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  1. As objectives increase in many-objective optimization (MaOO), often so do the number of non-dominated solutions, potentially resulting in solution sets with thousands of non-dominated solutions. Such a larger final solution set increases difficulty in visualization and decision-making. This raises the question: how can we reduce this large solution set to a more manageable size? In this paper, we present a new objective archive management (OAM) strategy that performs post-optimization solution set reduction to help the end-user make an informed decision without requiring expert knowledge of the field of MaOO. We create separate archives for each objective, selecting solutions based on their fitness as well as diversity criteria in both the objective and variable space. We can then look for solutions that belong to more than one archive to create a reduced final solution set. We apply OAM to NSGA-II and compare our approach to environmental selection finding that the obtained solution set has better hypervolume and spread. Furthermore, we compare results found by OAM-NSGA-II to NSGA-III and get competitive results. Additionally, we apply OAM to reduce the solutions found by NSGA-III and find that the selected solutions perform well in terms of overall fitness, successfully reducing the number of solutions. 
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    Free, publicly-accessible full text available December 5, 2024
  2. This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data. 
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    Free, publicly-accessible full text available October 22, 2024
  3. Morin, Pat ; Suri, Subhash (Ed.)
    Let γ be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if γ is self-overlapping by geometrically constructing a combinatorial word from γ. More recently, Zipei Nie, in an unpublished manuscript, computed the minimum homotopy area of γ by constructing a combinatorial word algebraically. We provide a unified framework for working with both words and determine the settings under which Blank’s word and Nie’s word are equivalent. Using this equivalence, we give a new geometric proof for the correctness of Nie’s algorithm. Unlike previous work, our proof is constructive which allows us to naturally compute the actual homotopy that realizes the minimum area. Furthermore, we contribute to the theory of self-overlapping curves by providing the first polynomial-time algorithm to compute a self-overlapping decomposition of any closed curve γ with minimum area. 
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  4. Performing general prognostics and health management (PHM), especially in electronic systems, continues to present significant challenges. The low availability of failure data makes learning generalized models difficult and constructing generalized models during the design phase often requires a level of understanding of the failure mechanisms that elude the designers. In this paper, we present a generalized approach to PHM based on two types of probabilistic models, Bayesian Networks (BNs) and Continuous-Time Bayesian Networks (CTBNs), and we pose the PHM problem from the perspective of risk mitigation rather than failure prediction. This paper also constitutes an extension of previous work where we proposed this framework initially [1]. In this extended version, we also provide a comparison of exact and approximate sample-based inference for CTBNs to provide practical guidance on conducting inference using the proposed framework. 
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    Free, publicly-accessible full text available August 1, 2024
  5. The Fréchet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to hand- writing recognition. More recently, the Fréchet distance has been generalized to a distance between two copies of the same graph embedded or immersed in a metric space; this more general setting opens up a wide range of more complex applications in graph analysis. In this paper, we initiate a study of some of the fundamental topological properties of spaces of paths and of graphs mapped to R^n under the Fréchet distance, in an eort to lay the theoretical groundwork for understanding how these distances can be used in practice. In particular, we prove whether or not these spaces, and the metric balls therein, are path-connected. 
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    Free, publicly-accessible full text available July 31, 2024
  6. Response curves exhibit the magnitude of the response of a sensitive system to a varying stimulus. However, response of such systems may be sensitive to multiple stimuli (i.e., input features) that are not necessarily independent. As a consequence, the shape of response curves generated for a selected input feature (referred to as “active feature”) might depend on the values of the other input features (referred to as “passive features”). In this work we consider the case of systems whose response is approximated using regression neural networks. We propose to use counterfactual explanations (CFEs) for the identification of the features with the highest relevance on the shape of response curves generated by neural network black boxes. CFEs are generated by a genetic algorithm-based approach that solves a multi-objective optimization problem. In particular, given a response curve generated for an active feature, a CFE finds the minimum combination of passive features that need to be modified to alter the shape of the response curve. We tested our method on a synthetic dataset with 1-D inputs and two crop yield prediction datasets with 2-D inputs. The relevance ranking of features and feature combinations obtained on the synthetic dataset coincided with the analysis of the equation that was used to generate the problem. Results obtained on the yield prediction datasets revealed that the impact on fertilizer responsivity of passive features depends on the terrain characteristics of each field. 
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  7. Blank, in his Ph.D. thesis on determining whether a planar closed curve $\gamma$ is self-overlapping, constructed a combinatorial word geometrically over the faces of $\gamma$ by drawing cuts from each face to a point at infinity and tracing their intersection points with $\gamma$. Independently, Nie, in an unpublished manuscript, gave an algorithm to determine the minimum area swept out by any homotopy from a closed curve $\gamma$ to a point. Nie constructed a combinatorial word algebraically over the faces of $\gamma$ inspired by ideas from geometric group theory, followed by dynamic programming over the subwords. In this paper, we examine the definitions of the two words and prove the equivalence between Blank's word and Nie's word under the right assumptions. 
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  8. In 2021, National Science Foundation (NSF) Computer and Information Science and Engineering (CISE) directorate implemented a Broadening Participation in Computing (BPC) plan requirement for all medium and larger research proposals in Core, CPS, and SaTC. This panel comprises faculty and administrators from US computing departments who have participated in the writing of Departmental or Project BPC plans, two in response to NSF’s encouragement and one prior. Panelists represent a range of institutions as well as departmental awareness of BPC prior to writing their plans. Regardless of where they or their departments lie in the spectrum of knowing about and implementing BPC activities, and regardless of the current demographic makeup of the students in their major, they all encountered challenges as they wrote their plans. They all also experienced successes, not the least of which is that they succeeded in getting a plan written in accordance with the current guidelines. With the support of a moderator, the three panelists will share their experiences developing BPC plans with the audience, offering lessons learned and tips for overcoming common challenges. Audience members will also receive helpful links and handouts to facilitate the writing of their own departmental or project plans 
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  9. Accurate uncertainty quantification is necessary to enhance the reliability of deep learning (DL) models in realworld applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic predictions of DL models. Such PIs are useful or “high-quality (HQ)” as long as they are sufficiently narrow and capture most of the probability density. In this article, we present a method to learn PIs for regression-based neural networks (NNs) automatically in addition to the conventional target predictions. In particular, we train two companion NNs: one that uses one output, the target estimate, and another that uses two outputs, the upper and lower bounds of the corresponding PI. Our main contribution is the design of a novel loss function for the PI-generation network that takes into account the output of the target-estimation network and has two optimization objectives: minimizing the mean PI width and ensuring the PI integrity using constraints that maximize the PI probability coverage implicitly. Furthermore, we introduce a self-adaptive coefficient that balances both objectives within the loss function, which alleviates the task of fine-tuning. Experiments using a synthetic dataset, eight benchmark datasets, and a real-world crop yield prediction dataset showed that our method was able to maintain a nominal probability coverage and produce significantly narrower PIs without detriment to its target estimation accuracy when compared to those PIs generated by three state-of-the-art neuralnetwork-based methods. In other words, our method was shown to produce higher quality PIs. 
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  10. Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in R d , the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph— and, more generally one-skeleton—reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs. 
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