title:
Quasi-Orthogonal Foliations of the Configuration Space: A Redundancy
  Resolution Approach at Position Level

abstract:
  High versatility and flexibility of robotic systems require kinematic
structures with many degrees of freedom. This usually renders the system
kinematically redundant, i.e., the main manipulation or interaction task does
not fully determine its maneuvers. Additional constraints or objectives are
required to solve the under-determined control and planning problems. The
state-of-the-art approaches arrange tasks in a hierarchy and decouple lower
from higher priority tasks on velocity or torque level. Velocities and torques
are elements of vector spaces. Thus the approaches are inherently based on
linear algebra tools. In this paper, we develop an approach to redundancy
resolution and decoupling on position level. That requires moving from vector
spaces and linear algebra to manifolds and differential geometry. We propose to
determine, another set of coordinate functions in addition to the task forward
kinematics. The Jacobian of those functions shall resemble the conditions known
from the linear algebra-based velocity- and torque-level decoupling to the best
extent possible. The approach provides a better insight into the topological
properties of robot kinematics and control problems, allowing a more global
geometric view. Quasi-decoupled coordinates can help to avoid or diminish some
practical and theoretical difficulties related to the classical projection
approaches at the cost of higher offline computational efforts. A condition for
the existence of these coordinates is derived. If the condition is not
satisfied, we still find approximate solutions by numerical optimization.
Finally, we show simulation results for both, trajectory tracking and classical
impedance control and validate the approach experimentally on a 7DoF robot.


title: Progress on stochastic analytic continuation of quantum Monte Carlo data

abstract:
  We report multipronged progress on the stochastic averaging approach to
numerical analytic continuation of quantum Monte Carlo data. With the sampled
spectrum parametrized with delta-functions in continuous frequency space, a
calculation of the configurational entropy lends support to a simple
goodness-of-fit criterion for the optimal sampling temperature. To further
investigate entropic effects, we compare spectra sampled in continuous
frequency with results of amplitudes sampled on a fixed frequency grid. We
demonstrate equivalences between sampling and optimizing spectral functions
with the maximum-entropy approach with different forms of the entropy. These
insights revise prevailing notions of the maximum-entropy method and its
relationship to stochastic analytic continuation. We further explore various
adjustable (optimized) constraints that allow sharp spectral features to be
resolved, in particular at the lower frequency edge. The constraints, e.g., the
location of the edge or the spectral weight of a quasi-particle peak, are
optimized using a statistical criterion. We show that this method can correctly
reproduce both narrow and broad quasi-particle peaks. We next introduce a
parametrization for more intricate spectral functions with sharp edges, e.g.,
power-law singularities. Tests with synthetic data as well as with real
simulation data for the spin-1/2 Heisenberg chain demonstrate that constrained
sampling methods can reproduce spectral functions with sharp edge features at
unprecedented fidelity. We present new results for S=1/2 Heisenberg 2-leg and
3-leg ladders to illustrate the ability of the methods to resolve spectral
features arising from both elementary and composite excitations. Finally, we
also propose how the methods developed here could be used as "pre processors"
for analytic continuation by machine learning.


title:
First moments of the nucleon transverse quark spin densities using
  lattice QCD

abstract:
  We present a calculation of the Mellin moments of the transverse quark spin
densities in the nucleon using lattice QCD. The densities are extracted from
the unpolarized and transversity generalized form factors extrapolated to the
continuum limit using three $N_f=2+1+1$ twisted mass fermion gauge ensembles
simulated with physical quark masses and spanning three lattice spacings. The
first moment of transversely polarized quarks in an unpolarized nucleon shows
an interesting distortion, which can be traced back to the sharp falloff of the
transversity generalized form factor $\bar{B}_{Tn0}(t)$. The isovector tensor
anomalous magnetic moment is determined to be $\kappa_T=1.051(94)$, which
confirms a negative and large Boer-Mulders function, $h_1^{\perp}$, in the
nucleon.


title:
Localized model reduction for nonlinear elliptic partial differential
  equations: localized training, partition of unity, and adaptive enrichment

abstract:
  We propose a component-based (CB) parametric model order reduction (pMOR)
formulation for parameterized {nonlinear} elliptic partial differential
equations (PDEs). CB-pMOR is designed to deal with large-scale problems for
which full-order solves are not affordable in a reasonable time frame or
parameters' variations induce topology changes that prevent the application of
monolithic pMOR techniques. We rely on the partition-of-unity method (PUM) to
devise global approximation spaces from local reduced spaces, and on Galerkin
projection to compute the global state estimate. We propose a randomized data
compression algorithm based on oversampling for the construction of the
components' reduced spaces: the approach exploits random boundary conditions of
controlled smoothness on the oversampling boundary. We further propose an
adaptive residual-based enrichment algorithm that exploits global reduced-order
solves on representative systems to update the local reduced spaces. We prove
exponential convergence of the enrichment procedure for linear coercive
problems; we further present numerical results for a two-dimensional nonlinear
diffusion problem to illustrate the many features of our proposal and
demonstrate its effectiveness.


title:
NetSentry: A Deep Learning Approach to Detecting Incipient Large-scale
  Network Attacks

abstract:
  Machine Learning (ML) techniques are increasingly adopted to tackle
ever-evolving high-profile network attacks, including DDoS, botnet, and
ransomware, due to their unique ability to extract complex patterns hidden in
data streams. These approaches are however routinely validated with data
collected in the same environment, and their performance degrades when deployed
in different network topologies and/or applied on previously unseen traffic, as
we uncover. This suggests malicious/benign behaviors are largely learned
superficially and ML-based Network Intrusion Detection System (NIDS) need
revisiting, to be effective in practice. In this paper we dive into the
mechanics of large-scale network attacks, with a view to understanding how to
use ML for Network Intrusion Detection (NID) in a principled way. We reveal
that, although cyberattacks vary significantly in terms of payloads, vectors
and targets, their early stages, which are critical to successful attack
outcomes, share many similarities and exhibit important temporal correlations.
Therefore, we treat NID as a time-sensitive task and propose NetSentry, perhaps
the first of its kind NIDS that builds on Bidirectional Asymmetric LSTM
(Bi-ALSTM), an original ensemble of sequential neural models, to detect network
threats before they spread. We cross-evaluate NetSentry using two practical
datasets, training on one and testing on the other, and demonstrate F1 score
gains above 33% over the state-of-the-art, as well as up to 3 times higher
rates of detecting attacks such as XSS and web bruteforce. Further, we put
forward a novel data augmentation technique that boosts the generalization
abilities of a broad range of supervised deep learning algorithms, leading to
average F1 score gains above 35%.


title: Single copy of the Ricci flow

abstract:
  The perturbative double copy is by now a highly established correspondence
between gravity and gauge theories. Non-perturbatively, information ranging
from classical solutions to topological quantities on both sides have been
related to each other via the double copy correspondence. In this paper, we add
another result, where we show that the single copy of the Ricci flow is the
Yang-Mills flow on the space of connections of a principal
$\text{U}(1)$-bundle.


title:
Trying to Outrun Causality with Machine Learning: Limitations of Model
  Explainability Techniques for Identifying Predictive Variables

abstract:
  Machine Learning explainability techniques have been proposed as a means of
`explaining' or interrogating a model in order to understand why a particular
decision or prediction has been made. Such an ability is especially important
at a time when machine learning is being used to automate decision processes
which concern sensitive factors and legal outcomes. Indeed, it is even a
requirement according to EU law. Furthermore, researchers concerned with
imposing overly restrictive functional form (e.g., as would be the case in a
linear regression) may be motivated to use machine learning algorithms in
conjunction with explainability techniques, as part of exploratory research,
with the goal of identifying important variables which are associated with an
outcome of interest. For example, epidemiologists might be interested in
identifying `risk factors' - i.e. factors which affect recovery from disease -
by using random forests and assessing variable relevance using importance
measures. However, and as we demonstrate, machine learning algorithms are not
as flexible as they might seem, and are instead incredibly sensitive to the
underling causal structure in the data. The consequences of this are that
predictors which are, in fact, critical to a causal system and highly
correlated with the outcome, may nonetheless be deemed by explainability
techniques to be unrelated/unimportant/unpredictive of the outcome. Rather than
this being a limitation of explainability techniques per se, we show that it is
rather a consequence of the mathematical implications of regression, and the
interaction of these implications with the associated conditional
independencies of the underlying causal structure. We provide some alternative
recommendations for researchers wanting to explore the data for important
variables.


title:
Performance Analysis of Optimally Coordinated Connected and Automated
  Vehicles in a Mixed Traffic Environment

abstract:
  Trajectory planning of connected and automated vehicles (CAVs) poses
significant challenges in a mixed traffic environment due to the presence of
human-driven vehicles (HDVs). In this paper, we apply a framework that allows
optimal coordination of CAVs and HDVs traveling through a traffic corridor
consisting of an on-ramp merging, a speed reduction zone, and a roundabout. We
study the impact of different penetration rates of CAVs and traffic volumes on
the efficiency of the corridor. We provide extensive simulation results and
report on the benefits in terms of total travel time and fuel economy.


title: On proportionality in multi-issue problems with crossed claims

abstract:
  In this paper, we analyze the problem of how to adapt the concept of
proportionality to situations where several perfectly divisible resources have
to be allocated among certain set of agents that have exactly one claim which
is used for all resources. In particular, we introduce the constrained
proportional awards rule, which extend the classical proportional rule to these
situations. Moreover, we provide an axiomatic characterization of this rule.


title: Resolution to Sutner's Conjecture

abstract:
  Consider a game played on a simple graph $G = (V,E)$ where each vertex
consists of a clickable light. Clicking any vertex $v$ toggles the on/off state
of $v$ and its neighbors. One wins the game by finding a sequence of clicks
that turns off all the lights. When $G$ is a $5 \times 5$ grid, this game was
commercially available from Tiger Electronics as Lights Out. Sutner was one of
the first to study these games mathematically. He found that when $d(G) =
\text{dim}(\text{ker}(A + I))$ over the field $GF(2)$, where $A$ is the
adjacency matrix of $G$, is 0 all initial configurations are solvable. When
investigating $n \times n$ grid graphs, Sutner conjectured that $d_{2n+1} =
2d_{n} + \delta_{n}, \delta_{n} \in \{0,2\}, \delta_{2n+1} = \delta_{n}$, where
$d_n = d(G)$ for $G$ an $n \times n$ grid graph. We resolve this conjecture in
the affirmative. We use results from Sutner that give $d_n$ as the GCD of two
polynomials in the ring $\mathbb{Z}_2[x]$. We then apply identities from
Hunziker, Machiavelo, and Park that relate the polynomials of $(2n+1) \times
(2n+1)$ grids and $n \times n$ grids. Finally, we use a result from Ore about
the GCD of two products. Together these results allow us to prove Sutner's
conjecture and describe exactly when $\delta_n$ is 0 or 2.


title:
On a non local non-homogeneous fractional Timoshenko system with
  frictional and viscoelastic damping terms

abstract:
  We are devoted to the study of a nonhomogeneous time-fractional Timoshenko
system with frictional and viscoelastic damping terms. We are concerned with
the well-posedness of the given problem. The approach relies on some
functional-analysis tools, operator theory, a prori estimates, and density
arguments.


title: Pairwise Nonlinear Dependence Analysis of Genomic Data

abstract:
  In The Cancer Genome Atlas (TCGA) dataset, there are many interesting
nonlinear dependencies between pairs of genes that reveal important
relationships and subtypes of cancer. Such genomic data analysis requires a
rapid, powerful and interpretable detection process, especially in a
high-dimensional environment. We study the nonlinear patterns among the
expression of genes from TCGA using a powerful tool called Binary Expansion
Testing. We find many nonlinear patterns, some of which are driven by known
cancer subtypes, some of which are novel.


title:
Observation of Long-Radial-Range-Correlation in Turbulence in
  High-Collisionality High-Confinement Fusion Plasmas

abstract:
  We report on the enhanced core electron density fluctuation with long radial
correlation length when the mean flow collapses in high-collisionality
\emph{H}-mode plasmas on DIII-D tokamak. This long-radial-range-correlation
(LRRC) fluctuation has a radially elongated, streamer-like mode structure
($k_{r}\rho_{s}=0.1-0.3$ and $k_{\theta}\rho_{s}=1-4$) and spans a broad radial
scale in the mid-radius region ($0.35<\rho<0.8$). It also shows intermittent
features, long-term memory effect, and the characteristic spectrum of
self-organized criticality. The amplitude and the radial correlation length of
LRRC turbulence increase substantially when the shearing rate of the mean flow
is reduced below the turbulent scattering rate of LRRC turbulence. The
enhancement of LRRC turbulence is also associated with an apparent degradation
of normalized energy confinement time. These findings constitute the first
experimental observation of long-radial-range turbulent transport events in
high-collisionality \emph{H}-mode fusion plasmas, and demonstrate the role of
mean shear flows in the formation and propagation of turbulence with
long-radial-range correlation.


title:
Electric Current and Heat Production by a Neutral Carrier: An Effect of
  the Axion

abstract:
  A general axion-electrodynamic formalism is presented on the phenomenological
level when the environment is dielectric (permittivity and permeability assumed
to be constants). Thereafter, a strong and uniform magnetic field is considered
in the $z$ direction, the field region having the form of a long material
cylinder (which corresponds to the haloscope setup). If the axion amplitude
depends on time only, the axions give rise to an oscillating electric current
in the $z$ direction. We estimate the magnitudes of the azimuthal magnetic
fields and the accompanying Joule heating in the cylinder, taking the cylinder
to have ordinary dissipative properties. We evaluate and calculate the electric
current and the heat production separately, without using the effective
approximation, both when there is a strong magnetic field and when there is a
strong electric one, showing that with the magnetic field there is a heat
production, while with the electric field there is not.
  The heat generation that we consider, is a nontrivial effect as it is
generated by the electrically neutral axions, and has obvious consequences for
axion thermodynamics. The heat production can moreover have an additional
advantage, since the effect is accumulative and so grows with time. The
boundary conditions (in a classical sense) are explained and the use of them in
a quantum mechanical context is discussed. This point is nontrivial,
accentuated in particular in connection with the Casimir effect. For comparison
purposes, we present finally some results for heat dissipation taken from the
theory of viscous cosmology.


title:
On Efficient Noncommutative Polynomial Factorization via Higman
  Linearization

abstract:
  In this paper we study the problem of efficiently factorizing polynomials in
the free noncommutative ring F<x_1,x_2,...,x_n> of polynomials in noncommuting
variables x_1,x_2,..., x_n over the field F. We obtain the following result:
  Given a noncommutative arithmetic formula of size s computing a
noncommutative polynomial f in F<x_1,x_2,...,x_n> as input, where F=F_q is a
finite field, we give a randomized algorithm that runs in time polynomial in s,
n and log q that computes a factorization of f as a product f=f_1f_2\cdots f_r,
where each f_i is an irreducible polynomial that is output as a noncommutative
algebraic branching program.
  The algorithm works by first transforming f into a linear matrix L using
Higman's linearization of polynomials. We then factorize the linear matrix L
and recover the factorization of f. We use basic elements from Cohn's theory of
free ideals rings combined with Ronyai's randomized polynomial-time algorithm
for computing invariant subspaces of a collection of matrices over finite
fields.


title:
Diurnal variations in the stratosphere of the ultrahot giant exoplanet
  WASP-121b

abstract:
  The temperature profile of a planetary atmosphere is a key diagnostic of
radiative and dynamical processes governing the absorption, redistribution, and
emission of energy. Observations have revealed dayside stratospheres that
either cool or warm with altitude for a small number of gas giant exoplanets,
while other dayside stratospheres are consistent with constant temperatures.
Here we report spectroscopic phase curve measurements for the gas giant
WASP-121b, which constrain stratospheric temperatures throughout the diurnal
cycle. Variations measured for a water vapour spectral feature reveal a
temperature profile that transitions from warming with altitude on the dayside
hemisphere to cooling with altitude on the nightside hemisphere. The data are
well explained by models assuming chemical equilibrium, with water molecules
thermally dissociating at low pressures on the dayside and recombining on the
nightside. Nightside temperatures are low enough for perovskite (CaTiO3) to
condense, which could deplete titanium from the gas phase and explain recent
non-detections at the day-night terminator. Nightside temperatures are also
consistent with the condensation of refractory species such as magnesium, iron,
and vanadium. Detections of these metals at the day-night terminator suggest,
however, that if they do form nightside clouds, cold trapping does not
efficiently remove them from the upper atmosphere. Horizontal winds and
vertical mixing could keep these refractory condensates aloft in the upper
atmosphere of the nightside hemisphere until they are recirculated to the
hotter dayside hemisphere and vaporised.


title:
On Optimal Early Stopping: Over-informative versus Under-informative
  Parametrization

abstract:
  Early stopping is a simple and widely used method to prevent over-training
neural networks. We develop theoretical results to reveal the relationship
between the optimal early stopping time and model dimension as well as sample
size of the dataset for certain linear models. Our results demonstrate two very
different behaviors when the model dimension exceeds the number of features
versus the opposite scenario. While most previous works on linear models focus
on the latter setting, we observe that the dimension of the model often exceeds
the number of features arising from data in common deep learning tasks and
propose a model to study this setting. We demonstrate experimentally that our
theoretical results on optimal early stopping time corresponds to the training
process of deep neural networks.


title:
High-throughput computational screening of nanoporous materials in
  targeted applications

abstract:
  Due to their chemical and structural diversity, nanoporous materials can be
used in a wide variety of applications, including fluid separation, gas
storage, heterogeneous catalysis, drug delivery, etc. Given the large and
rapidly increasing number of known nanoporous materials, and the even bigger
number of hypothetical structures, computational screening is an efficient
method to find the current best-performing materials and to guide the design of
future materials. This review highlights the potential of high-throughput
computational screenings in various applications. The achievements and the
challenges associated to the screening of several material properties are
discussed to give a broader perspective on the future of the field.


title:
Multiscale structure of poly(ionic liquid)s in bulk and solutions by
  small angle neutron scattering

abstract:
  Poly(ionic liquid)s (PILs), similar to their ionic liquid (IL) analogues,
present a nanostructure arising from local interactions. The influence of this
nanostructure on the macromolecular conformation of polymer chains is
investigated for the first time by means of an extensive use of small angle
neutron scattering on a series of poly(1-vinyl-3-alkylimidazolium)s with
varying alkyl side-chain length and counter-anion both in bulk and in dilute
solutions. Radii of gyration are found to increase with the side-chain length
in solution as a consequence of crowding interactions between neighboring
monomers. In bulk, however, a non monotonic evolution of the radius of gyration
reflects a change in chain flexibility and a potential screening of
electrostatic interactions. Additionally at smaller scale, SANS provides an
experimental estimation of both the chain diameter and the correlation length
between neighboring chains, comparison of which unveils clear evidence of
interdigitation of the alkyl side-chains. These structural features bring
precious insights in the understanding of the dynamic properties of PILs.


title: Benchmarking the Linear Algebra Awareness of TensorFlow and PyTorch

abstract:
  Linear algebra operations, which are ubiquitous in machine learning, form
major performance bottlenecks. The High-Performance Computing community invests
significant effort in the development of architecture-specific optimized
kernels, such as those provided by the BLAS and LAPACK libraries, to speed up
linear algebra operations. However, end users are progressively less likely to
go through the error prone and time-consuming process of directly using said
kernels; instead, frameworks such as TensorFlow (TF) and PyTorch (PyT), which
facilitate the development of machine learning applications, are becoming more
and more popular. Although such frameworks link to BLAS and LAPACK, it is not
clear whether or not they make use of linear algebra knowledge to speed up
computations. For this reason, in this paper we develop benchmarks to
investigate the linear algebra optimization capabilities of TF and PyT. Our
analyses reveal that a number of linear algebra optimizations are still
missing; for instance, reducing the number of scalar operations by applying the
distributive law, and automatically identifying the optimal parenthesization of
a matrix chain. In this work, we focus on linear algebra computations in TF and
PyT; we both expose opportunities for performance enhancement to the benefit of
the developers of the frameworks and provide end users with guidelines on how
to achieve performance gains.


title:
Memorize to Generalize: on the Necessity of Interpolation in High
  Dimensional Linear Regression

abstract:
  We examine the necessity of interpolation in overparameterized models, that
is, when achieving optimal predictive risk in machine learning problems
requires (nearly) interpolating the training data. In particular, we consider
simple overparameterized linear regression $y = X \theta + w$ with random
design $X \in \mathbb{R}^{n \times d}$ under the proportional asymptotics $d/n
\to \gamma \in (1, \infty)$. We precisely characterize how prediction (test)
error necessarily scales with training error in this setting. An implication of
this characterization is that as the label noise variance $\sigma^2 \to 0$, any
estimator that incurs at least $\mathsf{c}\sigma^4$ training error for some
constant $\mathsf{c}$ is necessarily suboptimal and will suffer growth in
excess prediction error at least linear in the training error. Thus, optimal
performance requires fitting training data to substantially higher accuracy
than the inherent noise floor of the problem.


title:
Deterministic Patterns for Multiple Access in Latency-Constrained
  Ultra-Reliable Communications

abstract:
  The grant-free access is envisioned as one of the enablers of the
ultra-reliable low-latency communications. Yet, when there are many devices
that tend to be active only intermittently, the fully orthogonal resource
allocation is largely inefficient. The solution is to employ a common, shared
pool of resources and account for the fact that some collisions and
interference will inevitably occur. In this contribution we study the
reliability aspects of such multi-user uplink communication scenario over a
shared pool of channel resources, where intermittently active devices utilize
multiple transmissions (K-repetition coding) to achieve diversity. We focus on
two access methods -- one where devices choose the K slots at random and one
where the access patterns are deterministic and follow a specific code design,
namely the Steiner System. We analyze the problem under two signal models that
involve different complexity for the receiver. Firstly, a model which treats
collisions as destructive, i.e. only those K' among K transmissions that do not
contain interference can be used and combined. Second, where receiver is
capable of utilizing all K replicas and applies maximum ratio combining (MRC)
treating interference as noise. Furthermore, in both cases we investigate the
receiver with and without successive interference cancellation (SIC)
capabilities. As one of the main contributions of this work, we develop useful
approximations and bounds for the outage probabilities in the aforementioned
scenarios that match very closely the simulation results. We also show that
deterministic patterns have the potential to significantly outperform fully
random selection, both in terms of raw performance and by simplifying the
system design.


title: Equivariant Graph Attention Networks for Molecular Property Prediction

abstract:
  Learning and reasoning about 3D molecular structures with varying size is an
emerging and important challenge in machine learning and especially in drug
discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage
the geometric and relational detail of the problem domain and are known to
learn expressive representations through the propagation of information between
nodes leveraging higher-order representations to faithfully express the
geometry of the data, such as directionality in their intermediate layers. In
this work, we propose an equivariant GNN that operates with Cartesian
coordinates to incorporate directionality and we implement a novel attention
mechanism, acting as a content and spatial dependent filter when propagating
information between nodes. We demonstrate the efficacy of our architecture on
predicting quantum mechanical properties of small molecules and its benefit on
problems that concern macromolecular structures such as protein complexes.


title: Comparing the Complexity of Robotic Tasks

abstract:
  We are motivated by the problem of comparing the complexity of one robotic
task relative to another. To this end, we define a notion of reduction that
formalizes the following intuition: Task 1 reduces to Task 2 if we can
efficiently transform any policy that solves Task 2 into a policy that solves
Task 1. We further define a quantitative measure of the relative complexity
between any two tasks for a given robot. We prove useful properties of our
notion of reduction (e.g., reflexivity, transitivity, and antisymmetry) and
relative complexity measure (e.g., nonnegativity and monotonicity). In
addition, we propose practical algorithms for estimating the relative
complexity measure. We illustrate our framework for comparing robotic tasks
using (i) examples where one can analytically establish reductions, and (ii)
reinforcement learning examples where the proposed algorithm can estimate the
relative complexity between tasks.


title: An obstacle problem for the p-elastic energy

abstract:
  In this paper we consider an obstacle problem for a generalization of the
p-elastic energy among graphical curves with fixed ends. Taking into account
that the Euler--Lagrange equation has a degeneracy, we address the question
whether solutions have a flat part, i.e. an open interval where the curvature
vanishes. We also investigate which is the main cause of the loss of
regularity, the obstacle or the degeneracy. Moreover, we give several
conditions on the obstacle that assure existence and nonexistence of solutions.
The analysis can be refined in the special case of the p-elastica functional,
where we obtain sharp existence results and uniqueness for symmetric
minimizers.


title:
Third-order affine and projective-invariant (systems of) PDEs in two
  independent variables as vanishing of the Fubini-Pick invariant

abstract:
  If one imposes that a $3^{\mathrm{rd}}$ order PDE
$\mathcal{E}:=\{F(x,y,u,u_x,\dots,u_{xyy},u_{yyy})=0\}$ in two independent
variables $x,y$ and one unknown function $u$ be invariant with respect to the
group of affine transformation $\mathrm{Aff}(3)$ of $\mathbb{R}^3=\{(x,y,u)\}$,
then it turns out that there is (up to a nowhere zero factor) only one choice
of $F$. In this paper we study more in depth the geometry behind the occurrence
of such PDE: after proving the relationship of $F$ with the Fubini-Pick
invariant, we derive $\mathcal{E}$ by using a general method introduced in
[D.V. Alekseevsky, J. Gutt, G. Manno, and G. Moreno: A general method to
construct invariant {PDEs} on homogeneous manifolds. Communications in
Contemporary Mathematics (2021)], which sheds light on some of its geometrical
properties.


title:
UX Research on Conversational Human-AI Interaction: A Literature Review
  of the ACM Digital Library

abstract:
  Early conversational agents (CAs) focused on dyadic human-AI interaction
between humans and the CAs, followed by the increasing popularity of polyadic
human-AI interaction, in which CAs are designed to mediate human-human
interactions. CAs for polyadic interactions are unique because they encompass
hybrid social interactions, i.e., human-CA, human-to-human, and human-to-group
behaviors. However, research on polyadic CAs is scattered across different
fields, making it challenging to identify, compare, and accumulate existing
knowledge. To promote the future design of CA systems, we conducted a
literature review of ACM publications and identified a set of works that
conducted UX (user experience) research. We qualitatively synthesized the
effects of polyadic CAs into four aspects of human-human interactions, i.e.,
communication, engagement, connection, and relationship maintenance. Through a
mixed-method analysis of the selected polyadic and dyadic CA studies, we
developed a suite of evaluation measurements on the effects. Our findings show
that designing with social boundaries, such as privacy, disclosure, and
identification, is crucial for ethical polyadic CAs. Future research should
also advance usability testing methods and trust-building guidelines for
conversational AI.


title: GGS-groups over primary trees: Branch structures

abstract:
  We study branch structures in Grigorchuk-Gupta-Sidki groups (GGS-groups) over
primary trees, that is, regular rooted trees of degree $p^n$ for a prime $p$.
Apart from a small set of exceptions for $p=2$, we prove that all these groups
are weakly regular branch over $G''$. Furthermore, in most cases they are
actually regular branch over $\gamma_3(G)$. This is a significant extension of
previously known results regarding periodic GGS-groups over primary trees and
general GGS-groups in the case $n=1$. We also show that, as in the case $n=1$,
a GGS-group generated by a constant vector is not branch.


title:
Collusion Resistant Federated Learning with Oblivious Distributed
  Differential Privacy

abstract:
  Privacy-preserving federated learning enables a population of distributed
clients to jointly learn a shared model while keeping client training data
private, even from an untrusted server. Prior works do not provide efficient
solutions that protect against collusion attacks in which parties collaborate
to expose an honest client's model parameters. We present an efficient
mechanism based on oblivious distributed differential privacy that is the first
to protect against such client collusion, including the "Sybil" attack in which
a server preferentially selects compromised devices or simulates fake devices.
We leverage the novel privacy mechanism to construct a secure federated
learning protocol and prove the security of that protocol. We conclude with
empirical analysis of the protocol's execution speed, learning accuracy, and
privacy performance on two data sets within a realistic simulation of 5,000
distributed network clients.


title: Quantum imaging and metrology with undetected photons: a tutorial

abstract:
  We present a tutorial on the phenomenon of induced coherence without induced
emission, and specifically its application to imaging and metrology. It is
based on a striking effect where two nonlinear crystals, by sharing a coherent
pump and one of two output beams each, can induce correlations between the
other two individual, non-interacting beams. This can be thought of as a type
of quantum-erasure effect, where the ``welcher-weg'' (which-way), or in this
case ``which-source'' information is erased when the shared beams are aligned.
With the correct geometry this effect can allow an object to be imaged using
only photons which have never interacted with the object -- in other words the
image is formed using undetected photons. Interest in this and related setups
has been accelerating in recent years due to a number of desirable properties,
mostly centered around the fact that the fields for detection and imaging
(since separate) may have different optical properties, entailing significant
advantages to various applications. The purpose of this tutorial is to
introduce researchers to this area of research, to provide practical tools for
setting up experiments as well as understanding the underlying theory, and to
also provide a comprehensive overview of the sub-field as a whole.


title: Adomian Decomposition Based Numerical Scheme for Flow Simulations

abstract:
  This paper proposes a numerical method based on the Adomian decomposition
approach for the time discretization, applied to Euler equations. A recursive
property is demonstrated that allows to formulate the method in an appropriate
and efficient way. To obtain a fully numerical scheme, the space discretization
is achieved using the classical DG techniques. The efficiency of the obtained
numerical scheme is demonstrated through numerical tests by comparison to exact
solution and the popular Runge-Kutta DG method results.


title:
A Linear Time, and Constant Space, Algorithm to Compute the Mixed
  Moments of the Multivariate Normal Distributions

abstract:
  Using recurrences gotten from the Apagodu-Zeilberger Multivariate
Almkvist-Zeilberger algorithm we present a linear-time, and constant-space,
algorithm to compute the general mixed moments of the k-variate general normal
distribution, with any covariance matrix, for any specific k. Besides their
obvious importance in statistics, these numbers are also very significant in
enumerative combinatorics, since they count in how many ways, in a species with
k different genders, a bunch of individuals can all get married, keeping track
of the different kinds of heterosexual marriages. We completely implement our
algorithm (with an accompanying Maple package, MVNM.txt) for the bivariate and
trivariate cases (and hence taking care of our own 2-sex society and a putative
3-sex society), but alas, the actual recurrences for larger k took too long for
us to compute. We leave them as computational challenges.


title:
Towards a Sociolinguistics-Based Framework for the Study of Politeness
  in Human-Computer Interaction

abstract:
  Politeness plays an important role in regulating communication and enhancing
social interactions.Research suggests that people treat interactive systems as
social agents and may expect those systems to exhibit polite behavior. We
augment early research in this area by proposing a framework that is grounded
in sociolinguistics and pragmatics. The framework focuses on two complementary
concepts - clarity and politeness. We suggest that these concepts are pertinent
to various domains of interactive technologies and provide examples for the
applicability of clarity and politeness rules to human-computer interaction
(HCI). We conducted a laboratory experiment, in which politeness and clarity
served as independent factors in the context of a cooperative computer game,
based on the Peekaboom game. The manipulation of clarity failed, yet politeness
was manipulated successfully based on the framework's rules of politeness. The
results provide empirical support for the basic propositions of the framework
and may facilitate more systematic research on politeness in various domains of
social computing and other areas related to HCI.


title: Complicated colorings, revisited

abstract:
  In a paper from 1997, Shelah asked whether
$Pr_1(\lambda^+,\lambda^+,\lambda^+,\lambda)$ holds for every inaccessible
cardinal $\lambda$. Here, we prove that an affirmative answer follows from
$\square(\lambda^+)$. Furthermore, we establish that for every pair
$\chi<\kappa$ of regular uncountable cardinals, $\square(\kappa)$ implies
$Pr_1(\kappa,\kappa,\kappa,\chi)$.


title:
KLLR: A scale-dependent, multivariate model class for regression
  analysis

abstract:
  The underlying physics of astronomical systems governs the relation between
their measurable properties. Consequently, quantifying the statistical
relationships between system-level observable properties of a population offers
insights into the astrophysical drivers of that class of systems. While purely
linear models capture behavior over a limited range of system scale, the fact
that astrophysics is ultimately scale-dependent implies the need for a more
flexible approach to describing population statistics over a wide dynamic
range. For such applications, we introduce and implement a class of
Kernel-Localized Linear Regression (KLLR) models. KLLR is a natural extension
to the commonly-used linear models that allows the parameters of the linear
model -- normalization, slope, and covariance matrix -- to be scale-dependent.
KLLR performs inference in two steps: (1) it estimates the mean relation
between a set of independent variables and a dependent variable and; (2) it
estimates the conditional covariance of the dependent variables given a set of
independent variables. We demonstrate the model's performance in a simulated
setting and showcase an application of the proposed model in analyzing the
baryonic content of dark matter halos. As a part of this work, we publicly
release a Python implementation of the KLLR method.


title:
Cyclic generators and an improved linear kernel for the rooted subtree
  prune and regraft distance

abstract:
  The rooted subtree prune and regraft (rSPR) distance between two rooted
binary phylogenetic trees is a well-studied measure of topological
dissimilarity that is NP-hard to compute. Here we describe an improved linear
kernel for the problem. In particular, we show that if the classical subtree
and chain reduction rules are augmented with a modified type of chain reduction
rule, the resulting trees have at most 9k-3 leaves, where k is the rSPR
distance; and that this bound is tight. The previous best-known linear kernel
had size O(28k). To achieve this improvement we introduce cyclic generators,
which can be viewed as cyclic analogues of the generators used in the
phylogenetic networks literature. As a corollary to our main result we also
give an improved weighted linear kernel for the minimum hybridization problem
on two rooted binary phylogenetic trees.


title: Social dilemmas of sociality due to beneficial and costly contagion

abstract:
  Levels of sociality in nature vary widely. Some species are solitary; others
live in family groups; some form complex multi-family societies. Increased
levels of social interaction can allow for the spread of useful innovations and
beneficial information, but can also facilitate the spread of harmful
contagions, such as infectious diseases. It is natural to assume that these
contagion processes shape the evolution of complex social systems, but an
explicit account of the dynamics of sociality under selection pressure imposed
by contagion remains elusive.
  We consider a model for the evolution of sociality strategies in the presence
of both a beneficial and costly contagion. We study the dynamics of this model
at three timescales: using a susceptible-infectious-susceptible (SIS) model to
describe contagion spread for given sociality strategies, a replicator equation
to study the changing fractions of two different levels of sociality, and an
adaptive dynamics approach to study the long-time evolution of the population
level of sociality.
  For a wide range of assumptions about the benefits and costs of infection, we
identify a social dilemma: the evolutionarily-stable sociality strategy (ESS)
is distinct from the collective optimum -- the level of sociality that would be
best for all individuals. In particular, the ESS level of social interaction is
greater (respectively less) than the social optimum when the good contagion
spreads more (respectively less) readily than the bad contagion.
  Our results shed light on how contagion shapes the evolution of social
interaction, but reveals that evolution may not necessarily lead populations to
social structures that are good for any or all.


title:
Quantum Computing of Schwarzschild-de Sitter Black Holes and
  Kantowski-Sachs Cosmology

abstract:
  The quantum mechanics of Schwarzschild-de Sitter black holes is of great
recent interest because of their peculiar thermodynamic properties as well as
their realization in modern dark energy cosmology which indicates the presence
of a small positive cosmological constant. We study Schwarzschild-de Sitter
black holes and also the Kantowki-Sachs Cosmology using quantum computing. In
these cases in addition to the Hamiltonian there is a Mass operator which plays
an important role in describing the quantum states of the black hole and
Kantowski-Sachs cosmology. We compute the spectrum of these operators using
classical and quantum computing. For quantum computing we use the Variational
Quantum Eigensolver which is hybrid classical-quantum algorithm that runs on
near term quantum hardware. We perform our calculations using 4, 6 and 8 qubits
in a harmonic oscillator basis, realizing the quantum operators of the
Schwarzschild-de Sitter black hole and Kantowski-Sachs cosmology in terms of 16
x 16, 64 x 64 and 256 x 256 matrices respectively. For the 4 qubit case we find
highly accurate results but for the other cases we find a more refined
variational ansatz will be necessary to represent the quantum states of a
Schwarzschild-de Sitter black hole or Kantowki-Sachs cosmology accurately on a
quantum computer.


title:
towards automatic transcription of polyphonic electric guitar music:a
  new dataset and a multi-loss transformer model

abstract:
  In this paper, we propose a new dataset named EGDB, that con-tains
transcriptions of the electric guitar performance of 240 tab-latures rendered
with different tones. Moreover, we benchmark theperformance of two well-known
transcription models proposed orig-inally for the piano on this dataset, along
with a multi-loss Trans-former model that we newly propose. Our evaluation on
this datasetand a separate set of real-world recordings demonstrate the
influenceof timbre on the accuracy of guitar sheet transcription, the
potentialof using multiple losses for Transformers, as well as the room
forfurther improvement for this task.


title: T-duality, vertical holonomy line bundles and loop Hori formulae

abstract:
  This paper is a step towards realizing T-duality and Hori formulae for loop
spaces. Here we prove T-duality and Hori formulae for winding q-loop spaces,
which are infinite dimensional subspaces of loop spaces.


title:
The IVP for certain dispersion generalized of the ZK equation in the
  cylinder space

abstract:
  We establish well-posedness for the Cauchy problem associated to the
dispersion generalized Zakharov-Kutnesov equation in the cylinder. Our main
ingredient is a localized Strichartz estimate and an argument of compactness


title: Representation Stability and Finite Orthogonal Groups

abstract:
  In this paper, we prove stability results about orthogonal groups over finite
commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we
construct a category $\mathbf{OrI}(R)$ and prove a Noetherianity theorem for
the category of $\mathbf{OrI}(R)$-modules. This implies an asymptotic structure
theorem for orthogonal groups. In addition, we show general homological
stability theorems for orthogonal groups, with both untwisted and twisted
coefficients, partially generalizing a result of Charney (1987).


title:
On Resolving Problems with Conditionality and Its Implications for
  Characterizing Statistical Evidence

abstract:
  The conditionality principle $C$ plays a key role in attempts to characterize
the concept of statistical evidence. The standard version of $C$ considers a
model and a derived conditional model, formed by conditioning on an ancillary
statistic for the model, together with the data, to be equivalent with respect
to their statistical evidence content. This equivalence is considered to hold
for any ancillary statistic for the model but creates two problems. First,
there can be more than one maximal ancillary in a given context and this leads
to $C$ not being an equivalence relation and, as such, calls into question
whether $C$ is a proper characterization of statistical evidence. Second, a
statistic $A$ can change from ancillary to informative (in its marginal
distribution) when another ancillary $B$ changes, from having one known
distribution $P_{B},$ to having another known distribution $Q_{B}.$ This means
that the stability of ancillarity differs across ancillary statistics and
raises the issue of when a statistic can be said to be truly ancillary. It is
therefore natural, and practically important, to limit conditioning to the set
of ancillaries whose distribution is irrelevant to the ancillary status of any
other ancillary statistic. This results in a family of ancillaries for which
there is a unique maximal member. This also gives a new principle for
inference, the stable conditionality principle, that satisfies the criteria
required for any principle whose aim is to characterize statistical evidence.


title:
Deep learning-guided weighted averaging for signal dropout compensation
  in diffusion-weighted imaging of the liver

abstract:
  Purpose: To develop an algorithm for the retrospective correction of signal
dropout artifacts in abdominal diffusion-weighted imaging (DWI) resulting from
cardiac motion.
  Methods: Given a set of image repetitions for a slice, a locally adaptive
weighted averaging is proposed which aims to suppress the contribution of image
regions affected by signal dropouts. Corresponding weight maps were estimated
by a sliding-window algorithm which analyzed signal deviations from a
patch-wise reference. In order to ensure the computation of a robust reference,
repetitions were filtered by a classifier that was trained to detect images
corrupted by signal dropouts. The proposed method, termed Deep Learning-guided
Adaptive Weighted Averaging (DLAWA), was evaluated in terms of dropout
suppression capability, bias reduction in the Apparent Diffusion Coefficient
(ADC) and noise characteristics.
  Results: In the case of uniform averaging, motion-related dropouts caused
signal attenuation and ADC overestimation in parts of the liver with the left
lobe being affected particularly. Both effects could be substantially mitigated
by DLAWA while preventing global penalties with respect to signal-to-noise
ratio (SNR) due to local signal suppression. Performing evaluations on patient
data, the capability to recover lesions concealed by signal dropouts was
demonstrated as well. Further, DLAWA allowed for transparent control of the
trade-off between SNR and signal dropout suppression by means of a few
hyperparameters.
  Conclusion: This work presents an effective and flexible method for the local
compensation of signal dropouts resulting from motion and pulsation. Since
DLAWA follows a retrospective approach, no changes to the acquisition are
required.


title:
Transmission-Aware Bandwidth Variable Transceiver Allocation in DWDM
  Optical Networks

abstract:
  This paper addresses the transmission-aware transceiver allocation problem of
flexible optical networks for a multi-period planning. The proposed approach
aims at assigning the best configuration of bandwidth variable transceivers
(BVTRX) considering the amplifier noise and nonlinear channel interferences
using the incoherent Extended Gaussian Noise (EGN) model. The proposed solution
improves the network throughput and spectrum utilization in the early planning
periods and allocates lower number of BV-TRXs in later periods in comparison to
algorithms presented recently. A heuristic approach to regenerator placement
has also been applied achieving up to 25% transceiver and 50% spectrum
utilization savings in comparison to configurations without regenerators.


title:
SOInter: A Novel Deep Energy Based Interpretation Method for Explaining
  Structured Output Models

abstract:
  We propose a novel interpretation technique to explain the behavior of
structured output models, which learn mappings between an input vector to a set
of output variables simultaneously. Because of the complex relationship between
the computational path of output variables in structured models, a feature can
affect the value of output through other ones. We focus on one of the outputs
as the target and try to find the most important features utilized by the
structured model to decide on the target in each locality of the input space.
In this paper, we assume an arbitrary structured output model is available as a
black box and argue how considering the correlations between output variables
can improve the explanation performance. The goal is to train a function as an
interpreter for the target output variable over the input space. We introduce
an energy-based training process for the interpreter function, which
effectively considers the structural information incorporated into the model to
be explained. The effectiveness of the proposed method is confirmed using a
variety of simulated and real data sets.


title: Derived right adjoints of parabolic induction: an example

abstract:
  Suppose $p \geq 5$ is a prime number, and let $G =
\textrm{SL}_2(\mathbb{Q}_p)$. We calculate the derived functors
$\textrm{R}^n\mathcal{R}_B^G(\pi)$, where $B$ is a Borel subgroup of $G$,
$\mathcal{R}_B^G$ is the right adjoint of smooth parabolic induction
constructed by Vign\'eras, and $\pi$ is any smooth, absolutely irreducible, mod
$p$ representation of $G$.


title:
Direct assessment of individual connotation and experience: An
  introduction to cognitive-affective mapping

abstract:
  We introduce cognitive-affective maps (CAMs) as a novel tool to assess
individual experiences and belief systems. CAMs were first presented by the
cognitive scientist and philosopher Paul Thagard as a graphical representation
of a mental network, visualizing attitudes, thoughts, and affective
connotations toward the topic of interest. While CAMs were originally used
primarily to visualize existing data, the recent release of the new software
tool Valence has facilitated the applicability of CAMs for empirical data
collection. In this article, we explain the concept and the theoretical
background of CAMs. We exemplify how CAMs can be applied in research practice,
including different options for analysis. We propose CAMs as a user-friendly
and versatile methodological bridge between qualitative and quantitative
research approaches and encourage incorporating the method into studies to
access and visualize human attitudes and experience.


title: Sharp threshold for rigidity of random graphs

abstract:
  We consider the Erd\H{o}s-R\'enyi evolution of random graphs, where a new
uniformly distributed edge is added to the graph in every step. For every fixed
$d\ge 1$, we show that with high probability, the graph becomes rigid in
$\mathbb R^d$ at the very moment its minimum degree becomes $d$.


title:
SRL-SOA: Self-Representation Learning with Sparse 1D-Operational
  Autoencoder for Hyperspectral Image Band Selection

abstract:
  The band selection in the hyperspectral image (HSI) data processing is an
important task considering its effect on the computational complexity and
accuracy. In this work, we propose a novel framework for the band selection
problem: Self-Representation Learning (SRL) with Sparse 1D-Operational
Autoencoder (SOA). The proposed SLR-SOA approach introduces a novel autoencoder
model, SOA, that is designed to learn a representation domain where the data
are sparsely represented. Moreover, the network composes of 1D-operational
layers with the non-linear neuron model. Hence, the learning capability of
neurons (filters) is greatly improved with shallow architectures. Using compact
architectures is especially crucial in autoencoders as they tend to overfit
easily because of their identity mapping objective. Overall, we show that the
proposed SRL-SOA band selection approach outperforms the competing methods over
two HSI data including Indian Pines and Salinas-A considering the achieved land
cover classification accuracies. The software implementation of the SRL-SOA
approach is shared publicly at https://github.com/meteahishali/SRL-SOA.


title: Line Bundle Twists for Unitary Bordism are Ghosts

abstract:
  We prove that the canonical twist $\zeta \colon K(\mathbb{Z},3) \rightarrow
BGL_1(MSpin^c)$ does not extend to a twist for unitary bordism by showing that
every continuous map $f \colon K(\mathbb{Z},3) \rightarrow BGL_1(MU)$ loops to
a null homotopic map.


title: Finite variations on the isoperimetric problem

abstract:
  The isoperimetric problem asks for the maximum area of a region of given
perimeter. It is natural to consider other measurements of a region, such as
the diameter and width, and ask for the extreme value of one when another is
fixed. The solution of these problems is known if the competing regions are
general convex disks, however several of these problems are still open if the
competing regions are polygons with at most a given number of sides. The
present work surveys these problems.


title:
Extending Flat Motion Planning to Non-flat Systems. Experiments on
  Aircraft Models Using Maple

abstract:
  Aircraft models may be considered as flat if one neglects some terms
associated to aerodynamics. But some maneuvers may be hard to achieve with this
flat approximation. Computational experiments in Maple show that in some cases
a suitably designed feed-back allows to follow such trajectories, when applied
to the non-flat model. We propose an iterated process to compute a more
achievable trajectory, starting from the flat reference trajectory. More
precisely, the unknown neglected terms in the flat model are iteratively
re-evaluated using the values obtained at the previous step. This process may
be interpreted as a new trajectory parametrization using an infinite number of
derivatives, a property that may be called generalized flatness. We illustrate
the pertinence of this approach in flight conditions of increasing
difficulties, from power-off gliding flight to aerobatics.


title: On $k$-regularity of sequences of valuations and last nonzero digits

abstract:
  Let $b \geq 2$ be an integer base with prime factors $p_1, \ldots, p_s$. In
this paper we study sequences of "$b$-adic valuations" and last nonzero digits
in $b$-adic expansions of the values $f(n) = (f_1(n), \ldots, f_s(n))$, where
each $f_i$ is a $p_i$-adic analytic function. We give a complete classification
concerning $k$-regularity of these sequences, which generalizes a result for
$b$ prime obtained by Shu and Yao. As an application, we strengthen a theorem
by Murru and Sanna on $b$-adic valuations of Lucas sequences of the first kind.
Moreover, we derive a method to determine precisely which terms of these
sequences can be represented by certain ternary quadratic forms.


title: Ancilla-free continuous-variable SWAP test

abstract:
  We propose a continuous-variable (CV) SWAP test that requires no ancilla
register, thereby generalizing the ancilla-free SWAP test for qubit registers.
In this ancilla-free CV SWAP test, the computational basis measurement is
replaced by photon number detection, and we calculate an upper bound on the
error of the fidelity estimate obtained from a finite Fock cutoff in the
detector. As an example, we show that estimation of the fidelity of pure,
centered, single-mode Gaussian states of energy $E$ and squeezed in opposite
quadratures can be obtained to error $\epsilon$ using photon statistics below a
Fock basis cutoff $O(E\ln \epsilon^{-1})$. This cutoff is greatly reduced to $E
+ O(\sqrt{E}\ln \epsilon^{-1})$ when the states have rapidly decaying Fock
tails, such as coherent states. We show how the ancilla-free CV SWAP test can
be extended to many modes and applied to quantum algorithms such as variational
compiling and entanglement spectroscopy in the CV setting. For the latter we
also provide a new algorithm which does not have an analog in qubit systems.
Finally, we use the ancilla-free CV SWAP test to calculate the vacuum
probability of a two-mode squeezed state on Xanadu's 8-mode photonic processor.


title:
Generalized Bayesian Additive Regression Trees Models: Beyond
  Conditional Conjugacy

abstract:
  Bayesian additive regression trees have seen increased interest in recent
years due to their ability to combine machine learning techniques with
principled uncertainty quantification. The Bayesian backfitting algorithm used
to fit BART models, however, limits their application to a small class of
models for which conditional conjugacy exists. In this article, we greatly
expand the domain of applicability of BART to arbitrary \emph{generalized BART}
models by introducing a very simple, tuning-parameter-free, reversible jump
Markov chain Monte Carlo algorithm. Our algorithm requires only that the user
be able to compute the likelihood and (optionally) its gradient and Fisher
information. The potential applications are very broad; we consider examples in
survival analysis, structured heteroskedastic regression, and gamma shape
regression.


title:
Tuning the entanglement growth in matrix-product-state evolution of
  quantum systems by nonunitary similarity transformations

abstract:
  The possibility of using similarity transformations to alter dynamical
entanglement growth in matrix-product-state simulations of quantum systems is
explored. By appropriately choosing the similarity transformation, the
entanglement growth rate is suppressed, improving the efficiency of numerical
simulations of quantum systems. The transformation can be applied to general
quantum-many-body systems.

categories: quant-ph cond-mat.stat-mech physics.chem-ph physics.comp-ph


title: Disentangling Autoencoders (DAE)

abstract:
  Noting the importance of factorizing (or disentangling) the latent space, we
propose a novel, non-probabilistic disentangling framework for autoencoders,
based on the principles of symmetry transformations in group-theory. To the
best of our knowledge, this is the first deterministic model that is aiming to
achieve disentanglement based on autoencoders without regularizers. The
proposed model is compared to seven state-of-the-art generative models based on
autoencoders and evaluated based on five supervised disentanglement metrics.
The experimental results show that the proposed model can have better
disentanglement when variances of each features are different. We believe that
this model leads to a new field for disentanglement learning based on
autoencoders without regularizers.


title: Mining Robust Default Configurations for Resource-constrained AutoML

abstract:
  Automatic machine learning (AutoML) is a key enabler of the mass deployment
of the next generation of machine learning systems. A key desideratum for
future ML systems is the automatic selection of models and hyperparameters. We
present a novel method of selecting performant configurations for a given task
by performing offline autoML and mining over a diverse set of tasks. By mining
the training tasks, we can select a compact portfolio of configurations that
perform well over a wide variety of tasks, as well as learn a strategy to
select portfolio configurations for yet-unseen tasks. The algorithm runs in a
zero-shot manner, that is without training any models online except the chosen
one. In a compute- or time-constrained setting, this virtually instant
selection is highly performant. Further, we show that our approach is effective
for warm-starting existing autoML platforms. In both settings, we demonstrate
an improvement on the state-of-the-art by testing over 62 classification and
regression datasets. We also demonstrate the utility of recommending
data-dependent default configurations that outperform widely used hand-crafted
defaults.


title: Spectra of Cosmic Ray Sodium and Aluminum and Unexpected Aluminum Excess

abstract:
  Since its launch, the Alpha Magnetic Spectrometer-02 (AMS-02) has delivered
outstanding quality measurements of the spectra of cosmic-ray (CR) species,
$\bar{p}$, $e^{\pm}$, and nuclei (H-Si, Fe), which resulted in a number of
breakthroughs. The most recent AMS-02 result is the measurement of the spectra
of CR sodium and aluminum up to $\sim$2 TV. Given their low solar system
abundances, a significant fraction of each element is produced in
fragmentations of heavier species, predominantly Ne, Mg, and Si. In this paper,
we use precise measurements of the sodium and aluminum spectra by AMS-02
together with ACE-CRIS and Voyager 1 data to test their origin. We show that
the sodium spectrum agrees well with the predictions made with the
GalProp-HelMod framework, while aluminum spectrum shows a significant excess in
the rigidity range from 2-7 GV. In this context, we discuss the origin of other
low-energy excesses in Li, F, and Fe found earlier. The observed excesses in
Li, F, and Al appear to be consistent with the local Wolf-Rayet (WR) stars
hypothesis, invoked to reproduce anomalous $^{22}$Ne/$^{20}$Ne,
$^{12}$C/$^{16}$O, and $^{58}$Fe/$^{56}$Fe ratios in CRs, while excess in Fe is
likely connected with a past SN activity in the solar neighborhood. We also
provide updated local interstellar spectra (LIS) of sodium and aluminum in the
rigidity range from few MV to $\sim$2 TV. Our calculations employ the
self-consistent GalProp-HelMod framework that has proved to be a reliable tool
in deriving the LIS of CR $\bar{p}$, $e^{-}$, and nuclei $Z\le28$.


title: Supernova Remnants in M83 as Observed with MUSE

abstract:
  Here we describe a new study of the SNRs and SNR candidates in nearby face-on
spiral galaxy M83, based primarily on MUSE integral field spectroscopy. Our
revised catalog of SNR candidates in M83 has 366 objects, 81 of which are
reported here for the first time. Of these, 229 lie within the MUSE observation
region, 160 of which have spectra with [SII]:Halpha ratios exceeding 0.4, the
value generally accepted as confirmation that an emission nebula is
shock-heated. Combined with 51 SNR candidates outside the MUSE region with high
[SII]:Halpha ratios, there are 211 spectroscopically-confirmed SNRs in M83, the
largest number of confirmed SNRs in any external galaxy. MUSE's combination of
relatively high spectral resolution and broad wavelength coverage has allowed
us to explore two other properties of SNRs that could serve as the basis of
future SNR searches. Specifically, most of the objects identified as SNRs on
the basis of [SII]:Halpha ratios exhibit more velocity broadening and lower
ratios of [SIII]:[SII] emission than HII regions. A search for nebulae with the
very broad emission lines expected from young, rapidly expanding remnants
revealed none, except for the previously identified B12-174a. The SNRs
identified in M83 are, with few exceptions, middle-aged ISM-dominated ones.
Smaller diameter candidates show a larger range of velocity broadening and a
larger range of gas densities than the larger diameter objects, as expected if
the SNRs expanding into denser gas brighten and then fade from view at smaller
diameters than those expanding into a more tenuous ISM


title: Conflict-Based Search for Explainable Multi-Agent Path Finding

abstract:
  In the Multi-Agent Path Finding (MAPF) problem, the goal is to find
non-colliding paths for agents in an environment, such that each agent reaches
its goal from its initial location. In safety-critical applications, a human
supervisor may want to verify that the plan is indeed collision-free. To this
end, a recent work introduces a notion of explainability for MAPF based on a
visualization of the plan as a short sequence of images representing time
segments, where in each time segment the trajectories of the agents are
disjoint. Then, the explainable MAPF problem asks for a set of non-colliding
paths that admits a short-enough explanation. Explainable MAPF adds a new
difficulty to MAPF, in that it is NP-hard with respect to the size of the
environment, and not just the number of agents. Thus, traditional MAPF
algorithms are not equipped to directly handle explainable-MAPF. In this work,
we adapt Conflict Based Search (CBS), a well-studied algorithm for MAPF, to
handle explainable MAPF. We show how to add explainability constraints on top
of the standard CBS tree and its underlying A* search. We examine the
usefulness of this approach and, in particular, the tradeoff between planning
time and explainability.


title: Deconstructing Distributions: A Pointwise Framework of Learning

abstract:
  In machine learning, we traditionally evaluate the performance of a single
model, averaged over a collection of test inputs. In this work, we propose a
new approach: we measure the performance of a collection of models when
evaluated on a $\textit{single input point}$. Specifically, we study a point's
$\textit{profile}$: the relationship between models' average performance on the
test distribution and their pointwise performance on this individual point. We
find that profiles can yield new insights into the structure of both models and
data -- in and out-of-distribution. For example, we empirically show that real
data distributions consist of points with qualitatively different profiles. On
one hand, there are "compatible" points with strong correlation between the
pointwise and average performance. On the other hand, there are points with
weak and even $\textit{negative}$ correlation: cases where improving overall
model accuracy actually $\textit{hurts}$ performance on these inputs. We prove
that these experimental observations are inconsistent with the predictions of
several simplified models of learning proposed in prior work. As an
application, we use profiles to construct a dataset we call CIFAR-10-NEG: a
subset of CINIC-10 such that for standard models, accuracy on CIFAR-10-NEG is
$\textit{negatively correlated}$ with accuracy on CIFAR-10 test. This
illustrates, for the first time, an OOD dataset that completely inverts
"accuracy-on-the-line" (Miller, Taori, Raghunathan, Sagawa, Koh, Shankar,
Liang, Carmon, and Schmidt 2021)


title: On large $\ell_1$-sums of Lipschitz-free spaces and applications

abstract:
  We prove that the Lipschitz-free space over a Banach space $X$ of density
$\kappa$, denoted by $\mathcal{F}(X)$, is linearly isomorphic to its
$\ell_1$-sum $\left(\bigoplus_{\kappa}\mathcal{F}(X)\right)_{\ell_1}$. This
provides an extension of a previous result from Kaufmann in the context of
non-separable Banach spaces. Further, we obtain a complete classification of
the spaces of real-valued Lipschitz functions that vanish at $0$ over a
$\mathcal{L}_p$-space. More precisely, we establish that, for every $1\leq
p\leq \infty$, if $X$ is a $\mathcal{L}_p$-space of density $\kappa$, then
$\mathrm{Lip}_0(X)$ is either isomorphic to $\mathrm{Lip}_0(\ell_p(\kappa))$ if
$p<\infty$, or $\mathrm{Lip}_0(c_0(\kappa))$ if $p=\infty$.


title:
Upper Bounds on the Feedback Error Exponent of Channels With States and
  Memory

abstract:
  As a class of state-dependent channels, Markov channels have been long
studied in information theory for characterizing the feedback capacity and
error exponent. This paper studies a more general variant of such channels
where the state evolves via a general stochastic process, not necessarily
Markov or ergodic. The states are assumed to be unknown to the transmitter and
the receiver, but the underlying probability distributions are known. For this
setup, we derive an upper bound on the feedback error exponent and the feedback
capacity with variable-length codes. The bounds are expressed in terms of the
directed mutual information and directed relative entropy. The bounds on the
error exponent are simplified to Burnashev's expression for discrete memoryless
channels. Our method relies on tools from the theory of martingales to analyze
a stochastic process defined based on the entropy of the message given the past
channel's outputs.


title: Hikita-Nakajima conjecture for the Gieseker variety

abstract:
  Let $Y, Y^!$ be a pair of symplectically dual conical symplectic
singularities. Assume that $Y$ has a symplectic resolution $X \rightarrow Y$.
The equivariant Hikita conjecture (that we call Hikita-Nakajima conjecture)
claims that there should be an isomorphism of (graded) algebras
$H^*_{S_Y}(X,\mathbb{C}) \simeq
\mathbb{C}[(Y^{!,\mathrm{univ}})^{\mathbb{C}^\times}]$, here $S_Y
\curvearrowright Y$ is the torus acting on $Y$ preserving the Poisson
structure, $Y^{!,\mathrm{univ}}$ is the universal deformation of $Y^!$,
$\mathbb{C}^\times$ is a generic one-dimensional torus acting on $Y^!$ and
$\mathbb{C}[(Y^{!,\mathrm{univ}})^{\mathbb{C}^\times}]$ is the algebra of
schematic $\mathbb{C}^\times$-fixed points of $Y^!$. We prove the
Hikita-Nakajima conjecture for $X=\mathfrak{M}(n,r)$ Gieseker variety ($ADHM$
space). We produce the isomorphism explicitly on generators. It turns out that
if we realize $\mathfrak{M}_0(n,r)^{!,\mathrm{univ}}$ as a Coulomb branch, then
Chern classes of the tautological bundle on $\mathfrak{M}(n,r)$ correspond to
Chern classes of the tautological bundle on the corresponding variety of
triples. We also describe the Hikita-Nakajima isomorphism above using
realization of $\mathfrak{M}_0(n,r)^{!,\mathrm{univ}}$ as a Nakajima quiver
variety and as the spectrum of the center of rational Cherednik algebra
corresponding to $S_n \ltimes (\mathbb{Z}/r\mathbb{Z})^n$ and identify all the
algebras that appear with the center of degenerate cyclotomic Hecke algebra
(generalizing some results of Shan, Varagnolo and Vasserot). Finally, we
formulate as a conjecture that when $X$ is a Nakajima quiver variety then the
Hikita-Nakajima isomorphism should identify Chern classes of tautological
bundles on $X$ with Chern classes of tautological bundles on the corresponding
variety of triples and describe possible approaches towards the proof.


title:
In the Arms of a Robot: Designing Autonomous Hugging Robots with
  Intra-Hug Gestures

abstract:
  Hugs are complex affective interactions that often include gestures like
squeezes. We present six new guidelines for designing interactive hugging
robots, which we validate through two studies with our custom robot. To achieve
autonomy, we investigated robot responses to four human intra-hug gestures:
holding, rubbing, patting, and squeezing. Thirty-two users each exchanged and
rated sixteen hugs with an experimenter-controlled HuggieBot 2.0. The robot's
inflated torso's microphone and pressure sensor collected data of the subjects'
demonstrations that were used to develop a perceptual algorithm that classifies
user actions with 88\% accuracy. Users enjoyed robot squeezes, regardless of
their performed action, they valued variety in the robot response, and they
appreciated robot-initiated intra-hug gestures. From average user ratings, we
created a probabilistic behavior algorithm that chooses robot responses in real
time. We implemented improvements to the robot platform to create HuggieBot 3.0
and then validated its gesture perception system and behavior algorithm with
sixteen users. The robot's responses and proactive gestures were greatly
enjoyed. Users found the robot more natural, enjoyable, and intelligent in the
last phase of the experiment than in the first. After the study, they felt more
understood by the robot and thought robots were nicer to hug.


title:
Adaptive Safe Merging Control for Heterogeneous Autonomous Vehicles
  using Parametric Control Barrier Functions

abstract:
  With the increasing emphasis on the safe autonomy for robots, model-based
safe control approaches such as Control Barrier Functions have been extensively
studied to ensure guaranteed safety during inter-robot interactions. In this
paper, we introduce the Parametric Control Barrier Function (Parametric-CBF), a
novel variant of the traditional Control Barrier Function to extend its
expressivity in describing different safe behaviors among heterogeneous robots.
Instead of assuming cooperative and homogeneous robots using the same safe
controllers, the ego robot is able to model the neighboring robots' underlying
safe controllers through different Parametric-CBFs with observed data. Given
learned parametric-CBF and proved forward invariance, it provides greater
flexibility for the ego robot to better coordinate with other heterogeneous
robots with improved efficiency while enjoying formally provable safety
guarantees. We demonstrate the usage of Parametric-CBF in behavior prediction
and adaptive safe control in the ramp merging scenario from the applications of
autonomous driving. Compared to traditional CBF, Parametric-CBF has the
advantage of capturing varying drivers' characteristics given richer
description of robot behavior in the context of safe control. Numerical
simulations are given to validate the effectiveness of the proposed method.


title:
On the $\mu$ equals zero conjecture for the fine Selmer group in Iwasawa
  theory

abstract:
  We study the Iwasawa theory of the fine Selmer group associated to certain
Galois representations. The vanishing of the $\mu$-invariant is shown to follow
in some cases from a natural property satisfied by Galois deformation rings. We
outline conditions under which the $\mu=0$ conjecture is shown to hold for
various Galois representations of interest.


title: Generative Target Update for Adaptive Siamese Tracking

abstract:
  Siamese trackers perform similarity matching with templates (i.e., target
models) to recursively localize objects within a search region. Several
strategies have been proposed in the literature to update a template based on
the tracker output, typically extracted from the target search region in the
current frame, and thereby mitigate the effects of target drift. However, this
may lead to corrupted templates, limiting the potential benefits of a template
update strategy.
  This paper proposes a model adaptation method for Siamese trackers that uses
a generative model to produce a synthetic template from the object search
regions of several previous frames, rather than directly using the tracker
output. Since the search region encompasses the target, attention from the
search region is used for robust model adaptation. In particular, our approach
relies on an auto-encoder trained through adversarial learning to detect
changes in a target object's appearance and predict a future target template,
using a set of target templates localized from tracker outputs at previous
frames. To prevent template corruption during the update, the proposed tracker
also performs change detection using the generative model to suspend updates
until the tracker stabilizes, and robust matching can resume through dynamic
template fusion.
  Extensive experiments conducted on VOT-16, VOT-17, OTB-50, and OTB-100
datasets highlight the effectiveness of our method, along with the impact of
its key components. Results indicate that our proposed approach can outperform
state-of-art trackers, and its overall robustness allows tracking for a longer
time before failure.


title: Schr\"{o}dinger Risk Diversification Portfolio

abstract:
  The mean-variance portfolio that considers the trade-off between expected
return and risk has been widely used in the problem of asset allocation for
multi-asset portfolios. However, since it is difficult to estimate the expected
return and the out-of-sample performance of the mean-variance portfolio is
poor, risk-based portfolio construction methods focusing only on risk have been
proposed, and are attracting attention mainly in practice. In terms of risk,
asset fluctuations that make up the portfolio are thought to have common
factors behind them, and principal component analysis, which is a dimension
reduction method, is applied to extract the factors. In this study, we propose
the Schr\"{o}dinger risk diversification portfolio as a factor risk
diversifying portfolio using Schr\"{o}dinger principal component analysis that
applies the Schr\"{o}dinger equation in quantum mechanics. The Schr\"{o}dinger
principal component analysis can accurately estimate the factors even if the
sample points are unequally spaced or in a small number, thus we can make
efficient risk diversification. The proposed method was verified to outperform
the conventional risk parity and other risk diversification portfolio
constructions.


title: Quasi-affine Nichols (Lie braided) Algebras with Rank $ 5$

abstract:
  All quasi-affine connected Generalized Dynkin Diagram with rank $= 5$ are
found. All quasi-affine Nichols (Lie braided) algebras with rank $ 5$ are also
found.


title:
Two-dimensional Helmholtz resonator arrays. Part I. Matched asymptotic
  expansions for thick- and thin-walled resonators

abstract:
  We present a novel multipole formulation for computing the band structures of
two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is
derived by combining existing multipole methods for arrays of ideal cylinders
with the method of matched asymptotic expansions. We construct asymptotically
close representations for the dispersion equations of the first band surface,
correcting and extending an established lowest-order (isotropic) result in the
literature for thin-walled resonator arrays. The descriptions we obtain for the
first band are accurate over a relatively broad frequency and Bloch vector
range and not simply in the long-wavelength and low-frequency regime, as is the
case in many classical treatments. Crucially, we are able to capture features
of the first band, such as low-frequency anisotropy, over a broad range of
filling fractions, wall thicknesses, and aperture angles. In addition to
describing the first band we use our formulation to compute the first band gap
for both thick- and thin-walled resonators, and find that thicker resonator
walls correspond to both a narrowing of the first band gap and an increase in
the central band gap frequency.


title:
Multiscale Crowd Counting and Localization By Multitask Point
  Supervision

abstract:
  We propose a multitask approach for crowd counting and person localization in
a unified framework. As the detection and localization tasks are
well-correlated and can be jointly tackled, our model benefits from a multitask
solution by learning multiscale representations of encoded crowd images, and
subsequently fusing them. In contrast to the relatively more popular
density-based methods, our model uses point supervision to allow for crowd
locations to be accurately identified. We test our model on two popular crowd
counting datasets, ShanghaiTech A and B, and demonstrate that our method
achieves strong results on both counting and localization tasks, with MSE
measures of 110.7 and 15.0 for crowd counting and AP measures of 0.71 and 0.75
for localization, on ShanghaiTech A and B respectively. Our detailed ablation
experiments show the impact of our multiscale approach as well as the
effectiveness of the fusion module embedded in our network. Our code is
available at: https://github.com/RCVLab-AiimLab/crowd_counting.


title:
Two-dimensional Helmholtz resonator arrays. Part II. Matched asymptotic
  expansions for specially-scaled resonators

abstract:
  We present a solution method which combines the method of matched asymptotics
with the method of multipole expansions to determine the band structure of
cylindrical Helmholtz resonators arrays in two dimensions. The resonator
geometry is considered in the limit as the wall thickness becomes very large
compared with the aperture width (the specially-scaled limit). In this regime,
the existing treatment in Part I, with updated parameters, is found to return
spurious spectral behaviour. We derive a regularised system which overcomes
this issue and also derive compact asymptotic descriptions for the
low-frequency dispersion equation in this setting. In the specially-scaled
limit, our asymptotic dispersion equation not only recovers the first band
surface but also extends to high, but still subwavelength, frequencies. A
homogenisation treatment is outlined for describing the effective bulk modulus
and effective density tensor of the resonator array for all wall thicknesses.
We demonstrate that specially-scaled resonators are able to achieve
exceptionally low Helmholtz resonant frequencies, and present closed-form
expressions for determining these explicitly. We anticipate that the analytical
expressions and the formulation outlined here may prove useful in industrial
and other applications.


title:
Sparse domination and $L^{p} \rightarrow L^{q}$ estimates for maximal
  functions associated with curvature

abstract:
  In this paper, we study maximal functions along some finite type curves and
hypersurfaces. In particular, various impacts of non-isotropic dilations are
considered. Firstly, we provide a generic scheme that allows us to deduce the
sparse domination bounds for global maximal functions under the assumption that
the corresponding localized maximal functions satisfy the $L^{p}$ improving
properties. Secondly, for the localized maximal functions with non-isotropic
dilations of curves and hypersurfaces whose curvatures vanish to finite order
at some points, we establish the $L^{p}\rightarrow L^{q}$ bounds $(q >p)$. As a
corollary, we obtain the weighted inequalities for the corresponding global
maximal functions, which generalize the known unweighted estimates.


title: Detection of nitrogen and oxygen in a galaxy at the end of reionization

abstract:
  We present observations of [NII] 205 $\mu$m, [OIII] 88 $\mu$m and dust
emission in a strongly-lensed, submillimeter galaxy (SMG) at $z=6.0$,
G09.83808, with the Atacama Large Millimeter/submillimeter Array (ALMA). Both
[NII] and [OIII] line emissions are detected at $>12\sigma$ in the
0.8$"$-resolution maps. Lens modeling indicates that the spatial distribution
of the dust continuum emission is well characterized by a compact disk with an
effective radius of 0.64$\pm$0.02 kpc and a high infrared surface brightness of
$\Sigma_\mathrm{IR}=(1.8\pm0.3)\times10^{12}~L_\odot$ kpc$^{-2}$. This result
supports that G09.83808 is the progenitors of compact quiescent galaxies at
$z\sim4$, where the majority of its stars are expected to be formed through a
strong and short burst of star formation. G09.83808 and other lensed SMGs show
a decreasing trend of the [NII] line to infrared luminosity ratio with
increasing continuum flux density ratio between 63 $\mu$m and 158 $\mu$m, as
seen in local luminous infrared galaxies (LIRGs). The decreasing trend can be
reproduced by photoionization models with increasing ionization parameters.
Furthermore, by combining the [NII]/[OIII] luminosity ratio with far-infrared
continuum flux density ratio in G09.83808, we infer that the gas phase
metallicity is already $Z\approx 0.5-0.7~Z_\odot$. G09.83808 is likely one of
the earliest galaxies that has been chemically enriched at the end of
reionization.


title:
IBIS-A: The IBIS data Archive. High resolution observations of the solar
  photosphere and chromosphere with contextual data

abstract:
  The IBIS data Archive (IBIS-A) stores data acquired with the Interferometric
BIdimensional Spectropolarimeter (IBIS), which was operated at the Dunn Solar
Telescope of the US National Solar Observatory from 2003 to 2019. The
instrument provided series of high-resolution narrowband spectropolarimetric
imaging observations of the photosphere and chromosphere in the range
5800$-$8600 \AA~ and co-temporal broadband observations in the same spectral
range and with the same field of view of the polarimetric data. We present the
data currently stored in IBIS-A, as well as the interface utilized to explore
such data and facilitate its scientific exploitation. To this purpose we also
describe the use of IBIS-A data in recent and undergoing studies relevant to
solar physics and space weather research. IBIS-A includes raw and calibrated
observations, as well as science-ready data. The latter comprise maps of the
circular, linear, and net circular polarization, and of the magnetic and
velocity fields derived for a significant fraction of the series available in
the archive. IBIS-A furthermore contains links to observations complementary to
the IBIS data, such as co-temporal high-resolution observations of the solar
atmosphere available from the instruments onboard the Hinode and IRIS
satellites, and full-disc multiband images from INAF solar telescopes. IBIS-A
currently consists of 30 TB of data taken with IBIS during 28 observing
campaigns performed in 2008 and from 2012 to 2019 on 159 days. Metadata and
movies of each calibrated and science-ready series are also available to help
users evaluating observing conditions. IBIS-A represents a unique resource for
investigating the plasma processes in the solar atmosphere and the solar origin
of space weather events.


title: Coverage-Guided Tensor Compiler Fuzzing with Joint IR-Pass Mutation

abstract:
  In the past decade, Deep Learning (DL) systems have been widely deployed in
various domains to facilitate our daily life. Meanwhile, it is extremely
challenging to ensure the correctness of DL systems (e.g., due to their
intrinsic nondeterminism), and bugs in DL systems can cause serious
consequences and may even threaten human lives. In the literature, researchers
have explored various techniques to test, analyze, and verify DL models, since
their quality directly affects the corresponding system behaviors. Recently,
researchers have also proposed novel techniques for testing the underlying
operator-level DL libraries (such as TensorFlow and PyTorch), which provide
general binary implementations for each high-level DL operator for running
various DL models on many platforms. However, there is still limited work
targeting the reliability of the emerging tensor compilers, which aim to
directly compile high-level tensor computation graphs into high-performance
binaries for better efficiency, portability, and scalability. In this paper, we
target the important problem of tensor compiler testing, and have proposed
Tzer, a practical fuzzing technique for the widely used TVM tensor compiler.
Tzer focuses on mutating the low-level Intermediate Representation (IR) for TVM
due to the limited mutation space for the high-level IR. More specifically,
Tzer leverages both general-purpose and tensor-compiler-specific mutators
guided by coverage feedback for evolutionary IR mutation; furthermore, Tzer
also performs pass mutation in tandem with IR mutation for more effective
fuzzing. Our results show that Tzer substantially outperforms existing fuzzing
techniques on tensor compiler testing, with 75% higher coverage and 50% more
valuable tests than the 2nd-best technique. To date, Tzer has detected 49
previously unknown bugs for TVM, with 37 bugs confirmed and 25 bugs fixed (PR
merged).


title: Dynamic Survival Analysis for non-Markovian Epidemic Models

abstract:
  We present a new method for analyzing stochastic epidemic models under
minimal assumptions. The method, dubbed DSA, is based on a simple yet powerful
observation, namely that population-level mean-field trajectories described by
a system of PDE may also approximate individual-level times of infection and
recovery. This idea gives rise to a certain non-Markovian agent-based model and
provides an agent-level likelihood function for a random sample of infection
and/or recovery times. Extensive numerical analyses on both synthetic and real
epidemic data from the FMD in the United Kingdom and the COVID-19 in India show
good accuracy and confirm method's versatility in likelihood-based parameter
estimation. The accompanying software package gives prospective users a
practical tool for modeling, analyzing and interpreting epidemic data with the
help of the DSA approach.


title: Quantum Information Scrambling in Molecules

abstract:
  Out-of-time-order correlators (OTOCs) can be used to probe how quickly a
quantum system scrambles information when the initial conditions of the
dynamics are changed. In sufficiently large quantum systems, one can extract
from the OTOC the quantum analog of the Lyapunov coefficient that describes the
time scale on which a classical chaotic system becomes scrambled. OTOCs have
been applied only to a very limited number of toy models, such as the SYK model
connected with black hole information scrambling, but they could find much
wider applicability for information scrambling in quantum systems that allow
comparison with experiments. The vibrations of polyatomic molecules are known
to undergo a transition from regular dynamics at low energy to facile energy
flow at sufficiently high energy. Molecules therefore represent ideal quantum
systems to study scrambling in many-body systems of moderate size (here 6 to 36
degrees of freedom). By computing quantum OTOCs and their classical
counterparts we quantify how information becomes 'scrambled' quantum
mechanically in molecular systems. Between early 'ballistic' dynamics, and late
'saturation' of the OTOC when the full density of states is explored, there is
indeed a regime where a quantum Lyapunov coefficient can be defined for all
molecules in this study. Comparison with experimental rate data shows that slow
scrambling as measured by the OTOC can reach the time scale of molecular
reaction dynamics. Even for the smallest molecules we discuss, the Maldacena
bound remains satisfied by regularized OTOCs, but not by unregularized OTOCs,
highlighting that the former are more useful for discussing information
scrambling in this type of moderate-size quantum system.


title:
CampNet: Context-Aware Mask Prediction for End-to-End Text-Based Speech
  Editing

abstract:
  The text-based speech editor allows the editing of speech through intuitive
cutting, copying, and pasting operations to speed up the process of editing
speech. However, the major drawback of current systems is that edited speech
often sounds unnatural due to cut-copy-paste operation. In addition, it is not
obvious how to synthesize records according to a new word not appearing in the
transcript. This paper proposes a novel end-to-end text-based speech editing
method called context-aware mask prediction network (CampNet). The model can
simulate the text-based speech editing process by randomly masking part of
speech and then predicting the masked region by sensing the speech context. It
can solve unnatural prosody in the edited region and synthesize the speech
corresponding to the unseen words in the transcript. Secondly, for the possible
operation of text-based speech editing, we design three text-based operations
based on CampNet: deletion, insertion, and replacement. These operations can
cover various situations of speech editing. Thirdly, to synthesize the speech
corresponding to long text in insertion and replacement operations, a
word-level autoregressive generation method is proposed. Fourthly, we propose a
speaker adaptation method using only one sentence for CampNet and explore the
ability of few-shot learning based on CampNet, which provides a new idea for
speech forgery tasks. The subjective and objective experiments on VCTK and
LibriTTS datasets show that the speech editing results based on CampNet are
better than TTS technology, manual editing, and VoCo method. We also conduct
detailed ablation experiments to explore the effect of the CampNet structure on
its performance. Finally, the experiment shows that speaker adaptation with
only one sentence can further improve the naturalness of speech. Examples of
generated speech can be found at https://hairuo55.github.io/CampNet.


title:
Semi-discrete and fully discrete weak Galerkin finite element methods
  for a quasistatic Maxwell viscoelastic model

abstract:
  This paper considers weak Galerkin finite element approximations for a
quasistatic Maxwell viscoelastic model. The spatial discretization uses
piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation,
degree $k+1$ for the velocity approximation, and degree $k$ for the numerical
trace of velocity on the inter-element boundaries. The temporal discretization
in the fully discrete method adopts a backward Euler difference scheme. We show
the existence and uniqueness of the semi-discrete and fully discrete solutions,
and derive optimal a priori error estimates. Numerical examples are provided to
support the theoretical analysis.


title: A wonderful triangle in compressed sensing

abstract:
  In order to determine the sparse approximation function which has a direct
metric relationship with the $\ell_{0}$ quasi-norm, we introduce a wonderful
triangle whose sides are composed of $\Vert \mathbf{x} \Vert_{0}$, $\Vert
\mathbf{x} \Vert_{1}$ and $\Vert \mathbf{x} \Vert_{\infty}$ for any non-zero
vector $\mathbf{x} \in \mathbb{R}^{n}$ by delving into the iterative
soft-thresholding operator in this paper. Based on this triangle, we deduce the
ratio $\ell_{1}$ and $\ell_{\infty}$ norms as a sparsity-promoting objective
function for sparse signal reconstruction and also try to give the sparsity
interval of the signal. Considering the $\ell_{1}/\ell_{\infty}$ minimization
from a angle $\beta$ of the triangle corresponding to the side whose length is
$\Vert \mathbf{x} \Vert_{\infty} - \Vert \mathbf{x} \Vert_{1}/\Vert \mathbf{x}
\Vert_{0}$, we finally demonstrate the performance of existing
$\ell_{1}/\ell_{\infty}$ algorithm by comparing it with $\ell_{1}/\ell_{2}$
algorithm.


title: LiDAR-guided Stereo Matching with a Spatial Consistency Constraint

abstract:
  The complementary fusion of light detection and ranging (LiDAR) data and
image data is a promising but challenging task for generating high-precision
and high-density point clouds. This study proposes an innovative LiDAR-guided
stereo matching approach called LiDAR-guided stereo matching (LGSM), which
considers the spatial consistency represented by continuous disparity or depth
changes in the homogeneous region of an image. The LGSM first detects the
homogeneous pixels of each LiDAR projection point based on their color or
intensity similarity. Next, we propose a riverbed enhancement function to
optimize the cost volume of the LiDAR projection points and their homogeneous
pixels to improve the matching robustness. Our formulation expands the
constraint scopes of sparse LiDAR projection points with the guidance of image
information to optimize the cost volume of pixels as much as possible. We
applied LGSM to semi-global matching and AD-Census on both simulated and real
datasets. When the percentage of LiDAR points in the simulated datasets was
0.16%, the matching accuracy of our method achieved a subpixel level, while
that of the original stereo matching algorithm was 3.4 pixels. The experimental
results show that LGSM is suitable for indoor, street, aerial, and satellite
image datasets and provides good transferability across semi-global matching
and AD-Census. Furthermore, the qualitative and quantitative evaluations
demonstrate that LGSM is superior to two state-of-the-art optimizing cost
volume methods, especially in reducing mismatches in difficult matching areas
and refining the boundaries of objects.