Identifying tire and vehicle parameters is an essential step in designing control and planning algorithms for autonomous vehicles. This paper proposes a new method: Simulation-Based Inference (SBI), a modern interpretation of Approximate Bayesian Com
putation methods (ABC) for parameter identification. The simulation-based inference is an emerging method in the machine learning literature and has proven to yield accurate results for many parameter sets in complex problems. We demonstrate in this paper that it can handle the identification of highly nonlinear vehicle dynamics parameters and gives accurate estimates of the parameters for the governing equations.
This paper concerns homological notions of regularity for noncommutative algebras. Properties of an algebra $A$ are reflected in the regularities of certain (complexes of) $A$-modules. We study the classical Tor-regularity and Castelnuovo-Mumford reg
ularity, which were generalized from the commutative setting to the noncommutative setting by J{o}rgensen and Dong-Wu. We also introduce two new numerical homological invariants: concavity and Artin-Schelter regularity. Artin-Schelter regular algebras occupy a central position in noncommutative algebra and noncommutative algebraic geometry, and we use these invariants to establish criteria which can be used to determine whether a noetherian connected graded algebra is Artin-Schelter regular.
Interconnected road lanes are a central concept for navigating urban roads. Currently, most autonomous vehicles rely on preconstructed lane maps as designing an algorithmic model is difficult. However, the generation and maintenance of such maps is c
ostly and hinders large-scale adoption of autonomous vehicle technology. This paper presents the first self-supervised learning method to train a model to infer a spatially grounded lane-level road network graph based on a dense segmented representation of the road scene generated from onboard sensors. A formal road lane network model is presented and proves that any structured road scene can be represented by a directed acyclic graph of at most depth three while retaining the notion of intersection regions, and that this is the most compressed representation. The formal model is implemented by a hybrid neural and search-based model, utilizing a novel barrier function loss formulation for robust learning from partial labels. Experiments are conducted for all common road intersection layouts. Results show that the model can generalize to new road layouts, unlike previous approaches, demonstrating its potential for real-world application as a practical learning-based lane-level map generator.
Robust sensing and perception in adverse weather conditions remains one of the biggest challenges for realizing reliable autonomous vehicle mobility services. Prior work has established that rainfall rate is a useful measure for adversity of atmosphe
ric weather conditions. This work presents a probabilistic hierarchical Bayesian model that infers rainfall rate from automotive lidar point cloud sequences with high accuracy and reliability. The model is a hierarchical mixture of expert model, or a probabilistic decision tree, with gating and expert nodes consisting of variational logistic and linear regression models. Experimental data used to train and evaluate the model is collected in a large-scale rainfall experiment facility from both stationary and moving vehicle platforms. The results show prediction accuracy comparable to the measurement resolution of a disdrometer, and the soundness and usefulness of the uncertainty estimation. The model achieves RMSE 2.42 mm/h after filtering out uncertain predictions. The error is comparable to the mean rainfall rate change of 3.5 mm/h between measurements. Model parameter studies show how predictive performance changes with tree depth, sampling duration, and crop box dimension. A second experiment demonstrate the predictability of higher rainfall above 300 mm/h using a different lidar sensor, demonstrating sensor independence.
We introduce the reflexive hull discriminant as a tool to study noncommutative algebras that are finitely generated, but not necessarily free, over their centers. As an example, we compute the reflexive hull discriminants for quantum generalized Weyl
algebras and use them to determine automorphism groups and other properties, recovering results of Su{a}rez-Alvarez, Vivas, and others.
We study actions of pointed Hopf algebras in the $ZZ$-graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the $ZZ$-grading. We also show that generically th
e invariant rings of Taft actions on quantum generalized Weyl algebras are commutative Kleinian singularities.
We study semisimple Hopf algebra actions on Artin-Schelter regular algebras and prove several upper bounds on the degrees of the minimal generators of the invariant subring, and on the degrees of syzygies of modules over the invariant subring. These
results are analogues of results for group actions on commutative polynomial rings proved by Noether, Fogarty, Fleischmann, Derksen, Sidman, Chardin, and Symonds.
An $m$-general set in $AG(n,q)$ is a set of points such that any subset of size $m$ is in general position. A $3$-general set is often called a capset. In this paper, we study the maximum size of an $m$-general set in $AG(n,q)$, significantly improvi
ng previous results. When $m=4$ and $q=2$ we give a precise estimate, solving a problem raised by Bennett.
Let $H$ be a weak Hopf algebra that is a finitely generated module over its affine center. We show that $H$ has finite self-injective dimension and so the Brown--Goodearl Conjecture holds in this special weak Hopf setting.
For each natural number $d$, we introduce the concept of a $d$-cap in $mathbb{F}_3^n$. A subset of $mathbb{F}_3^n$ is called a $d$-cap if, for each $k = 1, 2, dots, d$, no $k+2$ of the points lie on a $k$-dimensional flat. This generalizes the notion
of a cap in $mathbb{F}_3^n$. We prove that the $2$-caps in $mathbb{F}_3^n$ are exactly the Sidon sets in $mathbb{F}_3^n$ and study the problem of determining the size of the largest $2$-cap in $mathbb{F}_3^n$.
