Abstract
In the context of intuitionistic sequent calculus, naturality means permutation-freeness (the terminology is essentially due to Mints). We study naturality in the context of the lambda-calculus with generalized applications and its multiary extension, to cover, under the Curry-Howard correspondence, proof systems ranging from natural deduction (with and without general elimination rules) to a fragment of sequent calculus with an iterable left-introduction rule, and which can still be recognized as a call-by-name lambda-calculus. In this context, naturality consists of a certain restricted use of generalized applications. We consider the further restriction obtained by the combination of naturality with normality w.r.t. the commutative conversion engendered by generalized applications. This combination sheds light on the interpretation of naturality as a vectorization mechanism, allowing a multitude of different ways of structuring lambda-terms, and the structuring of a multitude of interesting fragments of the systems under study. We also consider a relaxation of naturality, called weak naturality: this not only brings similar structural benefits, but also suggests a new weak system of natural deduction with generalized applications which is exempt from commutative conversions. In the end, we use all of this evidence as a stepping stone to propose a computational interpretation of generalized application (whether multiary or not, and without any restriction): it includes, alongside the argument(s) for the function, a general list - a new, very general, vectorization mechanism, that structures the continuation of the computation.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Abstract
Machine learning algorithms have shown several advantages compared to humans, namely in terms of the scale of data that can be analysed, delivering high speed and precision. However, it is not always possible to understand how algorithms work. As a result of the complexity of some algorithms, users started to feel the need to ask for explanations, boosting the relevance of Explainable Artificial Intelligence. This field aims to explain and interpret models with the use of specific analytical methods that usually analyse how their predicted values and/or errors behave. While prediction analysis is widely studied, performance analysis has limitations for regression models. This paper proposes a rule-based approach, Error Distribution Rules (EDRs), to uncover atypical error regions, while considering multivariate feature interactions without size restrictions. Extracting EDRs is a form of subgroup mining. EDRs are model agnostic and a drill-down technique to evaluate regression models, which consider multivariate interactions between predictors. EDRs uncover regions of the input space with deviating performance providing an interpretable description of these regions. They can be regarded as a complementary tool to the standard reporting of the expected average predictive performance. Moreover, by providing interpretable descriptions of these specific regions, EDRs allow end users to understand the dangers of using regression tools for some specific cases that fall on these regions, that is, they improve the accountability of models. The performance of several models from different problems was studied, showing that our proposal allows the analysis of many situations and direct model comparison. In order to facilitate the examination of rules, two visualization tools based on boxplots and density plots were implemented. A network visualization tool is also provided to rapidly check interactions of every feature condition. An additional tool is provided by using a grid of boxplots, where comparison between quartiles of every distribution with a reference is performed. Based on this comparison, an extrapolation of counterfactual examples to regression was also implemented. A set of examples is described, including a setting where regression models performance is compared in detail using EDRs. Specifically, the error difference between two models in a dataset is studied by deriving rules highlighting regions of the input space where model performance difference is unexpected. The application of visual tools is illustrated using EDRs examples derived from public available datasets. Also, case studies illustrating the specialization of subgroups, identification of counter factual subgroups and detecting unanticipated complex models are presented. This paper extends the state of the art by providing a method to derive explanations for model performance instead of explanations for model predictions.

Abstract
Influence Analysis is one of the well-known areas of Social Network Analysis. However, discovering influencers from micro-blog networks based on topics has gained recent popularity due to its specificity. Besides, these data networks are massive, continuous and evolving. Therefore, to address the above challenges we propose a dynamic framework for topic modelling and identifying influencers in the same process. It incorporates dynamic sampling, community detection and network statistics over graph data stream from a social media activity management application. Further, we compare the graph measures against each other empirically and observe that there is no evidence of correlation between the sets of users having large number of friends and the users whose posts achieve high acceptance (i.e., highly liked, commented and shared posts). Therefore, we propose a novel approach that incorporates a user's reachability and also acceptability by other users. Consequently, we improve on graph metrics by including a dynamic acceptance score (integrating content quality with network structure) for ranking influencers in micro-blogs. Additionally, we analysed the topic clusters' structure and quality with empirical experiments and visualization.

Abstract
In a partitioned Bloom Filter (PBF) the bit vector is split into disjoint parts, one per hash function. Contrary to hardware designs, where they prevail, software implementations mostly ignore PBFs, considering them worse than standard Bloom filters (SBF), due to the slightly larger false positive rate (FPR). In this paper, by performing an in-depth analysis, first we show that the FPR advantage of SBFs is smaller than thought; more importantly, by deriving the per-element FPR, we show that SBFs have weak spots in the domain: elements that test as false positives much more frequently than expected. This is relevant in scenarios where an element is tested against many filters. Moreover, SBFs are prone to exhibit extremely weak spots if naive double hashing is used, something occurring in mainstream libraries. PBFs exhibit a uniform distribution of the FPR over the domain, with no weak spots, even using naive double hashing. Finally, we survey scenarios beyond set membership testing, identifying many advantages of having disjoint parts, in designs using SIMD techniques, for filter size reduction, test of set disjointness, and duplicate detection in streams. PBFs are better, and should replace SBFs, in general purpose libraries and as the base for novel designs.

Abstract

Abstract
This paper describes a methodology for task model design and analysis using the Alloy Analyzer, a formal, declarative modeling tool. Our methodology leverages (1) a formalization of the HAMSTERS task modeling notation in Alloy and (2) a method for encoding a concrete task model and compose it with a model of the interactive system. The Analyzer then automatically verifies the overall model against desired properties, revealing counter-examples (if any) in terms of interaction scenarios between the operator and the system. In addition, we demonstrate how Alloy can be used to encode various types of operator errors (e.g., inserting or omitting an action) into the base HAMSTERS model and generate erroneous interaction scenarios. Our methodology is applied to a task model describing the interaction of a traffic air controller with a semi-autonomous Arrival MANager (AMAN) planning tool. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.