title:
Asymmetric double-pulse interferometric frequency-resolved optical
  gating for visible-wavelength time-domain spectroscopy

abstract:
  Ultrafast science and technology have brought in burgeoning opportunities to
optical metrology, strong-field physics, non-equilibrium physics, etc., through
light-matter interaction due to ever-advancing temporal resolution and peak
power of ultrafast laser. The superior temporal and spectral resolution, has
brought forth pump-probe spectroscopy for ultrafast dynamic study of transient
states in various intriguing materials, such as quantum materials,
metamaterials, and plasmonic materials, by directly reporting spectroscopic
complex response function, using either time- or frequency-domain- based
probes. In stark contrast to its frequency-domain counterparts, e.g., FTIR and
ellipsometry, time-domain spectroscopy outstands by providing not only superb
spectroscopic phase sensitivity but also exceptional temporal resolution due to
its pulsed nature. To extend detection range of time-domain spectroscopy into
the challenging visible frequencies, we propose an interferometry-type
frequency-resolved optical gating (FROG). Our numerical simulation shows, when
operating in a carefully engineered double-pulse scheme, a unique phase-locking
mechanism can be activated, and therefore preserves both zero- and first-order
phases, that are otherwise inaccessible to standard FROG measurement. Followed
by time-domain signal reconstruction and analysis protocol, we show that
time-domain spectroscopy with subcycle temporal resolution is enabled and well
suits the need of ultrafast-compatible and ambiguity-free method for complex
dielectric function measurement at visible wavelengths.


title:
Global Attitude Synchronization of Networked Rigid Bodies Under Directed
  Topologies

abstract:
  The global attitude synchronization problem is studied for networked rigid
bodies under directed topologies. To avoid the asynchronous pitfall where only
vector parts converge to some identical value but scalar parts do not,
multiplicative quaternion errors are leveraged to develop attitude
synchronization protocols for rigid bodies with the absolute measurements. It
is shown that global synchronization of networked rigid bodies can be achieved
if and only if the directed topology is quasi-strongly connected.
Simultaneously, a novel double-energy-function analysis method, equipped with
an ordering permutation technique about scalar parts and a coordinate
transformation mechanism, is constructed for the quaternion behavior analysis
of networked rigid bodies. In particular, global synchronization is achieved
with our analysis method regardless of the highly nonlinear and strongly
coupling problems resulting from multiplicative quaternion errors, which
seriously hinder the traditional analysis of global synchronization for
networked rigid bodies. Simulations for networked spacecraft are presented to
show the global synchronization performances under different directed
topologies.


title:
Enhancement of giant magnetoelectric effect in Ni-doped
  CaBaCo$_{4}$O$_{7}$

abstract:
  The polar magnet CaBaCo$_{4}$O$_{7}$ is known to exhibit the largest
magnetic-field-driven electric polarization change ($\Delta P$) associated with
an antiferromagnetic (AFM)-ferrimagnetic (FIM) transition in a narrow
temperature range between 62 and 69 K. In this work, we investigate the effect
of Ni doping on its multiferroic properties, by means of magnetization,
electric polarization, dielectric constant, and magnetostriction measurements
on single crystals of CaBaCo$_{3.9}$Ni$_{0.1}$O$_{7}$ up to 50 T. In the doped
material, two kinds of AFM phases appear below 78 K, accompanying negative
$\Delta P$. Upon the application of a magnetic field along any crystallographic
axis, giant positive $\Delta P$ of up to $11 \sim 12$ mC/m$^{2}$ is observed
along with an AFM-FIM transition in the whole temperature range below 78 K. The
giant magnetoelectric effect inherent in CaBaCo$_{4}$O$_{7}$ can be further
enhanced just by a small amount of chemical substitution, in terms of (i)
increasing the magnitude of $\Delta P$ and (ii) expanding the temperature range
in which giant $\Delta P$ appears.


title:
Incorporating Gradient Similarity for Robust Time Delay Estimation in
  Ultrasound Elastography

abstract:
  Energy-based ultrasound elastography techniques minimize a regularized cost
function consisting of data and continuity terms to obtain local displacement
estimates based on the local time-delay estimation (TDE) between
radio-frequency (RF) frames. The data term associated with the existing
techniques takes only the amplitude similarity into account and hence is not
sufficiently robust to the outlier samples present in the RF frames under
consideration. This drawback creates noticeable artifacts in the strain image.
To resolve this issue, we propose to formulate the data function as a linear
combination of the amplitude and gradient similarity constraints. We estimate
the adaptive weight concerning each similarity term following an iterative
scheme. Finally, we optimize the non-linear cost function in an efficient
manner to convert the problem to a sparse system of linear equations which are
solved for millions of variables. We call our technique rGLUE: robust data term
in GLobal Ultrasound Elastography. rGLUE has been validated using simulation,
phantom, in vivo liver, and breast datasets. In all of our experiments, rGLUE
substantially outperforms the recent elastography methods both visually and
quantitatively. For simulated, phantom, and in vivo datasets, respectively,
rGLUE achieves 107%, 18%, and 23% improvements of signal-to-noise ratio (SNR)
and 61%, 19%, and 25% improvements of contrast-to-noise ratio (CNR) over GLUE,
a recently-published elastography algorithm.


title: Spacetime Stochasticity and Second Order Geometry

abstract:
  We discuss the Schwartz-Meyer second order geometry framework and its
relevance to theories of quantum gravity that incorporate a notion of spacetime
stochasticity or quantum foam. We illustrate the framework in the context of
Nelson's stochastic quantization.


title:
Perfectoid towers and their tilts : with an application to the \'etale
  cohomology groups of local log-regular rings

abstract:
  To initiate a systematic study on the applications of perfectoid method to
Noetherian rings, we introduce the notions of perfectoid towers and their
tilts, and examine their properties. Using these, we establish a comparison
theorem on finiteness of \'etale cohomology groups of a perfectoid tower and of
the tilt. We also specialize this to prove the finiteness of the
prime-to-$p$-torsion subgroup of the divisor class group of a local log-regular
ring that appears in logarithmic geometry in the mixed characteristic case.


title: Recognition of polar lows in Sentinel-1 SAR images with deep learning

abstract:
  In this paper, we explore the possibility of detecting polar lows in C-band
SAR images by means of deep learning. Specifically, we introduce a novel
dataset consisting of Sentinel-1 images labeled as positive; representing a
maritime mesocyclone, or negative; representing a normal sea state. The dataset
is constructed using the ERA5 dataset as baseline and it consists of 2004
annotated images. To our knowledge, this is the first dataset of its kind to be
publicly released. The dataset is used to train a deep learning model to
classify the labeled images. Evaluated on an independent test set, the model
yields an F-1 score of 0.95, indicating that polar lows can be consistently
detected from SAR images. Interpretability techniques applied to the deep
learning model reveal that atmospheric fronts and cyclonic eyes are key
features in the classification. Moreover, experimental results show that the
model is accurate even if: (i) such features are significantly cropped due to
the limited swath width of the SAR, (ii) the features are partly covered by sea
ice and (iii) land is covering significant parts of the images. By evaluating
the model performance on multiple input image resolutions (pixel sizes of 500m,
1km and 2km), it is found that higher resolution yield the best performance.
This emphasises the potential of using high resolution sensors like SAR for
detecting polar lows, as compared to conventionally used sensors such as
scatterometers.


title: A Unified Cosmological Dark Sector from a Bose-Einstein Condensate

abstract:
  We examine the viability of cosmological solution(s) describing a unified
picture of the dark side of the universe from a Bose-Einstein condensate (BEC)
of light bosons. The energy density of the BEC, together with its quantum
potential, can indeed account for such a unification, in the sense that the
(dust-like) cold dark matter and the dark energy components emerge from the
same source. In particular, the bulk of the dark energy can be attributed to
the quantum potential, in the quantum corrected Raychaudhuri-Friedmann
equation, when the `macroscopic' BEC wave-function is taken to be such that the
corresponding probability density is construed as the energy density of the
dusty fluid. However, there arises a purely quantum mechanical back-reaction
effect, of even the visible baryons, on the effective dark energy and dark
matter contents, which crucially determines the mass of the BEC. We determine
the constraint on such a back-reaction, and hence on the BEC mass, from
physical considerations, as well as estimate the same using recent
observational data.


title: The Secret Hyperbolic Life of Positive Scalar Curvature

abstract:
  This survey introduces to the hyperbolic unfolding correspondence that links
the geometric analysis of minimal hypersurfaces with that of Gromov hyperbolic
spaces. Problems caused from hypersurface singularities oftentimes become
solvable on associated Gromov hyperbolic spaces. Applied to scalar curvature
geometry this yields smoothing schemes that eliminate such singularities.


title:
Gamma-Ray Emission from Nova Shocks Expanding in the Red Giant Wind:
  Interpretation of the 2021 Outburst of the Recurrent Nova RS Ophiuchi

abstract:
  Nova outbursts take place in binary star systems comprising a white dwarf
(WD) and either a low-mass Sun-like star (classical novae) or, as in the case
of the symbiotic nova, a red giant. GeV gamma-ray emission has been detected
from a dozen of classical novae and from one symbiotic nova (V407 Cyg) by
Fermi-LAT. For classical novae, gamma-ray emission is generally thought to be
related to internal shocks formed as fast outflow collides with the slow
outflow. However, for the symbiotic nova V407 Cyg, the origin of the gamma-ray
emission has been debated, as both internal shock and external shock, resulted
from the collision between the nova ejecta and the ambient wind of the giant
companion, were suggested to explain the gamma-ray data. Recently, bright GeV
and TeV gamma-ray emission has been detected from a symbiotic Nova, RS
Ophiuchi, during its 2021 outburst, which shows a remarkably smooth powerlaw
decay in time up to about one month after the outburst. We show that this
temporal decay behavior can be interpreted as arising from an external shock,
which is in the self-similar deceleration phase. In this interpretation, the
gamma-rays are produced by shock-accelerated protons interacting with the dense
wind through the hadronic process. Our interpretation thus indicates that the
nova shock is able to accelerate cosmic ray protons up to TeV energies even
when it has been significantly decelerated.


title:
Labour by Design: Contributions of David Card, Joshua Angrist, and Guido
  Imbens

abstract:
  The 2021 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred
Nobel was awarded to David Card "for his empirical contributions to labour
economics" and to Joshua Angrist and Guido Imbens "for their methodological
contributions to the analysis of causal relationships." We survey these
contributions of the three laureates, and discuss how their empirical and
methodological insights transformed the modern practice of applied
microeconomics. By emphasizing research design and formalizing the causal
content of different econometric procedures, the laureates shed new light on
key questions in labour economics and advanced a robust toolkit for empirical
analyses across many fields.


title: PerfectDou: Dominating DouDizhu with Perfect Information Distillation

abstract:
  As a challenging multi-player card game, DouDizhu has recently drawn much
attention for analyzing competition and collaboration in imperfect-information
games. In this paper, we propose PerfectDou, a state-of-the-art DouDizhu AI
system that dominates the game, in an actor-critic framework with a proposed
technique named perfect information distillation. In detail, we adopt a
perfect-training-imperfect-execution framework that allows the agents to
utilize the global information to guide the training of the policies as if it
is a perfect information game and the trained policies can be used to play the
imperfect information game during the actual gameplay. To this end, we
characterize card and game features for DouDizhu to represent the perfect and
imperfect information. To train our system, we adopt proximal policy
optimization with generalized advantage estimation in a parallel training
paradigm. In experiments we show how and why PerfectDou beats all existing AI
programs, and achieves state-of-the-art performance.


title:
Hybrid Diffractive Optics Design via Hardware-in-the-Loop Methodology
  for Achromatic Extended-Depth-of-Field Imaging

abstract:
  End-to-end optimization of diffractive optical elements (DOEs) profile
through a digital differentiable model combined with computational imaging have
gained an increasing attention in emerging applications due to the compactness
of resultant physical setups. Despite recent works have shown the potential of
this methodology to design optics, its performance in physical setups is still
limited and affected by manufacturing artifacts of DOE, mismatch between
simulated and resultant experimental point spread functions, and calibration
errors. Additionally, the computational burden of the digital differentiable
model to effectively design the DOE is increasing, thus limiting the size of
the DOE that can be designed. To overcome the above mentioned limitations, the
broadband imaging system with phase-only spatial light modulator (SLM) as an
encoded DOE is proposed and developed in this paper. A co-design of the SLM
phase pattern and image reconstruction algorithm is produced following the
end-to-end strategy, using for optimization a convolutional neural network
equipped with quantitative and qualitative loss functions. The optics of the
imaging system is hybrid consisting of SLM as DOE and refractive lens. SLM
phase-pattern is optimized by applying the Hardware-in-the-loop technique,
which helps to eliminate the mismatch between numerical modeling and physical
reality of image formation as light propagation is not numerically modeled but
is physically done. In our experiments, the hybrid optics is implemented by the
optical projection of the SLM phase-pattern on a lens plane for a depth range
0.4-1.9m. Comparison with compound multi-lens optics such as Sony A7 III and
iPhone Xs Max cameras show that the proposed system is advanced in all-in-focus
sharp imaging.


title:
Learn2Sing 2.0: Diffusion and Mutual Information-Based Target Speaker
  SVS by Learning from Singing Teacher

abstract:
  Building a high-quality singing corpus for a person who is not good at
singing is non-trivial, thus making it challenging to create a singing voice
synthesizer for this person. Learn2Sing is dedicated to synthesizing the
singing voice of a speaker without his or her singing data by learning from
data recorded by others, i.e., the singing teacher. Inspired by the fact that
pitch is the key style factor to distinguish singing from speaking voice, the
proposed Learn2Sing 2.0 first generates the preliminary acoustic feature with
averaged pitch value in the phone level, which allows the training of this
process for different styles, i.e., speaking or singing, share same conditions
except for the speaker information. Then, conditioned on the specific style, a
diffusion decoder, which is accelerated by a fast sampling algorithm during the
inference stage, is adopted to gradually restore the final acoustic feature.
During the training, to avoid the information confusion of the speaker
embedding and the style embedding, mutual information is employed to restrain
the learning of speaker embedding and style embedding. Experiments show that
the proposed approach is capable of synthesizing high-quality singing voice for
the target speaker without singing data with 10 decoding steps.


title: On the Polygonal Faber-Krahn Inequality

abstract:
  It has been conjectured by P\'{o}lya and Szeg\"{o} seventy years ago that the
planar set which minimizes the first eigenvalue of the Dirichlet-Laplace
operator among polygons with $n$ sides and fixed area is the regular polygon.
Despite its apparent simplicity, this result has only been proved for triangles
and quadrilaterals. In this paper we prove that for each $n \ge 5$ the proof of
the conjecture can be reduced to a finite number of certified numerical
computations. Moreover, the local minimality of the regular polygon can be
reduced to a single numerical computation. For $n=5, 6,7, 8$ we perform this
computation and certify the numerical approximation by finite elements, up to
machine errors.


title:
Revised scattering exponents for a power-law distribution of surface and
  mass fractals

abstract:
  We consider scattering exponents arising in small-angle scattering from
power-law polydisperse surface and mass fractals. It is shown that a set of
fractals, whose sizes are distributed according to a power-law, can change its
fractal dimension when the power-law exponent is sufficiently big. As a result,
the scattering exponent corresponding to this dimension appears due to the
spatial correlations between positions of different fractals. For large values
of the momentum transfer, the correlations do not play any role, and the
resulting scattering intensity is given by a sum of intensities of all
composing fractals. The restrictions imposed on the power-law exponents are
found. The obtained results generalize Martin's formulas for the scattering
exponents of the polydisperse fractals.


title:
Initial transient stage of pin-to-pin nanosecond repetitively pulsed
  discharges in air

abstract:
  In this work, evolution of parameters of nanosecond repetitively pulsed (NRP)
discharges in pin-to-pin configuration in air was studied during transient
stage of initial twenty discharge pulses. Gas and plasma parameters in the
discharge gap were measured using coherent microwave scattering (CMS), optical
emission spectroscopy (OES) and laser Rayleigh scattering (LRS) for NRP
discharges at repetition frequencies of 1, 10 and 100 kHz. Memory effects (when
perturbations induced by the previous discharge pulse would not decay fully
till the subsequent pulse) were detected for the repetition frequencies of 10
and 100 kHz. For 10 kHz NRP discharge, the discharge parameters experienced
significant change after the first pulse and continued to substantially
fluctuate between the subsequent pulses due to rapid evolution of gas density
and temperature during the 100 us inter-pulse time caused by intense
redistribution of the flow field in the gap on that time scale. For 100 kHz NRP
discharge, the discharge pulse parameters reached a new steady state at about
five pulses after initiation. This new steady state was associated with
well-reproducible parameters between the discharge pulses and substantial
reduction of breakdown voltage, discharge pulse energy, and electron number
density in comparison with the first discharge pulse.


title: Skew and sphere fibrations

abstract:
  A great sphere fibration is a sphere bundle with total space $S^n$ and fibers
which are great $k$-spheres. Given a smooth great sphere fibration, the central
projection to any tangent hyperplane yields a \emph{nondegenerate} fibration of
$\mathbb{R}^n$ by pairwise skew, affine copies of $\mathbb{R}^k$ (though not
all nondegenerate fibrations can arise in this way). Here we study the topology
and geometry of nondegenerate fibrations, we show that every nondegenerate
fibration satisfies a notion of Continuity at Infinity, and we prove several
classification results. These results allow us to determine, in certain
dimensions, precisely which nondegenerate fibrations correspond to great sphere
fibrations via the central projection. We use this correspondence to reprove a
number of recent results about sphere fibrations in the simpler, more explicit
setting of nondegenerate fibrations. For example, we show that every germ of a
nondegenerate fibration extends to a global fibration, and we study the
relationship between nondegenerate line fibrations and contact structures in
odd-dimensional Euclidean space. We conclude with a number of partial results,
in hopes that the continued study of nondegenerate fibrations, together with
their correspondence with sphere fibrations, will yield new insights towards
the unsolved classification problems for sphere fibrations.


title: Learning Fair Models without Sensitive Attributes: A Generative Approach

abstract:
  Most existing fair classifiers rely on sensitive attributes to achieve
fairness. However, for many scenarios, we cannot obtain sensitive attributes
due to privacy and legal issues. The lack of sensitive attributes challenges
many existing works. Though we lack sensitive attributes, for many
applications, there usually exists features or information of various formats
that are relevant to sensitive attributes. For example, a personal purchase
history can reflect his or her race, which would be helpful for learning fair
classifiers on race. However, the work on exploring relevant features for
learning fair models without sensitive attributes is rather limited. Therefore,
in this paper, we study a novel problem of learning fair models without
sensitive attributes by exploring relevant features. We propose a probabilistic
generative framework to effectively estimate the sensitive attribute from the
training data with relevant features in various formats and utilize the
estimated sensitive attribute information to learn fair models. Experimental
results on real-world datasets show the effectiveness of our framework in terms
of both accuracy and fairness.


title:
Surface Vision Transformers: Attention-Based Modelling applied to
  Cortical Analysis

abstract:
  The extension of convolutional neural networks (CNNs) to non-Euclidean
geometries has led to multiple frameworks for studying manifolds. Many of those
methods have shown design limitations resulting in poor modelling of long-range
associations, as the generalisation of convolutions to irregular surfaces is
non-trivial. Motivated by the success of attention-modelling in computer
vision, we translate convolution-free vision transformer approaches to surface
data, to introduce a domain-agnostic architecture to study any surface data
projected onto a spherical manifold. Here, surface patching is achieved by
representing spherical data as a sequence of triangular patches, extracted from
a subdivided icosphere. A transformer model encodes the sequence of patches via
successive multi-head self-attention layers while preserving the sequence
resolution. We validate the performance of the proposed Surface Vision
Transformer (SiT) on the task of phenotype regression from cortical surface
metrics derived from the Developing Human Connectome Project (dHCP).
Experiments show that the SiT generally outperforms surface CNNs, while
performing comparably on registered and unregistered data. Analysis of
transformer attention maps offers strong potential to characterise subtle
cognitive developmental patterns.


title:
The impact of using voxel-level segmentation metrics on evaluating
  multifocal prostate cancer localisation

abstract:
  Dice similarity coefficient (DSC) and Hausdorff distance (HD) are widely used
for evaluating medical image segmentation. They have also been criticised, when
reported alone, for their unclear or even misleading clinical interpretation.
DSCs may also differ substantially from HDs, due to boundary smoothness or
multiple regions of interest (ROIs) within a subject. More importantly, either
metric can also have a nonlinear, non-monotonic relationship with outcomes
based on Type 1 and 2 errors, designed for specific clinical decisions that use
the resulting segmentation. Whilst cases causing disagreement between these
metrics are not difficult to postulate. This work first proposes a new
asymmetric detection metric, adapting those used in object detection, for
planning prostate cancer procedures. The lesion-level metrics is then compared
with the voxel-level DSC and HD, whereas a 3D UNet is used for segmenting
lesions from multiparametric MR (mpMR) images. Based on experimental results we
report pairwise agreement and correlation 1) between DSC and HD, and 2) between
voxel-level DSC and recall-controlled precision at lesion-level, with Cohen's
[0.49, 0.61] and Pearson's [0.66, 0.76] (p-values}<0.001) at varying cut-offs.
However, the differences in false-positives and false-negatives, between the
actual errors and the perceived counterparts if DSC is used, can be as high as
152 and 154, respectively, out of the 357 test set lesions. We therefore
carefully conclude that, despite of the significant correlations, voxel-level
metrics such as DSC can misrepresent lesion-level detection accuracy for
evaluating localisation of multifocal prostate cancer and should be interpreted
with caution.


title:
STeP-CiM: Strain-enabled Ternary Precision Computation-in-Memory based
  on Non-Volatile 2D Piezoelectric Transistors

abstract:
  We propose 2D Piezoelectric FET (PeFET) based compute-enabled non-volatile
memory for ternary deep neural networks (DNNs). PeFETs consist of a material
with ferroelectric and piezoelectric properties coupled with Transition Metal
Dichalcogenide channel. We utilize (a) ferroelectricity to store binary bits
(0/1) in the form of polarization (-P/+P) and (b) polarization dependent
piezoelectricity to read the stored state by means of strain-induced bandgap
change in Transition Metal Dichalcogenide channel. The unique read mechanism of
PeFETs enables us to expand the traditional association of +P (-P) with low
(high) resistance states to their dual high (low) resistance depending on read
voltage. Specifically, we demonstrate that +P (-P) stored in PeFETs can be
dynamically configured in (a) a low (high) resistance state for positive read
voltages and (b) their dual high (low) resistance states for negative read
voltages, without afflicting a read disturb. Such a feature, which we name as
Polarization Preserved Piezoelectric Effect Reversal with Dual Voltage Polarity
(PiER), is unique to PeFETs and has not been shown in hitherto explored
memories. We leverage PiER to propose a Strain-enabled Ternary Precision
Computation-in-Memory (STeP-CiM) cell with capabilities of computing the scalar
product of the stored weight and input, both of which are represented with
signed ternary precision. Further, using multi word-line assertion of STeP-CiM
cells, we achieve massively parallel computation of dot products of signed
ternary inputs and weights. Our array level analysis shows 91% lower delay and
improvements of 15% and 91% in energy for in-memory multiply-and-accumulate
operations compared to near-memory design approaches based on SRAM and PeFET
respectively. STeP-CiM exhibits upto 8.91x improvement in performance and 6.07x
average improvement in energy over SRAM/PeFET based near-memory design.


title:
Low-complexity Near-optimum Symbol Detection Based on Neural Enhancement
  of Factor Graphs

abstract:
  We consider the application of the factor graph framework for symbol
detection on linear inter-symbol interference channels. Based on the Ungerboeck
observation model, a detection algorithm with appealing complexity properties
can be derived. However, since the underlying factor graph contains cycles, the
sum-product algorithm (SPA) yields a suboptimal algorithm. In this paper, we
develop and evaluate efficient strategies to improve the performance of the
factor graph-based symbol detection by means of neural enhancement. In
particular, we consider neural belief propagation as an effective way to
mitigate the effect of cycles within the factor graph. We also investigate the
application of factor node generalizations and pruning techniques. By applying
a generic preprocessor to the channel output, we propose a simple technique to
vary the underlying factor graph in every SPA iteration. Using this dynamic
factor graph transition, we intend to preserve the extrinsic nature of the SPA
messages which is otherwise impaired due to cycles. Simulation results show
that the proposed methods can massively improve the detection performance, even
approaching the maximum a posteriori performance for various transmission
scenarios, while preserving a complexity which is linear in both the block
length and the channel memory.


title:
A Barrier-Certified Optimal Coordination Framework for Connected and
  Automated Vehicles

abstract:
  In this paper, we extend a framework that we developed earlier for
coordination of connected and automated vehicles (CAVs) at a signal-free
intersection by integrating a safety layer using control barrier functions.
First, in our motion planning module, each CAV computes the optimal control
trajectory using simple vehicle dynamics. The trajectory does not make any of
the state, control, and safety constraints active. A vehicle-level tracking
controller employs a combined feedforward-feedback control law to track the
resulting optimal trajectory from the motion planning module. Then, a
barrier-certificate module, acting as a middle layer between the vehicle-level
tracking controller and physical vehicle, receives the control law from the
vehicle-level tracking controller and using realistic vehicle dynamics ensures
that none of the state, control, and safety constraints becomes active. The
latter is achieved through a quadratic program, which can be solved efficiently
in real time. We demonstrate the effectiveness of our extended framework
through a numerical simulation.


title:
Intelligent Blockage Prediction and Proactive Handover for Seamless
  Connectivity in Vision-Aided 5G/6G UDNs

abstract:
  The upsurge in wireless devices and real-time service demands force the move
to a higher frequency spectrum. Millimetre-wave (mmWave) and terahertz (THz)
bands combined with the beamforming technology offer significant performance
enhancements for ultra-dense networks (UDNs). Unfortunately, shrinking cell
coverage and severe penetration loss experienced at higher spectrum render
mobility management a critical issue in UDNs, especially optimizing beam
blockages and frequent handover (HO). Mobility management challenges have
become prevalent in city centres and urban areas. To address this, we propose a
novel mechanism driven by exploiting wireless signals and on-road surveillance
systems to intelligently predict possible blockages in advance and perform
timely HO. This paper employs computer vision (CV) to determine obstacles and
users' location and speed. In addition, this study introduces a new HO event,
called block event {BLK}, defined by the presence of a blocking object and a
user moving towards the blocked area. Moreover, the multivariate regression
technique predicts the remaining time until the user reaches the blocked area,
hence determining best HO decision. Compared to typical wireless networks
without blockage prediction, simulation results show that our BLK detection and
PHO algorithm achieves 40\% improvement in maintaining user connectivity and
the required quality of experience (QoE).


title:
Unlikely and just likely intersections for high dimensional families of
  elliptic curves

abstract:
  Given two varieties V,W in the n-fold product of modular curves, we answer
affirmatively a question (formulated by Shou-Wu Zhang's AIM group) on whether
the set of points in V that are Hecke translations of some point on W is dense
in V. We need to make some (necessary) assumptions on the dimensions of V,W but
for instance, when V is a divisor and W is a curve, no further assumptions are
needed. We also examine the necessity of our assumptions in the case of
unlikely intersections and show that, contrary to exceptions, two curves in a
high dimensional space over a finite field can intersect infinitely often up to
Hecke translations.


title: OPD: Single-view 3D Openable Part Detection

abstract:
  We address the task of predicting what parts of an object can open and how
they move when they do so. The input is a single image of an object, and as
output we detect what parts of the object can open, and the motion parameters
describing the articulation of each openable part. To tackle this task, we
create two datasets of 3D objects: OPDSynth based on existing synthetic
objects, and OPDReal based on RGBD reconstructions of real objects. We then
design OPDRCNN, a neural architecture that detects openable parts and predicts
their motion parameters. Our experiments show that this is a challenging task
especially when considering generalization across object categories, and the
limited amount of information in a single image. Our architecture outperforms
baselines and prior work especially for RGB image inputs. Short video summary
at https://www.youtube.com/watch?v=P85iCaD0rfc


title: Zentropy Theory for Ferroelectrics: A Case Study of PbTiO3

abstract:
  Thermodynamics of ferroelectric to paraelectric (FE-PE) transitions is
commonly described by the phenomenological Landau theory and more recently by
effective Hamiltonian. Here we show that the zentropy theory, which considers
the total entropy of a macroscopic system (macrostate) as a weighted sum of
entropies of representative microscopic configurations (microstates) and the
configurational entropy among the microstates, can predict the FE-PE transition
without fitting parameters. In PbTiO3, the microstates are FE states with or
without domain walls. With the energetics of microstates determined from
first-principles calculations, the FE-PE transition for PbTiO3 is predicted
showing remarkable agreement with experiments, unveiling the microscopic
fundamentals of the transition.


title: Data-Driven Model Predictive Control for Linear Time-Periodic Systems

abstract:
  We consider the problem of data-driven predictive control for an unknown
discrete-time linear time-periodic (LTP) system of known period. Our proposed
strategy generalizes both Data-enabled Predictive Control (DeePC) and Subspace
Predictive Control (SPC), which are established data-driven control techniques
for linear time-invariant (LTI) systems. The approach is supported by an
extensive theoretical development of behavioral systems theory for LTP systems,
culminating in a generalization of the fundamental lemma. Our algorithm
produces results identical to standard Model Predictive Control (MPC) for
deterministic LTP systems. Robustness of the algorithm to noisy data is
illustrated via simulation of a regularized version of the algorithm applied to
a stochastic multi-input multi-output LTP system.


title: Quantum-Enhanced Doppler Radar/Lidar

abstract:
  We propose a quantum-enhanced protocol to estimate the radial velocity $v$ of
a moving target, using a frequency-entangled squeezed state composed of a
signal and an idler beam as a probe state. The signal beam illuminates the
moving object and it is reflected with its frequency shifted due to the Doppler
effect. Then, a joint measurement between signal and idler beams is performed
to estimate the velocity of the object. We aim at benchmarking this protocol
against the classical one, which comprises a coherent state with the same
energy illuminating the object. Indeed, employing squeezing and frequency
entanglement as quantum resources provides to a precision enhancement in the
estimation of the velocity of the object. We identify three distinct parameter
regimes. First, the frequency entanglement-dominant regime, where the advantage
is proportional to the degree of frequency entanglement and mostly insensitive
to the photon number. Second, the squeezing-dominant regime, with a quantum
advantage that is higher than the standard quantum limit. Third, the mixed
regime, where both squeezing and frequency entanglement are comparable and the
proposed quantum protocol attains the Heisenberg limit. We show that an optimal
measurement to achieve these results is frequency-resolved photon-number
counting. Losses in the signal beam are considered for the high frequency
entanglement regime. The protocol shows resilience, outperforming the classical
protocol for all channel transmissivities given a large enough frequency
entanglement.


title:
How do we walk? Using hybrid holonomy to approximate non-holonomic
  systems

abstract:
  Why do we move forward when we walk? Our legs undergo periodic motion and
thus possess no net change in position; however, our bodies do possess a net
change in position and we are propelled forward. From a geometric perspective,
this phenomenon of periodic input producing non-periodic output is holonomy. To
obtain non-zero holonomy and propel forward, we must alternate which leg is in
contact with the ground; a non-zero net motion can be obtained by concatenating
arcs that would individually produce no net motion. We develop a framework for
computing the holonomy group of hybrid systems and analyze their behavior in
the limit as the number of impacts goes to infinity.


title: Optimal Geodesic Curvature Constrained Dubins' Paths on a Sphere

abstract:
  In this article, we consider the motion planning of a rigid object on the
unit sphere with a unit speed. The motion of the object is constrained by the
maximum absolute value, $U_{max}$ of geodesic curvature of its path; this
constrains the object to change the heading at the fastest rate only when
traveling on a tight smaller circular arc of radius $r <1$, where $r$ depends
on the bound, $U_{max}$. We show in this article that if $0<r \le \frac{1}{2}$,
the shortest path between any two configurations of the rigid body on the
sphere consists of a concatenation of at most three circular arcs.
Specifically, if $C$ is the smaller circular arc and $G$ is the great circular
arc, then the optimal path can only be $CCC, CGC, CC, CG, GC, C$ or $G$. If $r>
\frac{1}{2}$, while paths of the above type may cease to exist depending on the
boundary conditions and the value of $r$, optimal paths may be concatenations
of more than three circular arcs.


title: Balanced MSE for Imbalanced Visual Regression

abstract:
  Data imbalance exists ubiquitously in real-world visual regressions, e.g.,
age estimation and pose estimation, hurting the model's generalizability and
fairness. Thus, imbalanced regression gains increasing research attention
recently. Compared to imbalanced classification, imbalanced regression focuses
on continuous labels, which can be boundless and high-dimensional and hence
more challenging. In this work, we identify that the widely used Mean Square
Error (MSE) loss function can be ineffective in imbalanced regression. We
revisit MSE from a statistical view and propose a novel loss function, Balanced
MSE, to accommodate the imbalanced training label distribution. We further
design multiple implementations of Balanced MSE to tackle different real-world
scenarios, particularly including the one that requires no prior knowledge
about the training label distribution. Moreover, to the best of our knowledge,
Balanced MSE is the first general solution to high-dimensional imbalanced
regression. Extensive experiments on both synthetic and three real-world
benchmarks demonstrate the effectiveness of Balanced MSE.


title: Vulnerability Detection in Open Source Software: An Introduction

abstract:
  This paper is an introductory discussion on the cause of open source software
vulnerabilities, their importance in the cybersecurity ecosystem, and a
selection of detection methods. A recent application security report showed 44%
of applications contain critical vulnerabilities in an open source component, a
concerning proportion. Most companies do not have a reliable way of being
directly and promptly notified when zero-day vulnerabilities are found and then
when patches are made available. This means attack vectors in open source exist
longer than necessary. Conventional approaches to vulnerability detection are
outlined alongside some newer research trends. A conclusion is made that it may
not be possible to entirely replace expert human inspection of open source
software, although it can be effectively augmented with techniques such as
machine learning, IDE plug-ins and repository linking to make implementation
and review less time intensive. Underpinning any technological advances should
be better knowledge at the human level. Development teams need trained, coached
and improved so they can implement open source more securely, know what
vulnerabilities to look for and how to handle them. It is the use of this
blended approach to detection which is key.


title:
Large Rashba Spin-Orbit Coupling and High-Temperature Quantum Anomalous
  Hall Effect in Re-Intercalated Graphene/CrI$_3$ Heterostructure

abstract:
  In 2010, quantum anomalous Hall effect (QAHE) in graphene was proposed in the
presence of Rashba spin-orbit coupling and ferromagnetic exchange field. After
a decade's experimental exploration, the anomalous Hall conductance can only
reach about 0.25 in the units of $2e^2/h$, which was attributed to the tiny
Rashba spin-orbit coupling. Here, we theoretically show that Re-intercalation
in graphene/CrI$_3$ heterostructure can not only induce sizeable Rashba
spin-orbit coupling ($>$ 40~meV), but also open up large band gaps at valleys
$K$ (22.2 meV) and $K' $ (30.3 meV), and a global band gap over 5.5 meV (19.5
meV with random Re distribution) hosting QAHE. A low-energy continuum model is
constructed to explain the underlying physical mechanism. We find that Rashba
spin-orbit coupling is robust against external stress whereas a tensile strain
can increase the global bulk gap. Furthermore, we also show that
Re-intercalated graphene with hexagonal boron-nitride can also realize QAHE
with bulk gap over 40~meV, indicating the tunability of $5d$-intercalated
graphene-based heterostructure. Our finding makes a great leap towards the
experimental realization of graphene-based QAHE, and will definitely accelerate
the practical application of graphene-based low-power electronics.


title:
Self consistent equation of state for water behind the strong shockwave
  front

abstract:
  The Mi-Grunneisen self-consistent analitical form of the equation of state
(EOS) for water behind the strong shock front is obtained using virial theorem.
Explicit form for the shock adiabatic, Gruneisen's coefficient and parameter,
depending on the temperature, the water compresion and on an exponent of the
intermolecular interaction potential are presented. In addition, the dependence
of the exponent of the Tait-Murnagham isothermal EQS of water on the
intermolecular force and on Gruneisen's parameter is obtained.


title:
Explicit Class number formulas for Siegel--Weil averages of ternary
  quadratic forms

abstract:
  In this paper, we investigate the interplay between positive-definite
integral ternary quadratic forms and class numbers. We generalize a result of
Jones relating the theta function for the genus of a quadratic form to the
Hurwitz class numbers, obtaining an asymptotic formula (with a main term and
error term away from finitely many bad square classes $t_j\mathbb{Z}^2$)
relating the number of lattices points in a quadratic space of a given norm
with a sum of class numbers related to that norm and the squarefree part of the
discriminant of the quadratic form on this lattice.


title:
Long-term Dynamics of Fairness Intervention in Connection Recommender
  Systems

abstract:
  Recommender system fairness has been studied from the perspectives of a
variety of stakeholders including content producers, the content itself and
recipients of recommendations. Regardless of which type of stakeholders are
considered, most works in this area assess the efficacy of fairness
intervention by evaluating a single fixed fairness criterion through the lens
of a one-shot, static setting. Yet recommender systems constitute dynamical
systems with feedback loops from the recommendations to the underlying
population distributions which could lead to unforeseen and adverse
consequences if not taken into account. In this paper, we study a connection
recommender system patterned after the systems employed by web-scale social
networks and analyze the long-term effects of intervening on fairness in the
recommendations. We find that, although seemingly fair in aggregate, common
exposure and utility parity interventions fail to mitigate amplification of
biases in the long term. We theoretically characterize how certain fairness
interventions impact the bias amplification dynamics in a stylized P\'{o}lya
urn model.


title:
CMEs and SEPs During November-December 2020: A Challenge for Real-Time
  Space Weather Forecasting

abstract:
  Predictions of coronal mass ejections (CMEs) and solar energetic particles
(SEPs) are a central issue in space weather forecasting. In recent years,
interest in space weather predictions has expanded to include impacts at other
planets beyond Earth as well as spacecraft scattered throughout the
heliosphere. In this sense, the scope of space weather science now encompasses
the whole heliospheric system, and multi-point measurements of solar transients
can provide useful insights and validations for prediction models. In this
work, we aim to analyse the whole inner heliospheric context between two
eruptive flares that took place in late 2020, i.e. the M4.4 flare of November
29 and the C7.4 flare of December 7. This period is especially interesting
because the STEREO-A spacecraft was located ~60{\deg} east of the Sun-Earth
line, giving us the opportunity to test the capabilities of "predictions at
360{\deg}" using remote-sensing observations from the Lagrange L1 and L5 points
as input. We simulate the CMEs that were ejected during our period of interest
and the SEPs accelerated by their shocks using the WSA-Enlil-SEPMOD modelling
chain and four sets of input parameters, forming a "mini-ensemble". We validate
our results using in-situ observations at six locations, including Earth and
Mars. We find that, despite some limitations arising from the models'
architecture and assumptions, CMEs and shock-accelerated SEPs can be reasonably
studied and forecast in real time at least out to several tens of degrees away
from the eruption site using the prediction tools employed here.


title: TubeDETR: Spatio-Temporal Video Grounding with Transformers

abstract:
  We consider the problem of localizing a spatio-temporal tube in a video
corresponding to a given text query. This is a challenging task that requires
the joint and efficient modeling of temporal, spatial and multi-modal
interactions. To address this task, we propose TubeDETR, a transformer-based
architecture inspired by the recent success of such models for text-conditioned
object detection. Our model notably includes: (i) an efficient video and text
encoder that models spatial multi-modal interactions over sparsely sampled
frames and (ii) a space-time decoder that jointly performs spatio-temporal
localization. We demonstrate the advantage of our proposed components through
an extensive ablation study. We also evaluate our full approach on the
spatio-temporal video grounding task and demonstrate improvements over the
state of the art on the challenging VidSTG and HC-STVG benchmarks. Code and
trained models are publicly available at
https://antoyang.github.io/tubedetr.html.


title:
Bloch-Beilinson conjectures for Hecke characters and Eisenstein
  cohomology of Picard surfaces

abstract:
  We consider certain families of Hecke characters $\phi$ over a quadratic
imaginary field $F$. The order of vanishing of the $L$-function $L(\phi,s)$ at
the central point $s=-1$, according to the Beilinson conjectures, should be
equal to the dimension of the space of extensions of the Tate motive
$\mathbb{Q}(1)$ by the motive associated with $\phi$. In this article,
candidates for the corresponding extensions of Hodge structure are constructed,
under the assumptions that the sign of the functional equation of $L(\phi,s)$
is $-1$ and that $L^\prime(\phi,-1) \neq 0$. This is achieved by means of the
cohomology of variations of Hodge structures over Picard modular surfaces
attached to $F$ and Harder's theory of Eisenstein cohomology. Moreover, we
provide a criterion for the non-triviality of these extensions, based on the
non-vanishing of a height pairing that we define and study.


title:
The Dirichlet problem for degenerate fully nonlinear elliptic equations
  on Riemannian manifolds

abstract:
  We derive the existence of $C^{1,1}$-solutions to the Dirichlet problem for
degenerate fully nonlinear elliptic equations on Riemannian manifolds under
appropriate assumptions.


title: Weakly supervised causal representation learning

abstract:
  Learning high-level causal representations together with a causal model from
unstructured low-level data such as pixels is impossible from observational
data alone. We prove under mild assumptions that this representation is
identifiable in a weakly supervised setting. This requires a dataset with
paired samples before and after random, unknown interventions, but no further
labels. Finally, we show that we can infer the representation and causal graph
reliably in a simple synthetic domain using a variational autoencoder with a
structural causal model as prior.


title:
Accelerated Performance and Accelerated Learning with Discrete-Time
  High-Order Tuners

abstract:
  We consider two high-order tuners that have been shown to have accelerated
performance, one based on Polyak's heavy ball method and another based on
Nesterov's acceleration method. We show that parameter estimates are bounded
and converge to the true values exponentially fast when the regressors are
persistently exciting. Simulation results corroborate the accelerated
performance and accelerated learning properties of these high-order tuners in
comparison to algorithms based on normalized gradient descent.


title: Self-dual Hadamard bent sequences

abstract:
  A new notion of bent sequence related to Hadamard matrices was introduced
recently, motivated by a security application ( Sol\'e et al, 2021). We study
the self dual class in length at most $196.$ We use three competing methods of
generation: Exhaustion, Linear Algebra and Groebner bases. Regular Hadamard
matrices and Bush-type Hadamard matrices provide many examples. We conjecture
that if $v$ is an even perfect square, a self-dual bent sequence of length $v$
always exist. We introduce the strong automorphism group of Hadamard matrices,
which acts on their associated self-dual bent sequences. We give an efficient
algorithm to compute that group.


title:
Classification of gamma-ray targets for velocity-dependent and
  subhalo-boosted dark-matter annihilation

abstract:
  Gamma-ray observations have long been used to constrain the properties of
dark matter (DM), with a strong focus on weakly interacting massive particles
annihilating through velocity-independent processes. However, in the absence of
clear-cut observational evidence for the simplest candidates, the interest of
the community in more complex DM scenarios involving a velocity-dependent
cross-section has been growing steadily over the past few years. We present the
first systematic study of velocity-dependent DM annihilation (in particular
$p$-wave annihilation and Sommerfeld enhancement) in a variety of astrophysical
objects, not only including the well-studied Milky Way dwarf satellite
galaxies, but nearby dwarf irregular galaxies and local galaxy clusters as
well. Particular attention is given to the interplay between velocity
dependence and DM halo substructure. Uncertainties related to halo mass,
phase-space and substructure modelling are also discussed in this
velocity-dependent context. We show that, for $s$-wave annihilation, extremely
large subhalo boost factors are to be expected, up to $10^{11}$ in clusters and
up to $10^6-10^7$ in dwarf galaxies where subhalos are usually assumed not to
play an important role. Boost factors for $p$-wave annihilation are smaller but
can still reach $10^3$ in clusters. The angular extension of the DM signal is
also significantly impacted, with e.g. the cluster typical emission radius
increasing by a factor of order 10 in the $s$-wave case. We also compute the
signal contrast of the objects in our sample with respect to annihilation
happening in the Milky Way halo. Overall, we find that the hierarchy between
the brightest considered targets depends on the specific details of the assumed
particle-physics model.


title: Mixed state representability of entropy-density pairs

abstract:
  In this note, we show the representability of density-entropy pairs with
canonical and grand-canonical states, and we provide bounds on the kinetic
energy of the representing states.


title:
Reliability and Validity of the Polar V800 Sports Watch for Estimating
  Vertical Jump Height

abstract:
  This study aimed to assess the reliability and validity of the Polar V800 to
measure vertical jump height. Twenty-two physically active healthy men (age:
22.89 +- 4.23 years; body mass: 70.74 +- 8.04 kg; height: 1.74 +- 0.76 m) were
recruited for the study. The reliability was evaluated by comparing
measurements acquired by the Polar V800 in two identical testing sessions one
week apart. Validity was assessed by comparing measurements simultaneously
obtained using a force platform (gold standard), high-speed camera and the
Polar V800 during squat jump (SJ) and countermovement jump (CMJ) tests. In the
test-retest reliability, high intraclass correlation coefficients (ICCs) were
observed (mean: 0.90, SJ and CMJ) in the Polar V800. There was no significant
systematic bias +- random errors (p > 0.05) between test-retest. Low
coefficients of variation (<5%) were detected in both jumps in the Polar V800.
In the validity assessment, similar jump height was detected among devices (p >
0.05). There was almost perfect agreement between the Polar V800 compared to a
force platform for the SJ and CMJ tests (Mean ICCs = 0.95; no systematic bias
+- random errors in SJ mean: -0.38 +- 2.10 cm, p > 0.05). Mean ICC between the
Polar V800 versus high-speed camera was 0.91 for the SJ and CMJ tests, however,
a significant systematic bias +- random error (0.97 +- 2.60 cm; p = 0.01) was
detected in CMJ test. The Polar V800 offers valid, compared to force platform,
and reliable information about vertical jump height performance in physically
active healthy young men.


title: 100 years of mathematical cosmology: Models, theories, and problems

abstract:
  An elementary survey of mathematical cosmology is presented. We cover certain
key ideas and developments in a qualitative way, from the time of the Einstein
static universe in 1917 until today. We divide our presentation into four main
parts, the first part containing important cosmologies discovered until 1960.
The second period (1960-80) contains discussions of geometric extensions of the
standard cosmology, singularities, chaotic behaviour, and the initial input of
particle physics ideas into cosmology. Our survey for the third period
(1980-2000) continues with brief descriptions of the main ideas of inflation,
the multiverse, quantum, Kaluza-Klein, and string cosmologies, wormholes and
baby universes, cosmological stability, and modified gravity. The last period
which ends today includes various more advanced topics such as M-theoretic
cosmology, braneworlds, the landscape, topological issues, the measure problem,
genericity, dynamical singularities, and dark energy. We emphasize certain
threads that run throughout the whole period of development of theoretical
cosmology and underline their importance in the overall structure of the field.
We end this outline with an inclusion of the abstracts of all papers
contributed to the Philosophical Transactions of the Royal Society A, Theme
Issue `The Future of Mathematical Cosmology'.

categories: physics.hist-ph astro-ph.CO gr-qc hep-th


title:
Accounting for iron-related off-target binding effects of 18F-AV1451 PET
  in the evaluation of cognition and microstructure in APOE-e4+ MCI

abstract:
  The pathology of Alzheimer's disease (AD) and mild cognitive impairment (MCI)
is characterized by the presence of beta-amyloid extracellular plaques and
neurofibrillary tangles containing hyper-phosphorylated tau. Individuals
carrying the apolipoprotein E-e4 (APOE-e4) allele are at increased risk of
cognitive decline and developing AD pathology. The development of positron
emission tomography (PET) radioligands sensitive to tau neurofibrillary
tangles, such as 18F-AV1451, has allowed for visualization and assessment of AD
pathology in vivo. The radioligand used in 18F-AV1451 binds with iron in
addition to tau neurofibrillary tangles. We employ multimodal neuroimaging
analyses, combining iron-sensitive measures from MRI with 18F-AV1451 PET, to
examine off-target binding effects in cohorts of 20 APOE-e4 negative, 20
APOE-e4 positive MCI, and 29 control participants. Increased tau pathology,
after controlling for tissue susceptibility, was found in the temporal lobe and
hippocampus of APOE-e4+ MCI participants as compared to APOE-e4 negative MCI
and control participants. Tau pathology in the hippocampus was significantly
related to memory, but only in APOE-e4+ participants. Correlations between
hippocampal 18F-AV1451 PET uptake and cognitive correlations did not
significantly differ when correcting for the influence of iron on 18F-AV1451
PET signal. However, controlling for susceptibility was found to influence
correlations between tau-PET uptake and diffusion metrics and the change in
this interaction may be due to the influence of iron on diffusivity. Taken
together, these results suggest that iron does not need to be accounted for in
group comparisons of tau-PET uptake or correlations between cognitive measures
and tau-PET SUVR. However, iron should be taken into account in correlations
between diffusion measures and tau-PET uptake.


title: Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs

abstract:
  In this work, we study the holographic entanglement entropy of two
dimensional $T\bar{T}$-deformed conformal field theory. We compute the
correction due to the deformation up to the leading order of the deformation
parameter in the framework of New massive gravity, General minimal massive
gravity, and Exotic general massive gravity. We also apply Song's prescription
to obtain the entanglement entropy for deformed theories. In each cases, we
find agreement between the results.


title: Near-Optimal Weighted Matrix Completion

abstract:
  Recent work in the matrix completion literature has shown that prior
knowledge of a matrix's row and column spaces can be successfully incorporated
into reconstruction programs to substantially benefit matrix recovery. This
paper proposes a general methodology related to many of these approaches, while
introducing novel methods that exploit matrix structure to severely reduce the
sampling complexity. The main result shows that a family of weighted nuclear
norm minimization programs incorporating a $\gamma r$-dimensional subspace of
$n\times n$ matrices (where $1 \leq \gamma \leq n$) allow accurate
approximation of a rank $r$ matrix lying in the subspace from a near-optimal
number of randomly observed entries (within a logarithmic factor of $\gamma r
\log(n))$. The result is robust, where the error is proportional to measurement
noise, applies to full rank matrices, and reflects degraded output when
erroneous subspaces are incorporated. Experiments are presented to explore and
compare several of the weighted approaches numerically.


title: Potential Theory on Gromov Hyperbolic Spaces

abstract:
  Gromov hyperbolic spaces have become an essential concept in geometry,
topology and group theory. Here we extend Ancona's potential theory on Gromov
hyperbolic manifolds and graphs of bounded geometry to a large class of
Schr\"odinger operators on Gromov hyperbolic metric measure spaces, unifying
these settings in a common framework ready for applications to singular spaces
such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack
inequalities and a complete classification of positive harmonic functions in
terms of the Martin boundary which is identified with the geometric Gromov
boundary.


title:
Operational regimes of lasers based on gain media with a large Raman
  scattering cross-section

abstract:
  We report on unusual regimes of operation of a laser with a gain medium with
a large Raman scattering cross-section, which is often inherent in new types of
gain media such as colloidal and epitaxial quantum dots and perovskite
materials. These media are characterized by a strong electron-phonon coupling.
Using the Fr\"ohlich Hamiltonian to describe the electron-phonon coupling in
such media, we analyze the operation of the system above the lasing threshold.
We show that below a critical value of the Fr\"ohlich constant, the laser can
only operate in the conventional regime: namely, there are coherent cavity
photons but no coherent phonons. Above the critical value, a new pump rate
threshold appears. Above this threshold, either joint self-oscillations of
coherent phonons in the gain medium and photons in a cavity or a chaotic regime
are established. We also find a range of the values of the Fr\"ohlich constant,
the pump rate, and the resonator eigenfrequency, in which more than one
dynamical regime of the system is stable. In this case the laser dynamics is
determined by the initial values of the resonator field, the active medium
polarization, the population inversion, and phonon amplitude.


title:
Analytic Solutions of Scalar Field Cosmology, Mathematical Structures
  for Early Inflation and Late Time Accelerated Expansion

abstract:
  We study the most general cosmological model with real scalar field which is
minimally coupled to gravity. Our calculations are based on
Friedmann-Lemaitre-Robertson-Walker (FLRW) background metric. Field equations
consist of three differential equations. We switch independent variable from
time to scale factor by change of variable $\dot{a}/a=H(a)$. Thus a new set of
differential equations are analytically solvable with known methods. We
formulate Hubble function, the scalar field, potential and energy density when
one of them is given in the most general form. $a(t)$ can be explicitly found
as long as methods of integration techniques are available. We investigate the
dynamics of the universe at early times as well as at late times in light of
these formulas. We find mathematical machinery which turns on and turns off
early accelerated expansion. On the other hand late time accelerated expansion
is explained by cosmic domain walls. We have compared our results with recent
observations of type Ia supernovae by considering the Hubble tension and
absolute magnitude tension. Eighty-nine percent of present universe may consist
of domain walls while rest is matter.


title: Domain walls seeding the electroweak phase transition

abstract:
  Topological defects can act as local impurities that seed cosmological phase
transitions. In this paper we study the case of domain walls, and how they can
affect the electroweak phase transition in the Standard Model extended with a
$Z_2$-odd scalar singlet. When the transition is two-step, the early breaking
of the $Z_2$ symmetry implies the formation of domain walls which can then act
as nucleation sites for the second step. We develop a method based on
dimensional reduction to calculate the rate of the catalyzed phase transition
within the 3d theory on the domain wall surface. By comparison with the
standard homogeneous rate, we conclude that the seeded phase transition is
generically faster and it ultimately determines the way the phase transition is
completed. We comment on the phenomenological implications for gravitational
waves and baryogenesis.


title:
Distributed Optimization of Average Consensus Containment with Multiple
  Stationary Leaders

abstract:
  In this paper, we consider the problem of containment control of multi-agent
systems with multiple stationary leaders, interacting over a directed network.
While, containment control refers to just ensuring that the follower agents
reach the convex hull of the leaders states, we focus on the problem where the
followers achieve a consensus to the average values of the leaders states. We
propose an algorithm that can be implemented in a distributed manner to achieve
the above consensus among followers. Next we optimize the convergence rate of
the followers to the average consensus by proper choice of weights for the
interaction graph. This optimization is also performed in a distributed manner
using Alternating Direction Method of Multipliers (ADMM). Finally, we
complement our results by illustrating them with numerical examples.


title: AI Gone Astray: Technical Supplement

abstract:
  This study is a technical supplement to "AI gone astray: How subtle shifts in
patient data send popular algorithms reeling, undermining patient safety." from
STAT News, which investigates the effect of time drift on clinically deployed
machine learning models. We use MIMIC-IV, a publicly available dataset, to
train models that replicate commercial approaches by Dascena and Epic to
predict the onset of sepsis, a deadly and yet treatable condition. We observe
some of these models degrade overtime; most notably an RNN built on Epic
features degrades from a 0.729 AUC to a 0.525 AUC over a decade, leading us to
investigate technical and clinical drift as root causes of this performance
drop.


title:
Numerical convergence and stability analysis for a nonlinear
  mathematical model of prostate cancer

abstract:
  The main target of this paper is to present an efficient method to solve a
nonlinear free boundary mathematical model of prostate tumor. This model
consists of two parabolics, one elliptic and one ordinary differential
equations that are coupled together and describe the growth of a prostate
tumor. We start our discussion by using the front fixing method to fix the free
domain. Then, after employing a nonclassical finite difference and the
collocation methods on this model, their stability and convergence are proved
analytically. Finally, some numerical results are considered to show the
efficiency of the mentioned methods.


title:
A New Diffusive Representation for Fractional Derivatives, Part II:
  Convergence Analysis of the Numerical Scheme

abstract:
  Recently, we have proposed a new diffusive representation for fractional
derivatives and, based on this representation, suggested an algorithm for their
numerical computation. From the construction of the algorithm, it is
immediately evident that the method is fast and memory efficient. Moreover, the
method's design is such that good convergence properties may be expected. This
paper here starts a systematic investigation of these convergence properties.


title:
Explicitising The Implicit Intrepretability of Deep Neural Networks Via
  Duality

abstract:
  Recent work by Lakshminarayanan and Singh [2020] provided a dual view for
fully connected deep neural networks (DNNs) with rectified linear units (ReLU).
It was shown that (i) the information in the gates is analytically
characterised by a kernel called the neural path kernel (NPK) and (ii) most
critical information is learnt in the gates, in that, given the learnt gates,
the weights can be retrained from scratch without significant loss in
performance. Using the dual view, in this paper, we rethink the conventional
interpretations of DNNs thereby explicitsing the implicit interpretability of
DNNs. Towards this, we first show new theoretical properties namely rotational
invariance and ensemble structure of the NPK in the presence of convolutional
layers and skip connections respectively. Our theory leads to two surprising
empirical results that challenge conventional wisdom: (i) the weights can be
trained even with a constant 1 input, (ii) the gating masks can be shuffled,
without any significant loss in performance. These results motivate a novel
class of networks which we call deep linearly gated networks (DLGNs). DLGNs
using the phenomenon of dual lifting pave way to more direct and simpler
interpretation of DNNs as opposed to conventional interpretations. We show via
extensive experiments on CIFAR-10 and CIFAR-100 that these DLGNs lead to much
better interpretability-accuracy tradeoff.


title: Effective Locality in the pure gluon sector

abstract:
  About twelve years ago the use of standard functional manipulations was
demonstrated to imply an unexpected property satisfied by the fermionic Green's
functions of $QCD$. This non-perturbative phenomenon is dubbed Effective
Locality. In a much simpler way than in $QCD$, the most remarkable and
intriguing aspects of Effective Locality are presented here, in the Yang--Mills
theory on Minkowski spacetime.


title: TSUBASA: Climate Network Construction on Historical and Real-Time Data

abstract:
  A climate network represents the global climate system by the interactions of
a set of anomaly time-series. Network science has been applied on climate data
to study the dynamics of a climate network. The core task and first step to
enable interactive network science on climate data is the efficient
construction and update of a climate network on user-defined time-windows. We
present TSUBASA, an algorithm for the efficient construction of climate
networks based on the exact calculation of Pearsons correlation of large
time-series. By pre-computing simple and low-overhead statistics, TSUBASA can
efficiently compute the exact pairwise correlation of time-series on arbitrary
time windows at query time. For real-time data, TSUBASA proposes a fast and
incremental way of updating a network at interactive speed. Our experiments
show that TSUBASA is faster than approximate solutions at least one order of
magnitude for both historical and real-time data and outperforms a baseline for
time-series correlation calculation up to two orders of magnitude.


title: Time-reversal-symmetry Breaking in the Superconducting State of ScS

abstract:
  We have studied the electronic properties of ScS, a transition-metal
monochalcogenide with rocksalt crystal structure, using magnetization, specific
heat, transport, and muon spin rotation/relaxation ($\mu$SR) measurements. All
measurements confirm the bulk superconducting in ScS with a transition
temperature of $T_{C}$ = 5.1(5) K. Specific heat together with transverse-field
$\mu$SR measurements indicate a full gap, while our zero-field $\mu$SR study
reveals the presence of spontaneous static or quasi-static magnetic fields
emerging when entering the superconducting state. We discuss various possible
microscopic origins of the observed time-reversal-symmetry breaking. As none of
them can be readily reconciled with a conventional pairing mechanism, this
introduces ScS as a novel candidate material for unconventional
superconductivity.


title:
A deep investigation of two poorly studied open clusters Haffner 22 and
  Melotte 71 in Gaia era

abstract:
  This paper presents a deep investigation of two open clusters, Haffner 22 and
Melotte 71, using astrometric and photometric data from Gaia EDR3. We
identified 382 and 597 most probable cluster members with membership
probability higher than 50 percent. Mean proper motion in RA and DEC are
estimated as -1.63 and 2.889 respectively for Haffner 22 and -2.398 and 4.210
for Melotte 71. A comparison of observed CMDs with theoretical isochrones leads
to an age of 2.25 and 1.27 Gyr for these clusters. The distances 2.88 and 2.28
kpc based on parallax are comparable with the values derived by isochrone
fitting method. Five and four blue straggler stars are identified as cluster
members in Haffner 22 and Melotte 71 respectively. Based on the relative number
of high velocity (binary) and single stars, we inferred binary fractions for
both clusters. We found binary content is larger in core region. Mass function
slope is in good agreement with the Salpeter's value while it is flat for
Haffner 22. Evidence for the existence of mass segregation effect is observed
in both clusters. Using the Galactic potential models, Galactic orbits are
derived, indicating that both clusters follow a circular path around the
Galactic center, evolving slowly.


title: Ordered community detection in directed networks

abstract:
  We develop a method to infer community structure in directed networks where
the groups are ordered in a latent one-dimensional hierarchy that determines
the preferred edge direction. Our nonparametric Bayesian approach is based on a
modification of the stochastic block model (SBM), which can take advantage of
rank alignment and coherence to produce parsimonious descriptions of networks
that combine ordered hierarchies with arbitrary mixing patterns between groups.
Since our model also includes directed degree correction, we can use it to
distinguish non-local hierarchical structure from local in- and out-degree
imbalance -- thus removing a source of conflation present in most ranking
methods. We also demonstrate how we can reliably compare with the results
obtained with the unordered SBM variant to determine whether a hierarchical
ordering is statistically warranted in the first place. We illustrate the
application of our method on a wide variety of empirical networks across
several domains.

categories: cs.SI physics.data-an physics.soc-ph stat.ME


title: Hook formulae from Segre-MacPherson classes

abstract:
  Nakada's colored hook formula is a vast generalization of many important
formulae in combinatorics, such as the classical hook length formula and the
Peterson's formula for the number of reduced expressions of minuscule Weyl
group elements. In this paper, we utilize cohomological properties of
Segre-MacPherson classes of Schubert cells and varieties to prove a
generalization of a cohomological version of Nakada's formula, in terms of
smoothness properties of Schubert varieties. A key ingredient in the proof is
the study of a decorated version of the Bruhat graph. Summing over weighted
paths of this graph give the terms in the generalized Nakada's formula, and
also provide algorithms to calculate structure constants of multiplications of
Segre-MacPherson classes of Schubert cells.


title: Convergence of gradient descent for deep neural networks

abstract:
  Optimization by gradient descent has been one of main drivers of the "deep
learning revolution". Yet, despite some recent progress for extremely wide
networks, it remains an open problem to understand why gradient descent often
converges to global minima when training deep neural networks. This article
presents a new criterion for convergence of gradient descent to a global
minimum, which is provably more powerful than the best available criteria from
the literature, namely, the Lojasiewicz inequality and its generalizations.
This criterion is used to show that gradient descent with proper initialization
converges to a global minimum when training any feedforward neural network with
smooth and strictly increasing activation functions, provided that the input
dimension is greater than or equal to the number of data points.


title:
Perfectly Accurate Membership Inference by a Dishonest Central Server in
  Federated Learning

abstract:
  Federated Learning is expected to provide strong privacy guarantees, as only
gradients or model parameters but no plain text training data is ever exchanged
either between the clients or between the clients and the central server. In
this paper, we challenge this claim by introducing a simple but still very
effective membership inference attack algorithm, which relies only on a single
training step. In contrast to the popular honest-but-curious model, we
investigate a framework with a dishonest central server. Our strategy is
applicable to models with ReLU activations and uses the properties of this
activation function to achieve perfect accuracy. Empirical evaluation on visual
classification tasks with MNIST, CIFAR10, CIFAR100 and CelebA datasets show
that our method provides perfect accuracy in identifying one sample in a
training set with thousands of samples. Occasional failures of our method lead
us to discover duplicate images in the CIFAR100 and CelebA datasets.


title:
Towards Interpretable Deep Reinforcement Learning Models via Inverse
  Reinforcement Learning

abstract:
  Artificial intelligence, particularly through recent advancements in deep
learning, has achieved exceptional performances in many tasks in fields such as
natural language processing and computer vision. In addition to desirable
evaluation metrics, a high level of interpretability is often required for
these models to be reliably utilized. Therefore, explanations that offer
insight into the process by which a model maps its inputs onto its outputs are
much sought-after. Unfortunately, current black box nature of machine learning
models is still an unresolved issue and this very nature prevents researchers
from learning and providing explicative descriptions for a model's behavior and
final predictions. In this work, we propose a novel framework utilizing
Adversarial Inverse Reinforcement Learning that can provide global explanations
for decisions made by a Reinforcement Learning model and capture intuitive
tendencies that the model follows by summarizing the model's decision-making
process.


title:
Can in-home laboratories foster learning, self-efficacy, and motivation
  during the COVID-19 pandemic? -- A case study in two engineering programs

abstract:
  The COVID-19 pandemic has represented a challenge for higher education in
terms to provide quality education despite the lockdown periods, the
transformation of the in-person classes to virtual classes, and the
demotivation and anxiety that are experimented by the students. Because the
basis of engineering is the experimentation through hands-on activities and
learning by doing, the lockdown periods and the temporary suspension of the
in-person classes and laboratories have meant a problem for educators that try
to teach and motivate the students despite the situation. In this context, this
study presents an educational methodology based on Problem-Based Learning (PBL)
and in-home laboratories in engineering. The methodology was carried out in two
phases during 2020, in the academic programs of Industrial Engineering and
Technology in Electronics with (n=44) students. The in-home laboratories were
sent to the students as part of "kits" with the devices needed in each subject.
Besides, due to the difficulties in monitoring the learning process, the
students made videos and blogs as a strategy to reinforce their learning and
evidence the progress in the courses. The outcomes of the methodology show
mainly the following points: (1) An improvement of the academic performance and
learning of the students in the courses. (2) A positive influence of the usage
of in-home laboratories in motivation, self-efficacy, and reduction of anxiety.
(3) Positive correlations between the usage of in-home laboratories, the blogs
and videos, and the teacher's feedback for learning, motivation, and
self-efficacy. Thus, these results evidence that other alternatives that gather
the cognitive and affective learning domains can emerge from engineering to
deal with the educational problems produced by the crisis periods.


title:
Social adaptive behavior and oscillatory prevalence in an epidemic model
  on evolving random geometric graphs

abstract:
  Our recent experience with COVID19 amply shows that spatial effects like
mobility and average interpersonal distance are very important in deciding the
outcome of an epidemic dynamics. Spatial connectivity structure of a population
is usually modelled via Random Geometric Graphs which are networks generated
from spatially distributed components where connections between components are
made based on a distance-dependent probability measure. Structural and
dynamical aspects of such graphs are important in describing processes with a
spatial dependence such as the spread of an airborne disease. In this work,
using a simple computational model of an epidemic, we investigate how spatial
factors like average separation between individuals and their mobility affect
the spread of a disease. We show that such spatial factors can give rise to
oscillatory prevalence in a society of adaptive individuals. We also show that
delays in executing non-pharmaceutical spatial mitigation strategies can
accentuate oscillatory prevalence and can have non-monotonic effects on the
peak prevalence. In both cases, we characterize the effects of different
parameters on the prevalence of the disease and peak infection and obtain
threshold values.


title: Crack-path selection in phase-field models for brittle fracture

abstract:
  This work presents a critical overview of the effects of different aspects of
model formulation on crack path selection in quasi-static phase field fracture.
We consider different evolution methods, mechanics formulations, fracture
dissipation energy formulations, and forms of the irreversibility condition.
The different model variants are implemented with common numerical methods
based on staggered solution of the phase-field and mechanics sub-problems via
FFT-based solvers. These methods mix standard approaches with novel elements,
such as the use of bound-constrained conjugate gradients for the phase field
sub-problem and a heuristic method for near-equilibrium evolution. We examine
differences in crack paths between model variants in simple model systems and
microstructures with randomly heterogeneous Young's modulus. Our results
indicate that near-equilibrium evolution methods are preferable for
quasi-static fracture of heterogeneous microstructures compared to minimization
and time-dependent methods. In examining mechanics formulations, we find
distinct effects of crack driving force and the model for contact implicit in
phase field fracture. Our results favor the use of a strain-spectral
decomposition for the crack driving force but not the contact model.
Irreversibility condition and fracture dissipation energy formulation were also
found to affect crack path selection, but systematic effects were difficult to
deduce due to the overall sensitivity of crack selection within the
heterogeneous microstructures. Our findings support the use of the AT1 model
over the AT2 model and irreversibility of the phase field within a crack set
rather than the entire domain. Sensitivity to these differences in formulation
was reduced but not eliminated by reducing the crack width parameter $\ell$
relative to the size scale of the random microstructures.


title: Magnetic structure and properties of a vanthoffite mineral Na6Mn(SO4)4

abstract:
  A detailed analysis of the magnetic properties of a vanthoffite type mineral
Na6Mn(SO4)4 basedon dc magnetization, low temperature neutron powder
diffraction and theoretical calculations is reported. The mineral crystallizes
in a monoclinic system with space group P21/c, where MnO6 octahedra are linked
via SO4 tetrahedra. This gives rise to super-exchange interaction between two
Mn2+ ions mediated by two nonmagnetic bridging anions and leads to an
antiferromagnetic ordering below 3 K. The magnetic structure derived from
neutron powder diffraction at 1.7 K depicts an antiferromagnetic spin
arrangement in the bc plane of the crystal. The magnetic properties are
modelled by numerical calculations using exact diagonalization technique, which
fits the experimental results and provides antiferromagnetic ground state of
Na6Mn(SO4)4.


title: Factorials and Legendre's three-square theorem: II

abstract:
  Let $\bar{S}$ denote the set of integers $n$ such that $n!$ cannot be written
as a sum of three squares. Let $\bar{S}(n)$ denote $\bar{S} \cap [1, n]$. We
establish an exact formula for $\bar{S}(2^k)$ and show that $\bar{S}(n) = 1/8*n
+ \mathcal{O}(\sqrt{n})$. We also list the lengths of gaps appearing in
$\bar{S}$. We make use of the software package Walnut to establish these
results.


title: Remember to correct the bias when using deep learning for regression!

abstract:
  When training deep learning models for least-squares regression, we cannot
expect that the training error residuals of the final model, selected after a
fixed training time or based on performance on a hold-out data set, sum to
zero. This can introduce a systematic error that accumulates if we are
interested in the total aggregated performance over many data points. We
suggest to adjust the bias of the machine learning model after training as a
default postprocessing step, which efficiently solves the problem. The
severeness of the error accumulation and the effectiveness of the bias
correction is demonstrated in exemplary experiments.


title: On sets with unit Hausdorff density in homogeneous groups

abstract:
  It is a longstanding conjecture that given a subset $E$ of a metric space, if
$E$ has finite Hausdorff measure in dimension $\alpha\ge 0$ and
$\mathscr{H}^\alpha\llcorner E$ has unit density almost everywhere, then $E$ is
an $\alpha$-rectifiable set. We prove this conjecture under the assumption that
the ambient metric space is a homogeneous group with a smooth-box norm.


title:
Multiple phonon modes in Feynman path-integral variational polaron
  mobility

abstract:
  The Feynman path-integral variational solution to the polaron problem
\cite{Feynman1955}, along with the associated FHIP linear-response mobility
theory \cite{Feynman1962}, provides a computationally amenable method to
predict the frequency-resolved temperature-dependent charge-carrier mobility,
and other experimental observables in polar semi-conductors. We show that the
FHIP mobility theory is capable of demonstrating non-Drude transport behaviour,
and provides good agreement with the recent diagrammatic Monte-Carlo mobility
simulations of Mishchenko et al. \cite{Mishchenko2019} for the abstract
Fr\"ohlich Hamiltonian. We extend this method to multiple variational
parameters in the model action, and to multiple phonon modes in the true
action. This enables a slightly better variational solution, as inferred from
the resulting energy. We carry forward this complexity into the mobility
theory, where it enables richer structure in the frequency and temperature
dependent mobility, due to the different phonon modes activating at different
energies.


title:
Time-Delayed Reservoir Computing Based on Dual-Waveband Quantum-Dot
  Spin-Polarized Vertical Cavity Surface-Emitting Laser

abstract:
  In this work we present numerical results concerning a time-delayed reservoir
computing scheme, where its single nonlinear node, is a Quantum-Dot spin
polarized Vertical Cavity Surface-Emitting Laser (QD s-VCSEL). The proposed
photonic neuromorphic scheme, exploits the complex temporal dynamics of
multiple energy states present in quantum dot materials and uses emission from
two discrete wavebands and two polarization states, so as to enhance
computational efficiency. The benchmark task used for this architecture, is the
equalization of a distorted 25Gbaud PAM-4 signal after 50Km of transmission at
1550nm. Results confirm that although typical ground-state emitting quantum-dot
nodes offer limited performance, due to bandwidth limitations; by exploiting
dual emission, we achieved a one-hundred-fold improvement in bit-error rate.
This performance boost can pave the way for the infiltration of quantum-dot
based devices in high-speed demanding neuromorphic driven applications.


title:
Zero Shot Crosslingual Eye-Tracking Data Prediction using Multilingual
  Transformer Models

abstract:
  Eye tracking data during reading is a useful source of information to
understand the cognitive processes that take place during language
comprehension processes. Different languages account for different brain
triggers , however there seems to be some uniform indicators. In this paper, we
describe our submission to the CMCL 2022 shared task on predicting human
reading patterns for multi-lingual dataset. Our model uses text representations
from transformers and some hand engineered features with a regression layer on
top to predict statistical measures of mean and standard deviation for 2 main
eye-tracking features. We train an end to end model to extract meaningful
information from different languages and test our model on two seperate
datasets. We compare different transformer models and show ablation studies
affecting model performance. Our final submission ranked 4th place for
SubTask-1 and 1st place for SubTask-2 for the shared task.


title: ConceptEvo: Interpreting Concept Evolution in Deep Learning Training

abstract:
  Deep neural networks (DNNs) have been widely used for decision making,
prompting a surge of interest in interpreting how these complex models work.
Recent literature on DNN interpretation has revolved around already-trained
models; however, much less research focuses on interpreting how the models
evolve as they are trained. Interpreting model evolution is crucial to monitor
network training and can aid proactive decisions about necessary interventions.
In this work, we present ConceptEvo, a general interpretation framework for
DNNs that reveals the inception and evolution of detected concepts during
training. Through a large-scale human evaluation with 260 participants and
quantitative experiments, we show that ConceptEvo discovers evolution across
different models that are meaningful to humans, helpful for early-training
intervention decisions, and crucial to the prediction for a given class.


title:
Differentially Private All-Pairs Shortest Path Distances: Improved
  Algorithms and Lower Bounds

abstract:
  We study the problem of releasing the weights of all-pair shortest paths in a
weighted undirected graph with differential privacy (DP). In this setting, the
underlying graph is fixed and two graphs are neighbors if their edge weights
differ by at most $1$ in the $\ell_1$-distance. We give an $\epsilon$-DP
algorithm with additive error $\tilde{O}(n^{2/3} / \epsilon)$ and an
$(\epsilon, \delta)$-DP algorithm with additive error $\tilde{O}(\sqrt{n} /
\epsilon)$ where $n$ denotes the number of vertices. This positively answers a
question of Sealfon (PODS'16), who asked whether a $o(n)$-error algorithm
exists. We also show that an additive error of $\Omega(n^{1/6})$ is necessary
for any sufficiently small $\epsilon, \delta > 0$.
  Finally, we consider a relaxed setting where a multiplicative approximation
is allowed. We show that, with a multiplicative approximation factor $k$, %$2k
- 1$, the additive error can be reduced to $\tilde{O}\left(n^{1/2 + O(1/k)} /
\epsilon\right)$ in the $\epsilon$-DP case and $\tilde{O}(n^{1/3 + O(1/k)} /
\epsilon)$ in the $(\epsilon, \delta)$-DP case, respectively.


title:
A Coronal Mass Ejection and Magnetic Ejecta Observed In Situ by STEREO-A
  and Wind at 55$^\circ$ Angular Separation

abstract:
  We present an analysis of {\it in situ} and remote-sensing measurements of a
coronal mass ejection (CME) that erupted on 2021 February 20 and impacted both
the Solar TErrestrial RElations Observatory (STEREO)-A and the {\it Wind}
spacecraft, which were separated longitudinally by 55$^\circ$. Measurements on
2021 February 24 at both spacecraft are consistent with the passage of a
magnetic ejecta (ME), making this one of the widest reported multi-spacecraft
ME detections. The CME is associated with a low-inclined and wide filament
eruption from the Sun's southern hemisphere, which propagates between STEREO-A
and {\it Wind} around E34. At STEREO-A, the measurements indicate the passage
of a moderately fast ($\sim 425$~km\,s$^{-1}$) shock-driving ME, occurring 2--3
days after the end of a high speed stream (HSS). At {\it Wind}, the
measurements show a faster ($\sim 490$~km\,s$^{-1}$) and much shorter ME, not
preceded by a shock nor a sheath, and occurring inside the back portion of the
HSS. The ME orientation measured at both spacecraft is consistent with a
passage close to the legs of a curved flux rope. The short duration of the ME
observed at {\it Wind} and the difference in the suprathermal electron
pitch-angle data between the two spacecraft are the only results that do not
satisfy common expectations. We discuss the consequence of these measurements
on our understanding of the CME shape and extent and the lack of clear
signatures of the interaction between the CME and the HSS.


title:
A Sequential Quadratic Programming Approach to the Solution of Open-Loop
  Generalized Nash Equilibria

abstract:
  Dynamic games can be an effective approach to modeling interactive behavior
between multiple non-cooperative agents and they provide a theoretical
framework for simultaneous prediction and control in such scenarios. In this
work, we propose a numerical method for the solution of local generalized Nash
equilibria (GNE) for the class of open-loop general-sum dynamic games for
agents with nonlinear dynamics and constraints. In particular, we formulate a
sequential quadratic programming (SQP) approach which requires only the
solution of a single convex quadratic program at each iteration. Central to the
robustness of our approach is a nonmonotonic line search method and a novel
merit function for SQP step acceptance. We show that our method achieves linear
convergence in the neighborhood of local GNE and we derive an update rule for
the merit function which helps to improve convergence from a larger set of
initial conditions. We demonstrate the effectiveness of the algorithm in the
context of multi-car racing, where we show up to 6x improvement of success rate
when comparing against a state-of-the-art solution approach for dynamic games.


title:
A phase-field model for ferroelectrics with general kinetics. Part I:
  Model formulation

abstract:
  When subjected to electro-mechanical loading, ferroelectrics see their
polarization evolve through the nucleation and evolution of domains. Existing
mesoscale phase-field models for ferroelectrics are typically based on a
gradient-descent law for the evolution of the order parameter. While this
implicitly assumes that domain walls evolve with linear kinetics, experiments
instead indicate that domain wall kinetics is nonlinear. This, in turn, is an
important feature for the modeling of rate-dependent effects in polarization
switching. We propose a new multiple-phase-field model for ferroelectrics,
which permits domain wall motion with nonlinear kinetics, with applications in
other solid-solid phase transformation problems. By means of analytical
traveling-wave solutions, we characterize the interfacial properties (energy
and width) and the interface kinetics of straight domain walls, as furnished by
the general kinetics model, and compare them to those of the classical
Allen-Cahn model. We show that the proposed model propagates domain walls with
arbitrarily chosen nonlinear kinetic relations, which can be tuned to differ
for the different types of domain walls in accordance with experimental
evidence. In a companion paper, we implement numerically the general kinetics
model and characterize the evolution of curved walls and junction points for
multiple phases.


title:
Realization of the Topological Hopf Term in a Two-Dimensional Lattice
  Model

abstract:
  It is known that 2-dimensional spin systems acquires a topological Hopf term
by coupling to massless Dirac fermions whose dispersion has a single cone. But
it is challenging to realize the Hopf term in condensed matter physics due to
fermion-doubling. In this work we discuss a scenario to realize the Hopf term
in a lattice model. The key step is to design the coupling between the spins
and the Dirac fermions such that the topological term contributed by the two
cones do not cancel each other. A minimal model needs four fermion bands, thus
a honeycomb lattice with px and py orbitals on each site is a good candidate.
By utilizing the orbital status of the Dirac fermions, a {\theta} = 2{\pi} Hopf
term is successfully generated after integrating out the fermions. If the
fermions have a small gap m0, then {\theta} is no longer equal to 2{\pi}, but
under renormalization group it may flow to 2{\pi}.The ground state and the
physical response of a spin system having the Hopf term is discussed.


title:
On Uncertainty, Tempering, and Data Augmentation in Bayesian
  Classification

abstract:
  Aleatoric uncertainty captures the inherent randomness of the data, such as
measurement noise. In Bayesian regression, we often use a Gaussian observation
model, where we control the level of aleatoric uncertainty with a noise
variance parameter. By contrast, for Bayesian classification we use a
categorical distribution with no mechanism to represent our beliefs about
aleatoric uncertainty. Our work shows that explicitly accounting for aleatoric
uncertainty significantly improves the performance of Bayesian neural networks.
We note that many standard benchmarks, such as CIFAR, have essentially no
aleatoric uncertainty. Moreover, we show data augmentation in approximate
inference has the effect of softening the likelihood, leading to
underconfidence and profoundly misrepresenting our honest beliefs about
aleatoric uncertainty. Accordingly, we find that a cold posterior, tempered by
a power greater than one, often more honestly reflects our beliefs about
aleatoric uncertainty than no tempering -- providing an explicit link between
data augmentation and cold posteriors. We show that we can match or exceed the
performance of posterior tempering by using a Dirichlet observation model,
where we explicitly control the level of aleatoric uncertainty, without any
need for tempering.