Niek Tax

Diego Calvanese, Angelo Casciani, Giuseppe De Giacomo et al. · oxford

This paper presents a manifesto that articulates the conceptual foundations of Agentic Business Process Management (APM), an extension of Business Process Management (BPM) for governing autonomous agents executing processes in organizations. From a management perspective, APM represents a paradigm shift from the traditional process view of the business process, driven by the realization of process awareness and an agent-oriented abstraction, where software and human agents act as primary functional entities that perceive, reason, and act within explicit process frames. This perspective marks a shift from traditional, automation-oriented BPM toward systems in which autonomy is constrained, aligned, and made operational through process awareness. We introduce the core abstractions and architectural elements required to realize APM systems and elaborate on four key capabilities that such APM agents must support: framed autonomy, explainability, conversational actionability, and self-modification. These capabilities jointly ensure that agents' goals are aligned with organizational goals and that agents behave in a framed yet proactive manner in pursuing those goals. We discuss the extent to which the capabilities can be realized and identify research challenges whose resolution requires further advances in BPM, AI, and multi-agent systems. The manifesto thus serves as a roadmap for bridging these communities and for guiding the development of APM systems in practice.

David S. Watson, Joshua O'Hara, Niek Tax et al.

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

Takuo Matsubara, Niek Tax, Richard Mudd et al.

This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to which model predictions differ from probabilities estimated from data. It offers (i) a clear interpretation, (ii) a consistent scale that is unaffected by class imbalance, and (iii) an enhanced visual representation with repect to the standard reliability diagram. In addition, we introduce an optimality criterion for the binning procedure of calibration error metrics based on a minimal estimation error of the empirical probabilities. We provide a novel computational algorithm for optimal bins under bin-size constraints. We demonstrate properties of TCE through a range of experiments, including multiple real-world imbalanced datasets and ImageNet 1000.

Daniel Haimovich, Fridolin Linder, Lorenzo Perini et al.

Multicalibration gradient boosting has recently emerged as a scalable method that empirically produces approximately multicalibrated predictors and has been deployed at web scale. Despite this empirical success, its convergence properties are not well understood. In this paper, we bridge the gap by providing convergence guarantees for multicalibration gradient boosting in regression with squared-error loss. We show that the magnitude of successive prediction updates decays at $O(1/\sqrt{T})$, which implies the same convergence rate bound for the multicalibration error over rounds. Under additional smoothness assumptions on the weak learners, this rate improves to linear convergence. We further analyze adaptive variants, showing local quadratic convergence of the training loss, and we study rescaling schemes that preserve convergence. Experiments on real-world datasets support our theory and clarify the regimes in which the method achieves fast convergence and strong multicalibration.

Riccardo Colini Baldeschi, Simone Di Gregorio, Simone Fioravanti et al.

Consider the problem of finding the best matching in a weighted graph where we only have access to predictions of the actual stochastic weights, based on an underlying context. If the predictor is the Bayes optimal one, then computing the best matching based on the predicted weights is optimal. However, in practice, this perfect information scenario is not realistic. Given an imperfect predictor, a suboptimal decision rule may compensate for the induced error and thus outperform the standard optimal rule. In this paper, we propose multicalibration as a way to address this problem. This fairness notion requires a predictor to be unbiased on each element of a family of protected sets of contexts. Given a class of matching algorithms $\mathcal C$ and any predictor $γ$ of the edge-weights, we show how to construct a specific multicalibrated predictor $\hat γ$, with the following property. Picking the best matching based on the output of $\hat γ$ is competitive with the best decision rule in $\mathcal C$ applied onto the original predictor $γ$. We complement this result by providing sample complexity bounds.

Ido Guy, Daniel Haimovich, Fridolin Linder et al.

A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly calibrated." When the predicted probabilities are perfectly calibrated simultaneously across several subpopulations, the probabilistic predictions are known as "perfectly multi-calibrated." In practice, predicted probabilities are seldom perfectly multi-calibrated, so a statistic measuring the distance from perfect multi-calibration is informative. A recently proposed metric for calibration, based on the classical Kuiper statistic, is a natural basis for a new metric of multi-calibration and avoids well-known problems of metrics based on binning or kernel density estimation. The newly proposed metric weights the contributions of different subpopulations in proportion to their signal-to-noise ratios; data analyses' ablations demonstrate that the metric becomes noisy when omitting the signal-to-noise ratios from the metric. Numerical examples on benchmark data sets illustrate the new metric.

Daniel Haimovich, Dima Karamshuk, Fridolin Linder et al.

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions. Additionally, we extend our analysis to more general classifiers and datasets, considering a wide range of loss-based sampling strategies and smooth convex training loss functions. We propose a novel algorithm called Adaptive-Weight Sampling (AWS) that utilizes SGD with an adaptive step size that achieves stochastic Polyak's step size in expectation. We establish convergence rate results for AWS for smooth convex training loss functions. Our numerical experiments demonstrate the efficiency of AWS on various datasets by using either exact or estimated loss values.

Thomas Robinson, Niek Tax, Richard Mudd et al.

Active learning can improve the efficiency of training prediction models by identifying the most informative new labels to acquire. However, non-response to label requests can impact active learning's effectiveness in real-world contexts. We conceptualise this degradation by considering the type of non-response present in the data, demonstrating that biased non-response is particularly detrimental to model performance. We argue that biased non-response is likely in contexts where the labelling process, by nature, relies on user interactions. To mitigate the impact of biased non-response, we propose a cost-based correction to the sampling strategy--the Upper Confidence Bound of the Expected Utility (UCB-EU)--that can, plausibly, be applied to any active learning algorithm. Through experiments, we demonstrate that our method successfully reduces the harm from labelling non-response in many settings. However, we also characterise settings where the non-response bias in the annotations remains detrimental under UCB-EU for specific sampling methods and data generating processes. Finally, we evaluate our method on a real-world dataset from an e-commerce platform. We show that UCB-EU yields substantial performance improvements to conversion models that are trained on clicked impressions. Most generally, this research serves to both better conceptualise the interplay between types of non-response and model improvements via active learning, and to provide a practical, easy-to-implement correction that mitigates model degradation.

Lorenzo Perini, Daniel Haimovich, Fridolin Linder et al.

We propose MCGrad, a novel and scalable multicalibration algorithm. Multicalibration - calibration in sub-groups of the data - is an important property for the performance of machine learning-based systems. Existing multicalibration methods have thus far received limited traction in industry. We argue that this is because existing methods (1) require such subgroups to be manually specified, which ML practitioners often struggle with, (2) are not scalable, or (3) may harm other notions of model performance such as log loss and Area Under the Precision-Recall Curve (PRAUC). MCGrad does not require explicit specification of protected groups, is scalable, and often improves other ML evaluation metrics instead of harming them. MCGrad has been in production at Meta, and is now part of hundreds of production models. We present results from these deployments as well as results on public datasets.

Niek Tax, Kees Jan de Vries, Mathijs de Jong et al.

Fraud detection and prevention play an important part in ensuring the sustained operation of any e-commerce business. Machine learning (ML) often plays an important role in these anti-fraud operations, but the organizational context in which these ML models operate cannot be ignored. In this paper, we take an organization-centric view on the topic of fraud detection by formulating an operational model of the anti-fraud departments in e-commerce organizations. We derive 6 research topics and 12 practical challenges for fraud detection from this operational model. We summarize the state of the literature for each research topic, discuss potential solutions to the practical challenges, and identify 22 open research challenges.

Niek Tax

This thesis focuses on process mining on event data where such a normative specification is absent and, as a result, the event data is less structured. The thesis puts special emphasis on one application domain that fits this description: the analysis of smart home data where sequences of daily activities are recorded. In this thesis we propose a set of techniques to analyze such data, which can be grouped into two categories of techniques. The first category of methods focuses on preprocessing event logs in order to enable process discovery techniques to extract insights into unstructured event data. In this category we have developed the following techniques: - An unsupervised approach to refine event labels based on the time at which the event took place, allowing for example to distinguish recorded eating events into breakfast, lunch, and dinner. - An approach to detect and filter from event logs so-called chaotic activities, which are activities that cause process discovery methods to overgeneralize. - A supervised approach to abstract low-level events into more high-level events, where we show that there exist situations where process discovery approaches overgeneralize on the low-level event data but are able to find precise models on the high-level event data. The second category focuses on mining local process models, i.e., collections of process model patterns that each describe some frequent pattern, in contrast to the single global process model that is obtained with existing process discovery techniques. Several techniques are introduced in the area of local process model mining, including a basic method, fast but approximate heuristic methods, and constraint-based techniques.

Anja F. Syring, Niek Tax, Wil M. P. van der Aalst

Process mining sheds new light on the relationship between process models and real-life processes. Process discovery can be used to learn process models from event logs. Conformance checking is concerned with quantifying the quality of a business process model in relation to event data that was logged during the execution of the business process. There exist different categories of conformance measures. Recall, also called fitness, is concerned with quantifying how much of the behavior that was observed in the event log fits the process model. Precision is concerned with quantifying how much behavior a process model allows for that was never observed in the event log. Generalization is concerned with quantifying how well a process model generalizes to behavior that is possible in the business process but was never observed in the event log. Many recall, precision, and generalization measures have been developed throughout the years, but they are often defined in an ad-hoc manner without formally defining the desired properties up front. To address these problems, we formulate 21 conformance propositions and we use these propositions to evaluate current and existing conformance measures. The goal is to trigger a discussion by clearly formulating the challenges and requirements (rather than proposing new measures). Additionally, this paper serves as an overview of the conformance checking measures that are available in the process mining area.

Stephan A. Fahrenkrog-Petersen, Niek Tax, Irene Teinemaa et al.

Predictive process monitoring is a family of techniques to analyze events produced during the execution of a business process in order to predict the future state or the final outcome of running process instances. Existing techniques in this field are able to predict, at each step of a process instance, the likelihood that it will lead to an undesired outcome.These techniques, however, focus on generating predictions and do not prescribe when and how process workers should intervene to decrease the cost of undesired outcomes. This paper proposes a framework for prescriptive process monitoring, which extends predictive monitoring with the ability to generate alarms that trigger interventions to prevent an undesired outcome or mitigate its effect. The framework incorporates a parameterized cost model to assess the cost-benefit trade-off of generating alarms. We show how to optimize the generation of alarms given an event log of past process executions and a set of cost model parameters. The proposed approaches are empirically evaluated using a range of real-life event logs. The experimental results show that the net cost of undesired outcomes can be minimized by changing the threshold for generating alarms, as the process instance progresses. Moreover, introducing delays for triggering alarms, instead of triggering them as soon as the probability of an undesired outcome exceeds a threshold, leads to lower net costs.

Niek Tax, Irene Teinemaa, Sebastiaan J. van Zelst

Data of sequential nature arise in many application domains in forms of, e.g. textual data, DNA sequences, and software execution traces. Different research disciplines have developed methods to learn sequence models from such datasets: (i) in the machine learning field methods such as (hidden) Markov models and recurrent neural networks have been developed and successfully applied to a wide-range of tasks, (ii) in process mining process discovery techniques aim to generate human-interpretable descriptive models, and (iii) in the grammar inference field the focus is on finding descriptive models in the form of formal grammars. Despite their different focuses, these fields share a common goal - learning a model that accurately describes the behavior in the underlying data. Those sequence models are generative, i.e, they can predict what elements are likely to occur after a given unfinished sequence. So far, these fields have developed mainly in isolation from each other and no comparison exists. This paper presents an interdisciplinary experimental evaluation that compares sequence modeling techniques on the task of next-element prediction on four real-life sequence datasets. The results indicate that machine learning techniques that generally have no aim at interpretability in terms of accuracy outperform techniques from the process mining and grammar inference fields that aim to yield interpretable models.

Irene Teinemaa, Niek Tax, Carlos Bentes

The RecSys Challenge 2018 focused on automatic playlist continuation, i.e., the task was to recommend additional music tracks for playlists based on the playlist's title and/or a subset of the tracks that it already contains. The challenge is based on the Spotify Million Playlist Dataset (MPD), containing the tracks and the metadata from one million real-life playlists. This paper describes the automatic playlist continuation solution of team Latte, which is based on a composition of collaborative filters that each capture different aspects of a playlist, where the optimal combination of those collaborative filters is determined using a Tree-structured Parzen Estimator (TPE). The solution obtained the 12th place out of 112 participating teams in the final leaderboard. Team Latte participated in the main track of the challenge of the RecSys Challenge 2018.

Irene Teinemaa, Niek Tax, Massimiliano de Leoni et al.

Predictive process monitoring is concerned with the analysis of events produced during the execution of a process in order to predict the future state of ongoing cases thereof. Existing techniques in this field are able to predict, at each step of a case, the likelihood that the case will end up in an undesired outcome. These techniques, however, do not take into account what process workers may do with the generated predictions in order to decrease the likelihood of undesired outcomes. This paper proposes a framework for prescriptive process monitoring, which extends predictive process monitoring approaches with the concepts of alarms, interventions, compensations, and mitigation effects. The framework incorporates a parameterized cost model to assess the cost-benefit tradeoffs of applying prescriptive process monitoring in a given setting. The paper also outlines an approach to optimize the generation of alarms given a dataset and a set of cost model parameters. The proposed approach is empirically evaluated using a range of real-life event logs.

Niek Tax, Marlon Dumas

Sequential pattern mining techniques extract patterns corresponding to frequent subsequences from a sequence database. A practical limitation of these techniques is that they overload the user with too many patterns. Local Process Model (LPM) mining is an alternative approach coming from the field of process mining. While in traditional sequential pattern mining, a pattern describes one subsequence, an LPM captures a set of subsequences. Also, while traditional sequential patterns only match subsequences that are observed in the sequence database, an LPM may capture subsequences that are not explicitly observed, but that are related to observed subsequences. In other words, LPMs generalize the behavior observed in the sequence database. These properties make it possible for a set of LPMs to cover the behavior of a much larger set of sequential patterns. Yet, existing LPM mining techniques still suffer from the pattern explosion problem because they produce sets of redundant LPMs. In this paper, we propose several heuristics to mine a set of non-redundant LPMs either from a set of redundant LPMs or from a set of sequential patterns. We empirically compare the proposed heuristics between them and against existing (local) process mining techniques in terms of coverage, redundancy, and complexity of the produced sets of LPMs.

Niek Tax, Natalia Sidorova, Wil M. P. van der Aalst

Process Discovery is concerned with the automatic generation of a process model that describes a business process from execution data of that business process. Real life event logs can contain chaotic activities. These activities are independent of the state of the process and can, therefore, happen at rather arbitrary points in time. We show that the presence of such chaotic activities in an event log heavily impacts the quality of the process models that can be discovered with process discovery techniques. The current modus operandi for filtering activities from event logs is to simply filter out infrequent activities. We show that frequency-based filtering of activities does not solve the problems that are caused by chaotic activities. Moreover, we propose a novel technique to filter out chaotic activities from event logs. We evaluate this technique on a collection of seventeen real-life event logs that originate from both the business process management domain and the smart home environment domain. As demonstrated, the developed activity filtering methods enable the discovery of process models that are more behaviorally specific compared to process models that are discovered using standard frequency-based filtering.

Niek Tax, Emin Alasgarov, Natalia Sidorova et al.

Process mining is a research field focused on the analysis of event data with the aim of extracting insights related to dynamic behavior. Applying process mining techniques on data from smart home environments has the potential to provide valuable insights in (un)healthy habits and to contribute to ambient assisted living solutions. Finding the right event labels to enable the application of process mining techniques is however far from trivial, as simply using the triggering sensor as the label for sensor events results in uninformative models that allow for too much behavior (overgeneralizing). Refinements of sensor level event labels suggested by domain experts have been shown to enable discovery of more precise and insightful process models. However, there exists no automated approach to generate refinements of event labels in the context of process mining. In this paper we propose a framework for the automated generation of label refinements based on the time attribute of events, allowing us to distinguish behaviourally different instances of the same event type based on their time attribute. We show on a case study with real life smart home event data that using automatically generated refined labels in process discovery, we can find more specific, and therefore more insightful, process models. We observe that one label refinement could have an effect on the usefulness of other label refinements when used together. Therefore, we explore four strategies to generate useful combinations of multiple label refinements and evaluate those on three real life smart home event logs.

Niek Tax, Natalia Sidorova, Reinder Haakma et al.

Process mining techniques focus on extracting insight in processes from event logs. Process mining has the potential to provide valuable insights in (un)healthy habits and to contribute to ambient assisted living solutions when applied on data from smart home environments. However, events recorded in smart home environments are on the level of sensor triggers, at which process discovery algorithms produce overgeneralizing process models that allow for too much behavior and that are difficult to interpret for human experts. We show that abstracting the events to a higher-level interpretation can enable discovery of more precise and more comprehensible models. We present a framework for the extraction of features that can be used for abstraction with supervised learning methods that is based on the XES IEEE standard for event logs. This framework can automatically abstract sensor-level events to their interpretation at the human activity level, after training it on training data for which both the sensor and human activity events are known. We demonstrate our abstraction framework on three real-life smart home event logs and show that the process models that can be discovered after abstraction are more precise indeed.

Niek Tax, Xixi Lu, Natalia Sidorova et al.

In process mining, precision measures are used to quantify how much a process model overapproximates the behavior seen in an event log. Although several measures have been proposed throughout the years, no research has been done to validate whether these measures achieve the intended aim of quantifying over-approximation in a consistent way for all models and logs. This paper fills this gap by postulating a number of axioms for quantifying precision consistently for any log and any model. Further, we show through counter-examples that none of the existing measures consistently quantifies precision.

Felix Mannhardt, Niek Tax

Process mining analyzes business processes based on events stored in event logs. However, some recorded events may correspond to activities on a very low level of abstraction. When events are recorded on a too low level of granularity, process discovery methods tend to generate overgeneralizing process models. Grouping low-level events to higher level activities, i.e., event abstraction, can be used to discover better process models. Existing event abstraction methods are mainly based on common sub-sequences and clustering techniques. In this paper, we propose to first discover local process models and then use those models to lift the event log to a higher level of abstraction. Our conjecture is that process models discovered on the obtained high-level event log return process models of higher quality: their fitness and precision scores are more balanced. We show this with preliminary results on several real-life event logs.

Niek Tax, Benjamin Dalmas, Natalia Sidorova et al.

Local Process Models (LPM) describe structured fragments of process behavior occurring in the context of less structured business processes. Traditional LPM discovery aims to generate a collection of process models that describe highly frequent behavior, but these models do not always provide useful answers for questions posed by process analysts aiming at business process improvement. We propose a framework for goal-driven LPM discovery, based on utility functions and constraints. We describe four scopes on which these utility functions and constrains can be defined, and show that utility functions and constraints on different scopes can be combined to form composite utility functions/constraints. Finally, we demonstrate the applicability of our approach by presenting several actionable business insights discovered with LPM discovery on two real life data sets.

Niek Tax, Ilya Verenich, Marcello La Rosa et al.

Predictive business process monitoring methods exploit logs of completed cases of a process in order to make predictions about running cases thereof. Existing methods in this space are tailor-made for specific prediction tasks. Moreover, their relative accuracy is highly sensitive to the dataset at hand, thus requiring users to engage in trial-and-error and tuning when applying them in a specific setting. This paper investigates Long Short-Term Memory (LSTM) neural networks as an approach to build consistently accurate models for a wide range of predictive process monitoring tasks. First, we show that LSTMs outperform existing techniques to predict the next event of a running case and its timestamp. Next, we show how to use models for predicting the next task in order to predict the full continuation of a running case. Finally, we apply the same approach to predict the remaining time, and show that this approach outperforms existing tailor-made methods.

Niek Tax, Emin Alasgarov, Natalia Sidorova et al.

Process mining is a research field focused on the analysis of event data with the aim of extracting insights in processes. Applying process mining techniques on data from smart home environments has the potential to provide valuable insights in (un)healthy habits and to contribute to ambient assisted living solutions. Finding the right event labels to enable application of process mining techniques is however far from trivial, as simply using the triggering sensor as the label for sensor events results in uninformative models that allow for too much behavior (overgeneralizing). Refinements of sensor level event labels suggested by domain experts have shown to enable discovery of more precise and insightful process models. However, there exist no automated approach to generate refinements of event labels in the context of process mining. In this paper we propose a framework for automated generation of label refinements based on the time attribute of events. We show on a case study with real life smart home event data that behaviorally more specific, and therefore more insightful, process models can be found by using automatically generated refined labels in process discovery.

Niek Tax, Natalia Sidorova, Reinder Haakma et al.

Process mining techniques focus on extracting insight in processes from event logs. In many cases, events recorded in the event log are too fine-grained, causing process discovery algorithms to discover incomprehensible process models or process models that are not representative of the event log. We show that when process discovery algorithms are only able to discover an unrepresentative process model from a low-level event log, structure in the process can in some cases still be discovered by first abstracting the event log to a higher level of granularity. This gives rise to the challenge to bridge the gap between an original low-level event log and a desired high-level perspective on this log, such that a more structured or more comprehensible process model can be discovered. We show that supervised learning can be leveraged for the event abstraction task when annotations with high-level interpretations of the low-level events are available for a subset of the sequences (i.e., traces). We present a method to generate feature vector representations of events based on XES extensions, and describe an approach to abstract events in an event log with Condition Random Fields using these event features. Furthermore, we propose a sequence-focused metric to evaluate supervised event abstraction results that fits closely to the tasks of process discovery and conformance checking. We conclude this paper by demonstrating the usefulness of supervised event abstraction for obtaining more structured and/or more comprehensible process models using both real life event data and synthetic event data.

Niek Tax, Natalia Sidorova, Reinder Haakma et al.

Process mining techniques aim to extract insights in processes from event logs. One of the challenges in process mining is identifying interesting and meaningful event labels that contribute to a better understanding of the process. Our application area is mining data from smart homes for elderly, where the ultimate goal is to signal deviations from usual behavior and provide timely recommendations in order to extend the period of independent living. Extracting individual process models showing user behavior is an important instrument in achieving this goal. However, the interpretation of sensor data at an appropriate abstraction level is not straightforward. For example, a motion sensor in a bedroom can be triggered by tossing and turning in bed or by getting up. We try to derive the actual activity depending on the context (time, previous events, etc.). In this paper we introduce the notion of label refinements, which links more abstract event descriptions with their more refined counterparts. We present a statistical evaluation method to determine the usefulness of a label refinement for a given event log from a process perspective. Based on data from smart homes, we show how our statistical evaluation method for label refinements can be used in practice. Our method was able to select two label refinements out of a set of candidate label refinements that both had a positive effect on model precision.

Niek Tax

Background: Relevance to industry and scientific rigor have long been an area of friction in IS research. However little work has been done on how to evaluate IS research relevance. Kitchenham et al [13] proposed one of the few relevance evaluating instruments in literature, later revised by Daneva et al [7]. Aim: To analyze the practitioner/consultant perspective checklist1 for relevance in order to evaluate its comprehensibility and applicability from the point of view of the practitioner/consultant in the context of an advanced university classroom. Method: Five master level students in the field of IS assessed a set of 24 papers using the relevance checklist1. For each question in the checklist, inter-rater agreement has been calculated and the reasoning that the practitioners applied has been reconstructed from comments. Results: Inter-rater agreement only showed to be slight for three questions and poor for all other questions. Analysis of comments provided by the practitioners showed only two questions that were interpreted in the same way by all practitioners. These two questions showed significantly higher inter-rater agreement than other questions. Conclusions: The generally low inter-rater agreement could be explained as an indication that the checklist1 is in its current form not appropriate for measuring industry relevance of IS research. The different interpretations found for the checklist questions provide useful insight for reformulation of questions. Reformulations are proposed for some questions.