This section collects a number of required notions from spectral graph theory and puts spectral modification in perspective with important recent discoveries that inspire it.

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Causal inference in randomized experiments typically assumes that the units of randomization and the units of analysis are one and the same. In some applications, however, these two roles are played by distinct entities linked by a bipartite graph. The key challenge in such bipartite settings is how to avoid interference bias, which would typically arise if we simply randomized the treatment at the level of analysis units. One effective way of minimizing interference bias in standard experiments is through cluster randomization, but this design has not been studied in the bipartite setting where conventional clustering schemes can lead to poorly powered experiments. This paper introduces a novel clustering objective and a corresponding algorithm that partitions a bipartite graph so as to maximize the statistical power of a bipartite experiment on that graph. Whereas previous work relied on balanced partitioning, our formulation suggests the use of a correlation clustering objective. We use a publicly-available graph of Amazon user-item reviews to validate our solution and illustrate how it substantially increases the statistical power in bipartite experiments.

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We thank the reviewers for the time they spent evaluating our manuscript and for their valuable comments. We agree that having theoretical guarantees would be a big plus. As for scalability, the bottleneck of our method is the single-linkage algorithm. Similarly to Monath et al. (NeurIPS 2017), our idea consists Given the significant body of additional material, we feel that this topic is best left to a future publication. Line 8,56,70,93: I would suggest a more cautious usage of the word "equivalent".

Intrusion Tolerant Systems (ITSs) have become increasingly critical due to the rise of multi-domain adversaries exploiting diverse attack surfaces. ITS architectures aim to tolerate intrusions, ensuring system compromise is prevented or mitigated even with adversary presence. Existing ITS solutions often employ Risk Managers leveraging public security intelligence to adjust system defenses dynamically against emerging threats. However, these approaches rely heavily on databases like NVD and ExploitDB, which require manual analysis for newly discovered vulnerabilities. This dependency limits the system's responsiveness to rapidly evolving threats. HAL 9000, an ITS Risk Manager introduced in our prior work, addressed these challenges through machine learning. By analyzing descriptions of known vulnerabilities, HAL 9000 predicts and assesses new vulnerabilities automatically. To calculate the risk of a system, it also incorporates the Exploitability Probability Scoring system to estimate the likelihood of exploitation within 30 days, enhancing proactive defense capabilities. Despite its success, HAL 9000's reliance on NVD and ExploitDB knowledge is a limitation, considering the availability of other sources of information. This extended work introduces a custom-built scraper that continuously mines diverse threat sources, including security advisories, research forums, and real-time exploit proofs-of-concept. This significantly expands HAL 9000's intelligence base, enabling earlier detection and assessment of unverified vulnerabilities. Our evaluation demonstrates that integrating scraper-derived intelligence with HAL 9000's risk management framework substantially improves its ability to address emerging threats. This paper details the scraper's integration into the architecture, its role in providing additional information on new threats, and the effects on HAL 9000's management.

This paper studies an application of a recurrent neural network to clustering method for the S-P chart: a binary data set used widely in education. As the number of students increases, the S-P chart becomes hard to handle. In order to classify the large chart into smaller charts, we present a simple clustering method based on the network dynamics. In the method, the network has multiple fixed points and basins of attraction give clusters corresponding to small S-P charts. In order to evaluate the clustering performance, we present an important feature quantity: average caution index that characterizes singularity of students answer oatterns. Performing fundamental experiments, effectiveness of the method is confirmed.

--Traditional recommender systems aim to generate a recommendation list comprising the most relevant or similar items to the user's profile. These approaches can create recommendation lists that omit item genres from the less prominent areas of a user's profile, thereby undermining the user's experience. T o solve this problem, the calibrated recommendation system provides a guarantee of including less representative areas in the recommended list. The calibrated context works with three distributions. The first is from the user's profile, the second is from the candidate items, and the last is from the recommendation list. These distributions are G-dimensional, where G is the total number of genres in the system. This high dimensionality requires a different evaluation method, considering that traditional recommenders operate in a one-dimensional data space. In this sense, we implement fifteen models that help to understand how these distributions are structured. We evaluate the users' patterns in three datasets from the movie domain. The results indicate that the models of outlier detection provide a better understanding of the structures. The calibrated system creates recommendation lists that act similarly to traditional recommendation lists, allowing users to change their groups of preferences to the same degree. Commonly, traditional recommender systems generate recommendations with miscalibration [1]. Miscalibration means that the recommendation lists do not follow the user preferences distribution, instead suggesting items from user's dominant area of interest. It creates an overspecialized recommendation list in which the items from the less dominant area are overwhelmed. This effect puts the user in a filter bubble or an echo chamber problem [2]. For instance, when a specific area dominates the recommended list, the user likely has few other options to interact with, aside from items within that dominant area. Then, the subsequent lists are recommended, with the dominant area becoming more overspecialized. In recent years, calibrated recommendation systems have attracted attention [3]-[8] from the recommender system community to overcome this issue. This type of system demonstrates the capacity to improve several objectives, such as diversity [3], control of popularity bias [4], item coverage [5], precision [6], and the reduction of miscalibration [7]. To illustrate how calibrated recommendation works, consider a scenario: if a user's preferences distribution indicates Corresponding author is Diego Corr ˆ ea da Silva.

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