Evaluation of off-road terrain with static stereo and monoscopic displays

The National Aeronautics and Space Administration is currently funding research into the design of a Mars rover vehicle. This unmanned rover will be used to explore a number of scientific and geologic sites on the Martian surface. Since the rover can not be driven from Earth in real-time, due to lengthy communication time delays, a locomotion strategy that optimizes vehicle range and minimizes potential risk must be developed. In order to assess the degree of on-board artificial intelligence (AI) required for a rover to carry out its' mission, researchers conducted an experiment to define a no AI baseline. In the experiment 24 subjects, divided into stereo and monoscopic groups, were shown video snapshots of four terrain scenes. The subjects' task was to choose a suitable path for the vehicle through each of the four scenes. Paths were scored based on distance travelled and hazard avoidance. Study results are presented with respect to: (1) risk versus range; (2) stereo versus monocular video; (3) vehicle camera height; and (4) camera field-of-view

ForestMonkey: Toolkit for Reasoning with AI-based Defect Detection and Classification Models

Artificial intelligence (AI) reasoning and explainable AI (XAI) tasks have gained popularity recently, enabling users to explain the predictions or decision processes of AI models. This paper introduces Forest Monkey (FM), a toolkit designed to reason the outputs of any AI-based defect detection and/or classification model with data explainability. Implemented as a Python package, FM takes input in the form of dataset folder paths (including original images, ground truth labels, and predicted labels) and provides a set of charts and a text file to illustrate the reasoning results and suggest possible improvements. The FM toolkit consists of processes such as feature extraction from predictions to reasoning targets, feature extraction from images to defect characteristics, and a decision tree-based AI-Reasoner. Additionally, this paper investigates the time performance of the FM toolkit when applied to four AI models with different datasets. Lastly, a tutorial is provided to guide users in performing reasoning tasks using the FM toolkit.Comment: 6 pages, 5 figures, accepted in 2023 IEEE symposium series on computational intelligence (SSCI

On the Connectivity of Token Graphs of Trees

Let $k$ and $n$ be integers such that $1\leq k \leq n-1$, and let $G$ be a simple graph of order $n$. The $k$-token graph $F_k(G)$ of $G$ is the graph whose vertices are the $k$-subsets of $V(G)$, where two vertices are adjacent in $F_k(G)$ whenever their symmetric difference is an edge of $G$. In this paper we show that if $G$ is a tree, then the connectivity of $F_k(G)$ is equal to the minimum degree of $F_k(G)$

Partitioning edge-coloured complete graphs into monochromatic cycles and paths

A conjecture of Erd\H{o}s, Gy\'arf\'as, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertex-disjoint monochromatic cycles. So far, this conjecture has been proven only for r = 2. In this paper we show that in fact this conjecture is false for all r > 2. In contrast to this, we show that in any edge-colouring of a complete graph with three colours, it is possible to cover all the vertices with three vertex-disjoint monochromatic paths, proving a particular case of a conjecture due to Gy\'arf\'as. As an intermediate result we show that in any edge-colouring of the complete graph with the colours red and blue, it is possible to cover all the vertices with a red path, and a disjoint blue balanced complete bipartite graph.Comment: 25 pages, 3 figure

A quartet of fermionic expressions for M(k,2k±1)M(k,2k\pm1) Virasoro characters via half-lattice paths

We derive new fermionic expressions for the characters of the Virasoro minimal models $M(k,2k\pm1)$ by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of the $\phi_{2,1}$ and $\phi_{1,5}$ integrable perturbations. We find that they arise by imposing a simple restriction on the RSOS quasiparticle states of the unitary models $M(p,p+1)$. In fact, four fermionic expressions are obtained for each generating function of half-lattice paths of finite length $L$, and these lead to four distinct expressions for most characters $\chi^{k,2k\pm1}_{r,s}$. These are direct analogues of Melzer's expressions for $M(p,p+1)$, and their proof entails revisiting, reworking and refining a proof of Melzer's identities which used combinatorial transforms on lattice paths. We also derive a bosonic version of the generating functions of length $L$ half-lattice paths, this expression being notable in that it involves $q$-trinomial coefficients. Taking the $L\to\infty$ limit shows that the generating functions for infinite length half-lattice paths are indeed the Virasoro characters $\chi^{k,2k\pm1}_{r,s}$.Comment: 29 pages. v2: minor improvements, references adde