The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Decision Making for Rapid Information Acquisition in the Reconnaissance of Random Fields

Research into several aspects of robot-enabled reconnaissance of random fields is reported. The work has two major components: the underlying theory of information acquisition in the exploration of unknown fields and the results of experiments on how humans use sensor-equipped robots to perform a simulated reconnaissance exercise. The theoretical framework reported herein extends work on robotic exploration that has been reported by ourselves and others. Several new figures of merit for evaluating exploration strategies are proposed and compared. Using concepts from differential topology and information theory, we develop the theoretical foundation of search strategies aimed at rapid discovery of topological features (locations of critical points and critical level sets) of a priori unknown differentiable random fields. The theory enables study of efficient reconnaissance strategies in which the tradeoff between speed and accuracy can be understood. The proposed approach to rapid discovery of topological features has led in a natural way to to the creation of parsimonious reconnaissance routines that do not rely on any prior knowledge of the environment. The design of topology-guided search protocols uses a mathematical framework that quantifies the relationship between what is discovered and what remains to be discovered. The quantification rests on an information theory inspired model whose properties allow us to treat search as a problem in optimal information acquisition. A central theme in this approach is that "conservative" and "aggressive" search strategies can be precisely defined, and search decisions regarding "exploration" vs. "exploitation" choices are informed by the rate at which the information metric is changing.Comment: 34 pages, 20 figure

Spatial and Temporal Hierarchy for Autonomous Navigation using Active Inference in Minigrid Environment

Robust evidence suggests that humans explore their environment using a combination of topological landmarks and coarse-grained path integration. This approach relies on identifiable environmental features (topological landmarks) in tandem with estimations of distance and direction (coarse-grained path integration) to construct cognitive maps of the surroundings. This cognitive map is believed to exhibit a hierarchical structure, allowing efficient planning when solving complex navigation tasks. Inspired by human behaviour, this paper presents a scalable hierarchical active inference model for autonomous navigation, exploration, and goal-oriented behaviour. The model uses visual observation and motion perception to combine curiosity-driven exploration with goal-oriented behaviour. Motion is planned using different levels of reasoning, i.e., from context to place to motion. This allows for efficient navigation in new spaces and rapid progress toward a target. By incorporating these human navigational strategies and their hierarchical representation of the environment, this model proposes a new solution for autonomous navigation and exploration. The approach is validated through simulations in a mini-grid environment.Comment: arXiv admin note: text overlap with arXiv:2309.0986

Towards an Efficient Discovery of the Topological Representative Subgraphs

With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is still very high to be efficiently used in any further exploration. Feature selection for graph data is a way to reduce the high number of frequent subgraphs based on exact or approximate structural similarity. However, current structural similarity strategies are not efficient enough in many real-world applications, besides, the combinatorial nature of graphs makes it computationally very costly. In order to select a smaller yet structurally irredundant set of subgraphs, we propose a novel approach that mines the top-k topological representative subgraphs among the frequent ones. Our approach allows detecting hidden structural similarities that existing approaches are unable to detect such as the density or the diameter of the subgraph. In addition, it can be easily extended using any user defined structural or topological attributes depending on the sought properties. Empirical studies on real and synthetic graph datasets show that our approach is fast and scalable

A biologically inspired meta-control navigation system for the Psikharpax rat robot

A biologically inspired navigation system for the mobile rat-like robot named Psikharpax is presented, allowing for self-localization and autonomous navigation in an initially unknown environment. The ability of parts of the model (e. g. the strategy selection mechanism) to reproduce rat behavioral data in various maze tasks has been validated before in simulations. But the capacity of the model to work on a real robot platform had not been tested. This paper presents our work on the implementation on the Psikharpax robot of two independent navigation strategies (a place-based planning strategy and a cue-guided taxon strategy) and a strategy selection meta-controller. We show how our robot can memorize which was the optimal strategy in each situation, by means of a reinforcement learning algorithm. Moreover, a context detector enables the controller to quickly adapt to changes in the environment-recognized as new contexts-and to restore previously acquired strategy preferences when a previously experienced context is recognized. This produces adaptivity closer to rat behavioral performance and constitutes a computational proposition of the role of the rat prefrontal cortex in strategy shifting. Moreover, such a brain-inspired meta-controller may provide an advancement for learning architectures in robotics

Improving search order for reachability testing in timed automata

Standard algorithms for reachability analysis of timed automata are sensitive to the order in which the transitions of the automata are taken. To tackle this problem, we propose a ranking system and a waiting strategy. This paper discusses the reason why the search order matters and shows how a ranking system and a waiting strategy can be integrated into the standard reachability algorithm to alleviate and prevent the problem respectively. Experiments show that the combination of the two approaches gives optimal search order on standard benchmarks except for one example. This suggests that it should be used instead of the standard BFS algorithm for reachability analysis of timed automata