjusting the measured
quantities within their uncertainties to fulfill the kinematic constraints. The
ParticleFlow concept, based on the reconstruction of individual particles in a
jet allows understanding the individual jet-level uncertainties at an
unprecedented level. The modeling of the jet uncertainties and the resulting
fit performance will be discussed for the example of the ILD detector. Applied
to $H\rightarrow b\bar{b}/c\bar{c}$ events, the combination of the neutrino
correction with the kinematic fit improves the Higgs mass reconstruction
significantly, both in terms of resolution and peak position.


Abstract:
  A variational discrete element method is applied to simulate quasi-static
crack propagation. Cracks are considered to propagate between the mesh cells
through the mesh facets. The elastic behaviour is parametrized by the
continuous mechanical parameters (Young modulus and Poisson ratio). A discrete
energetic cracking criterion coupled to a discrete kinking criterion guide the
cracking process. Two-dimensional numerical examples are presented to
illustrate the robustness and versatility of the method.


Abstract:
  In this article, we consider convergence of stochastic gradient descent
schemes (SGD) under weak assumptions on the underlying landscape. More
explicitly, we show that on the event that the SGD stays local we have
convergence of the SGD if there is only a countable number of critical points
or if the target function/landscape satisfies Lojasiewicz-inequalities around
all critical levels as all analytic functions do. In particular, we show that
for neural networks with analytic activation function such as softplus, sigmoid
and the hyperbolic tangent, SGD converges on the event of staying local, if the
random variables modeling the signal and response in the training are compactly
supported.


Abstract:
  We present a directed variant of Salop (1979) model to analyze bus transport
dynamics. The players are operators competing in cooperative and
non-cooperative games. Utility, like in most bus concession schemes in emerging
countries, is proportional to the total fare collection. Competition for
picking up passengers leads to well documented and dangerous driving practices
that cause road accidents, traffic congestion and pollution. We obtain
theoretical results that support the existence and implementation of such
practices, and give a qualitative description of how they come to occur. In
addition, our results allow to compare the current or base transport system
with a more cooperative one.


Abstract:
  In reinforcement learning (RL), the goal is to obtain an optimal policy, for
which the optimality criterion is fundamentally important. Two major optimality
criteria are average and discounted rewards, where the later is typically
considered as an approximation to the former. While the discounted reward is
more popular, it is problematic to apply in environments that have no natural
notion of discounting. This motivates us to revisit a) the progression of
optimality criteria in dynamic programming, b) justification for and
complication of an artificial discount factor, and c) benefits of directly
maximizing the average reward. Our contributions include a thorough examination
of the relationship between average and discounted rewards, as well as a
discussion of their pros and cons in RL. We emphasize that average-reward RL
methods possess the ingredient and mechanism for developing the general
discounting-free optimality criterion (Veinott, 1969) in RL.


Abstract:
  We use the crystal isomorphisms of the Fock space to describe two maps on
partitions and multipartitions which naturally appear in the crystal basis
theory for quantum groups in affine type A and in the representation theory of
Hecke algebras of type G(l, l, n).


Abstract:
  We prove that Strings-and-Coins -- the combinatorial two-player game
generalizing the dual of Dots-and-Boxes -- is strongly PSPACE-complete on
multigraphs. This result improves the best previous result, NP-hardness, argued
in Winning Ways. Our result also applies to the Nimstring variant, where the
winner is determined by normal play; indeed, one step in our reduction is the
standard reduction (also from Winning Ways) from Nimstring to
Strings-and-Coins.