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PublicationLeveraging Classification Metrics for Quantitative System-Level Analysis with Temporal Logic Specifications(Institute of Electrical and Electronics Engineers, 2022-02)In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models.
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PublicationHypergraph Turán Problems in ℓ2-Norm(Cambridge University Press, 2022)There are various different notions measuring extremality of hypergraphs. In this survey we compare the recently introduced notion of the codegree squared extremal function with the Turán function, the minimum codegree threshold and the uniform Turán density.
The codegree squared sum co₂(G) of a 3-uniform hypergraph G is defined to be the sum of codegrees squared d(x, y)² over all pairs of vertices x, y. In other words, this is the square of the ℓ2-norm of the codegree vector. We are interested in how large co₂(G) can be if we require G to be H-free for some 3-uniform hypergraph H. This maximum value of co₂(G) over all H- free n-vertex 3-uniform hypergraphs G is called the codegree squared extremal function, which we denote by exco₂(n, H).
We systemically study the extremal codegree squared sum of various 3- uniform hypergraphs using various proof techniques. Some of our proofs rely on the flag algebra method while others use more classical tools such as the stability method. In particular, we (asymptotically) determine the codegree squared extremal numbers of matchings, stars, paths, cycles, and F₅, the 5- vertex hypergraph with edge set {123,124,345}.
Additionally, our paper has a survey format, as we state several conjectures and give an overview of Turán densities, minimum codegree thresholds and codegree squared extremal numbers of popular hypergraphs. -
PublicationParameters Evolution in Source-Sink Space Population Evolutionary Models( 2024-07-30)MOCAT-SSEM is a Source-Sink model that predicts the Low Earth Orbit (LEO) space population divided into families using a predefined set of interaction parameters. Thanks to data from the Monte Carlo version of the model (MOCAT-MC), which propagates singularly every object, it is possible to estimate such parameters, assumed as additional stochastic variables. Thus, this paper proposed a new set of parameters so that the new Source-Sink model prediction better fits the computationally expensive and accurate MOCAT-MC simulation. Estimation is performed by extracting stochastic quantities from the space population, which has been analyzed to fit common probability density functions.
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PublicationMarkers Identification for Relative Pose Estimation of an Uncooperative Target( 2024-07-30)This paper introduces a novel method using chaser spacecraft image processing and Convolutional Neural Networks (CNNs) to detect structural markers on the European Space Agency's (ESA) Environmental Satellite (ENVISAT) for safe de-orbiting. Advanced image pre-processing techniques, including noise addition and blurring, are employed to improve marker detection accuracy and robustness. Initial results show promising potential for autonomous space debris removal, supporting proactive strategies for space sustainability. The effectiveness of our approach suggests that our estimation method could significantly enhance the safety and efficiency of debris removal operations by implementing more robust and autonomous systems in actual space missions.
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PublicationSCAN: A Spatial Context Attentive Network for Joint Multi-Agent Intent Prediction( 2021-01-29)Safe navigation of autonomous agents in human centric environments requires the ability to understand and predict motion of neighboring pedestrians. However, predicting pedestrian intent is a complex problem. Pedestrian motion is governed by complex social navigation norms, is dependent on neighbors' trajectories, and is multimodal in nature. In this work, we propose SCAN, a Spatial Context Attentive Network that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene. SCAN encodes the influence of spatially close neighbors using a novel spatial attention mechanism in a manner that relies on fewer assumptions, is parameter efficient, and is more interpretable compared to state-of-the-art spatial attention approaches. Through experiments on several datasets we demonstrate that our approach can also quantitatively outperform state of the art trajectory prediction methods in terms of accuracy of predicted intent.