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1-parameter persistent homology, a cornerstone in Topological Data Analysis (TDA), studies the evolution of topological features such as connected components and cycles hidden in data. It has been applied to enhance the representation power of deep learning models, such as Graph Neural Networks (GNNs). To enrich the representations of topological features, here we propose to study 2-parameter persistence modules induced by bi-filtration functions. In order to incorporate these representations into machine learning models, we introduce a novel vector representation called Generalized Rank Invariant Landscape (GRIL) for 2-parameter persistence modules. We show that this vector representation is 1-Lipschitz stable and differentiable with respect to underlying filtration functions and can be easily integrated into machine learning models to augment encoding topological features. We present an algorithm to compute the vector representation efficiently. We also test our methods on synthetic and benchmark graph datasets, and compare the results with previous vector representations of 1-parameter and 2-parameter persistence modules. Further, we augment GNNs with GRIL features and observe an increase in performance indicating that GRIL can capture additional features enriching GNNs. We make the complete code for the proposed method available at https://github.com/soham0209/mpml-graph. 

We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the module. We then define the meta-diagram of a 2-parameter persistence module to be the Möbius inversion of the meta-rank, resulting in a function that takes values from signed 1-parameter persistence modules. We show that the meta-rank and meta-diagram contain information equivalent to the rank invariant and the signed barcode. This equivalence leads to computational benefits, as we introduce an algorithm for computing the meta-rank and meta-diagram of a 2-parameter module M indexed by a bifiltration of n simplices in O(n^3) time. This implies an improvement upon the existing algorithm for computing the signed barcode, which has O(n^4) time complexity. This also allows us to improve the existing upper bound on the number of rectangles in the rank decomposition of M from O(n^4) to O(n^3). In addition, we define notions of erosion distance between meta-ranks and between meta-diagrams, and show that under these distances, meta-ranks and meta-diagrams are stable with respect to the interleaving distance. Lastly, the meta-diagram can be visualized in an intuitive fashion as a persistence diagram of diagrams, which generalizes the well-understood persistent diagram in the 1-parameter setting. 

Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We propose an algorithm called FastZigzag which narrows this efficiency gap. Our main result is that an input simplex-wise zigzag filtration can be converted to a cell-wise non-zigzag filtration of a ∆-complex with the same length, where the cells are copies of the input simplices. This conversion step in FastZigzag incurs very little cost. Furthermore, the barcode of the original filtration can be easily read from the barcode of the new cell-wise filtration because the conversion embodies a series of diamond switches known in topological data analysis. This seemingly simple observation opens up the vast possibilities for improving the computation of zigzag persistence because any efficient algorithm/software for standard persistence can now be applied to computing zigzag persistence. Our experiment shows that this indeed achieves substantial performance gain over the existing state-of-the-art softwares. 

Context The extent of post-release use of software affects the number of faults, thus biasing quality metrics and adversely affecting associated decisions. The proprietary nature of usage data limited deeper exploration of this subject in the past. Objective To determine how software faults and software use are related and how, based on that, an accurate quality measure can be designed. Method Via Google Analytics we measure new users, usage intensity, usage frequency, exceptions, and release date and duration for complex proprietary mobile applications for Android and iOS. We utilize Bayesian Network and Random Forest models to explain the interrelationships and to derive the usage independent release quality measure. To increase external validity, we also investigate the interrelationship among various code complexity measures, usage (downloads), and number of issues for 520 NPM packages. We derived a usage-independent quality measure from these analyses, and applied it on 4430 popular NPM packages to construct timelines for comparing the perceived quality (number of issues) and our derived measure of quality during the lifetime of these packages. Results We found the number of new users to be the primary factor determining the number of exceptions, and found no direct link between the intensity and frequency of software usage and software faults. Crashes increased with the power of 1.02-1.04 of new user for the Android app and power of 1.6 for the iOS app. Release quality expressed as crashes per user was independent of other usage-related predictors, thus serving as a usage independent measure of software quality. Usage also affected quality in NPM, where downloads were strongly associated with numbers of issues, even after taking the other code complexity measures into consideration. Unlike in mobile case where exceptions per user decrease over time, for 45.8% of the NPM packages the number of issues per download increase. Conclusions We expect our result and our proposed quality measure will help gauge release quality of a software more accurately and inspire further research in this area. 

Aim In contrast to studies of defects found during code review, we aim to clarify whether code review measures can explain the prevalence of post-release defects. Method We replicate McIntosh et al.’s (Empirical Softw. Engg. 21(5): 2146–2189, 2016) study that uses additive regression to model the relationship between defects and code reviews. To increase external validity, we apply the same methodology on a new software project. We discuss our findings with the first author of the original study, McIntosh. We then investigate how to reduce the impact of correlated predictors in the variable selection process and how to increase understanding of the inter-relationships among the predictors by employing Bayesian Network (BN) models. Context As in the original study, we use the same measures authors obtained for Qt project in the original study. We mine data from version control and issue tracker of Google Chrome and operationalize measures that are close analogs to the large collection of code, process, and code review measures used in the replicated the study. Results Both the data from the original study and the Chrome data showed high instability of the influence of code review measures on defects with the results being highly sensitive to variable selection procedure. Models without code review predictors had as good or better fit than those with review predictors. Replication, however, confirms with the bulk of prior work showing that prior defects, module size, and authorship have the strongest relationship to post-release defects. The application of BN models helped explain the observed instability by demonstrating that the review-related predictors do not affect post-release defects directly and showed indirect effects. For example, changes that have no review discussion tend to be associated with files that have had many prior defects which in turn increase the number of post-release defects. We hope that similar analyses of other software engineering techniques may also yield a more nuanced view of their impact. Our replication package including our data and scripts is publicly available (Replication package 2018). 

Background: Bots help automate many of the tasks performed by software developers and are widely used to commit code in various social coding platforms. At present, it is not clear what types of activities these bots perform and understanding it may help design better bots, and find application areas which might benefit from bot adoption. Aim: We aim to categorize the Bot Commits by the type of change (files added, deleted, or modified), find the more commonly changed file types, and identify the groups of file types that tend to get updated together. Method: 12,326,137 commits made by 461 popular bots (that made at least 1000 commits) were examined to identify the frequency and the type of files added/ deleted/ modified by the commits, and association rule mining was used to identify the types of files modified together. Result: Majority of the bot commits modify an existing file, a few of them add new files, while deletion of a file is very rare. Commits involving more than one type of operation are even rarer. Files containing data, configuration, and documentation are most frequently updated, while HTML is the most common type in terms of the number of files added, deleted, and modified. Files of the type "Markdown", "Ignore List", "YAML", "JSON" were the types that are updated together with other types of files most frequently. Conclusion: We observe that majority of bot commits involve single file modifications, and bots primarily work with data, configuration, and documentation files. A better understanding if this is a limitation of the bots and, if overcome, would lead to different kinds of bots remains an open question.