Khairidine Benali

Jean-François Brethé

François Guérin

Marc Gorka

Ali Sayah

A HUMANOID TORSO FOR PALLETIZATION IN LOGISTICS WAREHOUSES

This paper presents a new motion controller for object manipulation in 6D-space with a dual-arm robot manipulator. Current industrial systems often consist of a single robot arm commanded through a teach pendant. These systems are unable to pick and place boxes with different dimensions because in most of the pick and place applications, the robot arm is using a specific endeffector (generally an electric or pneumatic gripper) to pick the object. Hence the variety of objects is highly limited. This is the reason why the gripper manufacturers offer a wide variety of grippers to cover a wide range of applications. In the specific context of warehouse, the robot has to deal with a large variety of object, and has for instance to grasp boxes of different dimensions. It is then difficult to use robots in a similar manner as before. We proposed in this project to introduce a dual-arm manipulator, settled on a humanoid torso to grasp boxes of different dimensions by applying a contact on the lateral faces of the boxes and control the contact forces. Our work involves a dual-arm humanoid robot with two Universal Robots (UR10) arms and a torso (CROM) for manipulating big and/or heavy objects. The motion controller has been designed for coordinated manipulation according to the desired trajectory of the object. To prevent the objects from drifting and falling, an hybrid forcemotion controller is implemented using sensors located at the end-effectors. The different components (arms, torso, camera, force sensors...) of the system are controlled using ROS, which is an open-source meta-operating system distributed for research and development in robotics.

Introduction

Industrial robots have been used in manufacturing lines for many years for their simplicity of programming through a teach pendant by giving a set of points for following a trajectory in order to achieve repetitive tasks. But in most of the pick and place applications, the robot arm is using a specific end-effector (generally an electric or pneumatic gripper) to pick the object. Hence the variety of objects is highly limited. This is the reason why the gripper manufacturers offer a wide variety of grippers to cover a wide range of applications. In the specific context of warehouse, the robot has to deal with a large variety of object, and has for instance to grasp boxes of different dimensions. It is then difficult to use robots in a similar manner as before. We proposed in this project to introduce a dual-arm manipulator, settled on a humanoid torso to grasp boxes of different dimensions by applying a contact on the lateral faces of the boxes and control the contact forces. Some works have already been done in the field with successful results. The authors in [START_REF] Fernando Almeida | Force impedance control: a new control strategy of robotic manipulators[END_REF] proposed a Force-Impedance control by switching between two behaviors. The first is a limited impedance control and the second one is a position limited force control. The control is based on two cascaded controllers: a standard impedance controller, as an internal loop controller and an integral force controller used as an external loop controller. The simulation of the proposed controllers, provides a good tracking in position, impedance and force. Some other research works also focus in control of dual arms in the context of sliding mode control [START_REF] Nurkan Yagiz | Load transportation by dual arm robot using sliding mode control[END_REF], [START_REF] Woosoon Yim | Sliding mode cooperative motion control of dual arm manipulators[END_REF], which involves the control in presence of the dynamic parameters of the robots and the objects. The main idea presented is a sliding mode controller which is implemented for the trajectory tracking by taking into account the internal forces. A study of the dynamics of dual arms working together to move an object is also derived to design the sliding mode controller and then compute the control law. The problem of chattering in the controller is solved by replacing the switching sliding mode with a continuous saturation function. A robust control strategy is proposed by the authors in [START_REF] Liu | Robust control of planar dualarm cooperative manipulators[END_REF] for a planar dual arm manipulator robot. It is based on a dynamic study of the object and on the grasping constraints (desired force, contact and friction conditions) considered to move an object by a multiple arm cooperative manipulator. They have proposed some conditions to be satisfied for no slippage by friction constraints and contact. An algorithm is applied for the optimization of the energy consumed by the arms subjected to two cases of equality and inequality constraints of grasping. The proposed controller was a switching sliding algorithm. For eliminating the phenomenon of chattering, it is replaced by a saturation function.

Other works concentrate on impedance control. It is based on the internal force of dual arm for coordinated manipulation objects. These works propose a robust control law for dual arm manipulators by computing the minimum desired internal force by using a data force sensor. It also introduces the frictional constraints for computing the Cartesian-space impedance control for each manipulator. The stability of the control was studied to validate the frictional constraints. The experiment was executed with two PUMA arms manipulating a rigid object and the results, show a robust control of pose in grasping object [START_REF] Bonitz | Robust internalforce based impedance control for coordinating manipulators -theory and experiments[END_REF].

In [START_REF] Thomas Wimbock | Towards Service Robots for Everyday Environments[END_REF] the authors describe a dual arm control for complex operations. In this work a singular perturbation analysis was done and they design an architecture of control using a separate Cartesian impedance control for dual arm. The experiment consisted in grasping a flat object from a table with grasping points hence to prove the robustness of the controller. The authors in [START_REF] Hamid Sadeghian | Global impedance control of dual-arm manipulation for safe interaction[END_REF] developed a strategy of a centralized impedance control to implement a compliant behavior to the object grasping by the dual arms. They use the compliance in three levels i.e. the object, the endeffector and the body. A dynamic modeling of manipulators along with the object is done. Internal and external null space impedance control is proposed in series, to impose an impedance behavior between object/environment, end effectors/object interaction and body/enviro -ment interactions. The control loop is verified through simulations using two 7-DOF KUKA robots. The approach developed in [START_REF] Yun | An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations[END_REF] presents simultaneous control of trajectory and interaction forces in dual arm configurations. A system composed of two planar robots and an object realising a closed chain kinematics is presented and the dynamic equation of motion is computed by the Lagrange multipliers. A non linear feedback control is proposed by applying a systematic nonlinear feedback technique to motion equations of the closed chain. A simulation of the model has been presented for indicating the advantages of this controller.

More recently a hybrid position/force controller is used by the authors in [START_REF] Kraus | Hybrid position/force coordination for dual arm IROS[END_REF], [START_REF] Benali | Dual arm robot manipulator for grasping boxes of different dimensions in a logistics warehouse[END_REF] to achieve the coordination of dual arm manipulation through a master/slave action by controlling the force in each direction for the manipulation of flexible materials. The strategy of control is developed by studying the bending of a flexible beam, consisting of providing a motion along a certain direction. The other directions are controlled in force. The control loop used, consists in computing the position whereas the force controllers are translated to joint space velocities via the Jacobian pseudoinverse. Another work presents a control strategy for simultaneously inserting multiple boxes in a master box using dual arms. The controller uses the forces applied by the arms and is based on the virtual spring damper hypothesis. The task planning is inspired from human beings meaning, to make contact with each end of the box and press them together with a suitable force to be able to grasp the multiple boxes [START_REF] Kim | Control strategy for simultaneously inserting multiple boxes with dual arm manipulator[END_REF]. The industrial robots are able to do repetitive tasks without any kind of interaction. A sensor based dual arm is a novel system used for general tasks with bimanual hybrid motion/force control. The operator can use hand motion gestures to achieve a desired position of the object and a 3D camera can track the movements in real time and at the same time the force control tries to maintain the grasping. The whole control in this work consists of a software ROBOT RACONTEUR using a 15 DOF Yaskawa Motoman with a kinect 3D camera and force /torque sensors for the feedback [START_REF] Daniel Kruse | A sensor-based dual-arm tele-robotic system[END_REF].

The main goal of our work is to study and develop an industrial robust system able to manipulate big and/or heavy loads by coordinated manipulations and respect of the force applied by both arms. In this paper we present a new controller for dual industrial arms for grasping and manipulation of a rigid object. The control strategy was developed (hybrid force/position controller) on the ROS middleware. Compared to the related works, our goal consists in making the cardboardbox move according to a desired trajectory and to derive from that the motion of each arm. Our work consists in motion control of dual arms for palletizing/depalletizing tasks in the logistics industry, when the parcels have different sizes. In this industry there is a need to manipulate products with a large variability in size, weight and texture.

Dual arm system description

The platform used is shown on figure 1.

Figure 1: The CROM robot with dual UR10

It is a semi humanoid dual arm robot consisting of two universal robot arms UR10 each with 6-DOF and a torso CROM with 1-DOF. The CROM is composed of a head equipped with a camera XTION 3D actuated by two dynamixel pro H42 for the pan tilt movements. The end of each arm is equipped with a Robotiq force/torque Sensor FT 150.

The components of our system are coordinated by ROS (Robot Operating System) that provides interprocess message passing services (IPC) in a network.

Modeling of the Robot

The simplified kinematic model of the UR10 arm is shown on figure 2.

Figure 2: Kinematic model of UR10 arm

In order to adjust the robot's controller, a kinematic modeling is done by the Denavit Hartenberg (DH) method for its simplicity and capability to modeling any kind of serial manipulator. The system at hand consists of three branches including one torso and two arms (we denoted the arms as arm left and arm right). Each arm branch has six DOF (3 for the desired position and 3 for the orientation of the end effector). Each arm is modeled by using the DH convention.

Figure 3: Denavit-Hartenberg (DH) parameter

A homogeneous transformation for each link has been calculated by computing the overall matrix and by multiplying the individual transformations matrix from the origin to the goal point.

We can compute the transformation between the base frame and the effector frames with the following equations:

= (1)
Let us consider the grasping problem by a dual arm. For studying the transformation between the base frame of the robot and the object grasped we consider that a closed kinematic chain is formed by the torso CROM and the dual UR10 arms. Considering the forward kinematic model of each arm is known, we can locate the object in the base frame by the geometric relationship. We assume that the center of gravity (Xg;Yg;Zg) located at the center of the cardboard box. The coordinates of the other component of the system are defined such as shown on figure 4. .

π

-.

-. . π .

π .

[X b ,Y b ,Z ]: Torso frame.

[X l ,Y l ,Z l ]: Left arm end effector frame.

[X r ,Y r ,Z r ]: Right arm end effector frame.

[X ,Y ,Z ]: Object frame.

[X l ,Y l ,Z l ]: Base frame of the left arm (fixed to the body of the torso).

[X r ,Y r ,Z r ]: Base frame of the right arm (fixed to the body of the torso). are dependent on the installation of the system i.e they are constant relative to the geometry of the torso.

Task space control

The task space control [START_REF] De Wit | Task space control[END_REF] provides the ability to control the end effector in 6D space by controlling the positions and the orientation of the end effector by minimizing or eliminating the position and orientation error. UR10 is a 6-DOF serial link manipulator, provided with an internal low level dynamic controller which is able to compensate the gravity and the non-linearities. This controller cannot be modified to the access constraints. However the input of many industrial robots such as UR10, is a vector of 6 joints angles calculated through a trajectory generator (such as the ROS package Moveit).

Figure 5: Diagram of the task space control

With is the desired position and the actual position. The angular ̇ and linear velocities are related to the joint velocities by:

ϑ l =J q q l ̇ (3) ϑ r =J q q r ̇
and are the joints angles vector of the left arm and right arm respectively, is the Jacobian matrix. l and r contain the linear and angular velocities of the left and right end effectors.

l =[ ω ] r =[ ω ] (4)
The joint velocities are computed by solving the differential equation for ̇ at measured joint angles and the joint positions q(t) can then be obtained by integration the velocity solution over time.

Given the desired position and orientation of the end effector ( , ) and the actual pose ( , ), let us denote the position and orientation error by: e = -and =ф( ) We define ф as a quaternion vector to represent the orientation. The relationship between the angular velocity and the quaternion velocity can be expressed by:

ф ̇ =[ J ф) ]ω (5)
is the Jacobian related the angular velocity to the quaternion velocity. We can adjust the Jacobian to change from joint velocity to quaternion velocity:

ф ̇ = J ф ̇) J ω ̇ = J ω ф ̇, ) ̇ (6)
J is the Jacobian associated with the end effector angular velocity.

The task space controller will then map the end effectors error to joint velocities and the task space kinematic control law for both arms can be written as:

̇= -K. e (7) With =[ J ω ф ̇, ] (8)
e is the error vector [e ,e r ] , K is the gain matrix and J † = -is the pseudoinverse of the matrix .

Force control

The main objective of the admittance controller is to follow the forces acting in the end effector in each direction of the task space, by imposing a dynamic relation between the position of the end effector and the force applied to the object. The measurement from a force/torque sensor is used for designing the control law with a gain factor K. The output is then a desired Cartesian velocity resulting from the input force.

The UR10 arm does not provide any directly accessible means for the control via joint torques. We can use a force sensor, to implement an admittance controller, i.e. a controller which generates velocity commands based on the measured forces.

Figure 6: Diagram of the UR10 arm with admittance control

Denote that X l,r = (P rl, ,R l,r ). As recommended in [START_REF] Joris Sijs | Combined position&force control for a robotic manipulator[END_REF], [START_REF] Wilfinger | Integral force control with robustness enhancement[END_REF] for force control, the control law can be written:

ϑ l = λK e l ϑ r = λK e r [START_REF] Kraus | Hybrid position/force coordination for dual arm IROS[END_REF] with K is a diagonal matrix of damping coefficients, λ is a constant, such as λ ϵ [0,1[ when e < 0 (moving forward) and λ =1 when e > 0 (moving backwards).

In our case, we are just interested in the force between the two arms i.e. the grip force applied by the two end effectors. These forces lie along the line between the contacts, i.e. the line which is passing through both contact points. We then compute the normal (between the two grippers) vector of the two arms as :

η= - || -|| (10)
The projection of the forces at the normal vector between the two end effectors (left arm and right arm) provides a possibility of controlling the robot for maintaining a stable grasp at the time of movement with respect to the direction of grasping.

= η = η

The force measured by the force/torque sensors are ( , ). The force error of each arm is projected along the normal vector between the two end effectors meaning it is projected along the center of the sensors (force/torque sensor of each arm) to apply an equal force on the object. The force control law is:

X l,r = λK ( , -, ) η (12)
, the desired force.

By combining ( 7) and ( 12), the hybrid force/position control law becomes:

̇= -K. e + -λK (13)

Results

The low-level interface of the UR10 arm controller is executed with a frequency of 125 Hz. The time necessary for the robot to update a new command joint angle is 8ms for a valid consideration of input. We created our controllers using the package controller manager [START_REF] Wilfinger | Integral force control with robustness enhancement[END_REF] implemented in ROS provide a hard-real time architecture consisting of loading, unloading, starting and stopping controllers. The experiments were conducted to move a cardboard box following a circular trajectory with radius of 0.2 m along a horizontal plan (figure 7).

=[ , Y - , Z dr , , , ] (14)
The trajectory chosen for the object is: -+ -= is the radius of the circle, is the gripped object frame. , are the left and right end effector frames.

The box is grasped from an initial position and while still holding it, a trajectory is executed in space by both arms to check the performance of the controller. The performance is related to the fact that both the arms should enforce a good grasp so that the box doesn't fall down by slipping. The result is evaluated by observing the process and also monitoring the gripping distance between the two arms. This distance is equal to the width of the box. If the distance between arms remains the same from the starting point to the end of the trajectory or either it remains within a certain bound of minimal error, which still ensures good grasp by both arms. In the plots (figure 8) it can be observed that the grip force applied by the robot varies proportionally to the position error. It is observable that the force profile is almost constant when the offset (error) between the end effector position is minimum.

Figure 8: Position error (P(t)-P0) and force

The results shows the proportionality between the error and the force in the direction of the movement, in order to compensate the error and avoid falling of the box due to slippage. The robot was able to hold the box along a path with a collaborative behavior that is a composition of force and position for the compensation of the error.

Figure 9: Position error (P(t)-P0) and force in velocity x8

To evaluate the behavior of the controller a similar experience was derived in case of a velocity 8 times more than the previous one (x8). In this case (figure 9) the errors increased with the increase of speed. It was found that the maximum error was 1.4mm for the first experiment, and increased to 5.2mm when the speed is multiplied by 8 on the same trajectory. This show that the grip force applied also increases proportionally to compensate the error. The robot behavior show a good compensation, allowing small deviations from the desired trajectory and a good reaction to the position error during the trajectory.

8

Discussion and future work

In this research work we have tested a hybrid force position controller in a dual arm arrangement to test the grasping of packages in the industrial environment. The present controller has shown good performance with some limitations for handling a box. This leads to further investigation for the refinement of the controller for an optimal performance, in the presence of limitations and constraints which are, fixed orientation of the grippers, the material of the package, the rigidity and flexibility, and the speed of handling. This work has given an insight into the complexities involved in the process of grasping and placing in the industry, and what effective strategy can be employed to overcome the challenges.

Figure 4 :

 4 Figure 4: Closed kinematic chain The kinematic equation is computed by considering the left and the right arms:

.

1

 1

Figure 7 :

 7 Figure 7: Trajectories of the left and right arms obtained from the trajectory of the cardboard box. Our work consist in considering the trajectory of the object (figure 4) and deriving the motion of the arms. For this a path planning has been done to compute the postures of each arm according to the desired trajectory of the object chosen by the user. =[ , Y , Z , , , ] =[ , Y + , Z dl , , , ] (14) =[ , Y -, Z dr , , , ]


Jorge Martinez-Gil
email: jorge.martinez-gil@scch.at

Optimizing Readability Using Genetic Algorithms

Keywords: Text readability, Text Optimization, Genetic Algorithms

This research presents ORUGA, a method that tries to automatically optimize the readability of any text in English. The core idea behind the method is that certain factors affect the readability of a text, some of which are quantifiable (number of words, syllables, presence or absence of adverbs, and so on). The nature of these factors allows us to implement a genetic learning strategy to replace some existing words with their most suitable synonyms to facilitate optimization. In addition, this research seeks to preserve both the original text's content and form through multi-objective optimization techniques. In this way, neither the text's syntactic structure nor the semantic content of the original message is significantly distorted. An exhaustive study on a substantial number and diversity of texts confirms that our method was able to optimize the degree of readability in all cases without significantly altering their form or meaning. The source code of this approach is available at https://github.

Introduction

Readability is a measure that tells us how easy it is to read a text. It corresponds to the level of literacy that is expected from the readers in the target audience. In this way, readability is considered one of the most critical factors that facilitate the user experience when consuming information. It is crucial because it is key to establishing a trusting relationship between information producers and consumers. It must be considered that some factors, such as complexity, legibility, or typography, contribute to making a text readable. However, not all factors are quantifiable and cannot be optimized by automatic techniques. In this paper, we focus solely and exclusively on factors of a quantifiable nature, which always revolve around basic or advanced statistics associated with the text to be optimized.

Therefore, text readability refers to how simple it is to read and comprehend a given text, depending on its unique characteristics. These characteristics are usually measurable through metrics like the number of syllables in a sentence. The diversity of words used to create a readability score can be used to gauge this measure [START_REF] Collins-Thompson | Computational assessment of text readability: A survey of current and future research[END_REF]. Therefore, ORUGA is intended to facilitate the reader's ability to understand a text by optimizing its readability.

In the context of this work, a clear distinction between readability and quality should be made.

Quality emphasizes essential elements like grammar, spelling, and voice. However, the goal of producing textual information as plainly as possible and better matching it with its audience is what is meant when a text is said to be readable. In this way, text readability partially overlaps with the notion of text difficulty, which is also an essential aspect of human language, and has an impact on the daily lives of most people who consume written information.

Our research is based on the premise that readability can be measured by considering metrics related to the text and then using a specific mathematical formula to calculate it. Because different readability scores are calculated using different mathematical formulas, it is possible to design a strategy that replaces many of the terms in the text with synonyms using a global optimization scheme. Such optimization is about maximizing or minimizing the result yielded by such mathematical formulas at the user's convenience. In practice, such a strategy can be implemented through a genetic algorithm, as shown throughout this work.

Therefore, our research offers a viewpoint from the field of computer science, concentrating on the fundamental text representations and metrics utilized by readability assessment methods. In this way, the most significant contributions of this work to state-of-the-art are the following:

• We present, for the first time, a technique that can automatically optimize the readability of any text, i.e., we can minimize or maximize the degree of readability of a text automatically without substantive changes.

• We study which are the best sources of synonyms currently available for text readability optimization. Specifically, we have studied Wordnet, word2vec, and web scraping and established a classification around optimizing up to ten texts of different natures.

• We present an additional method based on multi-objective optimization, whose mission is to ensure that the minimum number of words needed in the original text is replaced in such a way that the structure of the text is not impacted.

• Last but not least, we studied several strategies that allow us to measure (and therefore optimize) the semantic distance between the original text and the generated text. In this way, the impact on the original text's meaning can be controlled.

This research work is structured as follows: Section 2 shows state-of-the-art methods and tools for improving text readability. Section 3 presents the technical details of our proposal; these technical details are based on the design of a genetic cutting strategy that allows us to explore a vast search space while consuming a reasonable amount of resources. Section 4 explains how to minimize the impact on the form of the original text using a multi-objective optimization technique. Section 5 shows how to preserve the essence of the original text by ensuring that the distance between the original text and the text obtained is kept as small as possible. It is necessary to remark that sections 3, 4, and 5 present information about the design of different experiments and the raw results obtained, and their subsequent analysis. Finally, we conclude with the main lessons that can be learned from this research.

State-of-the-art

Let us begin with a formal definition of readability; for instance, [START_REF] Chall | Readability revisited: The new Dale-Chall readability formula[END_REF] defines readability as the "total number of elements in a given text that affect a reader's success." This reader's success is a measure of how well a text that is read at an optimal speed can be understood. At the same time, [START_REF] Mc Laughlin | Smog grading-a new readability formula[END_REF] defines readability as "the level at which certain people find reading material convincing and understandable." Beyond these definitions, we are particularly interested in the quantifiable aspects of readability, i.e., what can be objectively measured. Otherwise, it would not be easy to proceed to its optimization using a computer. Let us see what the literature says about these quantifiable aspects.

Text readability in the scientific literature

Readability metrics usually use simple features to calculate the degree of readability of a text. Some commonly used features are the number of sentences or words, the ratio of unique words, the total number of syllables, the proportion of unique words in the text, the number of digits, the number of words with many syllables, etc. Although, at first, it may seem that these metrics are simplistic, they are very commonly used for two important reasons: they are much cheaper and faster to use than the alternatives consisting of human surveys, and according to experts, they usually give exceptionally reliable results that are in line with reality.

The goal of improving readability is to increase the chances that readers can understand the thoughts and ideas reflected in the text. So that misunderstanding is minimized, information processing is facilitated without requiring much effort and energy consumption. With this goal in mind, many sources can be found that advise how to improve a text's readability. However, these are manually compiled protocols that a human operator must translate into reality by modifying the text manually. For example, for a given metric, it is better to shorten sentences; for another, it is better to replace complex words with simpler ones, etc. This is precisely where our contribution to the state-of-the-art lies. Optimizing texts automatically using a metric as a target means we do not have to concern about taking any manual action leading to altering the text. The genetic algorithm will find a way to proceed automatically.

Why is text readability important?

There are several contexts and population groups for which readability is critical. Especially when it is necessary to convey a written message to an audience. For example,

• Teachers need to be sure of the readability of a text before deciding whether it is appropriate for their students. This is particularly important in language learning. With the method presented here, the text can be optimized for a certain niche of learners.

• In the world of advertising, readability allows for building a trust relationship between advertisers and potential consumers. Advertising goods or services using texts with high readability is usually not a good idea since the message might not reach an essential part of the population. This is even more important in the search engine optimization sector, as many search engines use readability metrics as a ranking factor when responding to user searches.

• Readability is also relevant for professionals who work on websites [START_REF] Pantula | A machine learning-based model to evaluate readability and assess grade level for the web pages[END_REF], news [START_REF] Qin | Comparable study on readability of machine generated news and human news[END_REF], or even educational materials [START_REF] Ante | The relationship between readability and scientific impact: Evidence from emerging technology discourses[END_REF]. In some countries, there is even a legal requirement that government agencies provide textual information with certain readability levels to reach the entire population.

Readability metrics

There are several metrics to quantify how readable a text is [START_REF] Meade | Readability formulas: cautions and criteria[END_REF]. Most metrics have been designed for the English language [START_REF] Maqsood | Assessing english language sentences readability using machine learning models[END_REF], although works also explore readability in other languages [START_REF] Madrazo Azpiazu | Is cross-lingual readability assessment possible[END_REF]. Without being exhaustive, we can mention, in chronological order, some of the metrics that enjoy or have enjoyed more significant popularity when dealing with the English language.

Text readability depends not only on the characteristics of the text but also on the educational background of the individuals interested in understanding the text. We will see this reflected below when measuring readability using formulas. We will see how readability metrics take a text as input and calculate a numerical score that usually corresponds to the level of education required to understand the text.

Dale-Chall readability

The Dale-Chall readability formula [START_REF] Dale | A formula for predicting readability: Instructions[END_REF]) requires a list of 3,000 words that fourth-grade U.S. students could reliably understand, as shown in Equation 1.

DCRF = 0.1579
dif f icult words total words × 100 + 0.0496 total words total sentences

(1)

SMOG readability

The SMOG readability level [START_REF] Mc Laughlin | Smog grading-a new readability formula[END_REF] can be assessed through a formula originally used for checking health messages, as shown in Equation 2. It corresponds to the years of education necessary to understand the text.

SM OG = 1.0430 number of polysyllables × 30 number of sentences + 3.1291

(2)

ARI readability

The ARI assesses the U.S. grade level required to read a text [START_REF] Senter | Automated readability index[END_REF]. In some ways, it is similar to other formulas. Its difference is that rather than counting syllables, it counts characters: the more characters, the more complex the word. It also counts sentences as shown in Equation 3. This sets it apart from some other formulas. 4, is a metric based on grade levels that is used commonly in the insurance industry. Grade levels made it much easier for people to understand [START_REF] Kincaid | Derivation of new readability formulas (automated readability index, fog count and flesch reading ease formula) for navy enlisted personnel[END_REF]. A Flesch Kincaid Grade Level (FKGL) between 8 and 10 means that the text should be accessible to the public. FKGL remains the most widely-used formula today.

F KGL = 206.835 -1.015 total words total sentences -84.6 total syllables total words (4)

Over the past decade, several natural language processing (NLP) techniques have been proposed to determine the readability of a text. Thus, as opposed to the classical approach of using formulas that measure a limited set of text features, these new variants have attempted to measure the difficulty of understanding sentences and words and even the complexity of the syntax [START_REF] Martinc | Supervised and unsupervised neural approaches to text readability[END_REF]. Even some techniques based on predictors of readability, such as cohesion and coherence, have received considerable attention. However, so far, these approaches have yet to be able to predict the readability of a text better than the classical techniques discussed here [START_REF] Todirascu | Are cohesive features relevant for text readability evaluation[END_REF].

Semantic Similarity

The field of semantic similarity measurement (Martinez-Gil, 2022) is one of the most active in several different research communities (information retrieval, database integration, natural language processing, and so on) [START_REF] Rus | SEMILAR: the semantic similarity toolkit[END_REF]. This is due to its significant implications on many available frameworks, methods, and tools [START_REF] Navigli | An overview of word and sense similarity[END_REF] both in industry and academia. The literature around this topic has skyrocketed in the last few years [START_REF] Chandrasekaran | Evolution of semantic similarity -A survey[END_REF]. However, most research works focus on determining the similarity between words [START_REF] Zhu | Computing semantic similarity of concepts in knowledge graphs[END_REF], phrases, or documents [START_REF] Martinez-Gil | Automatic design of semantic similarity controllers based on fuzzy logics[END_REF][START_REF] Martinez-Gil | A novel method based on symbolic regression for interpretable semantic similarity measurement[END_REF].

In this way, rarely the likelihood of effectively throwing out the most similar words to a given one has been discussed. To this effect, there are synonym libraries that have been manually compiled and some word embedding techniques that do the job well. The most promi-nent solutions in this direction are WordNet [START_REF] Pedersen | Wordnet: : Similarity -measuring the relatedness of concepts[END_REF], word2vec [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF], or BERT [START_REF] Devlin | BERT: pre-training of deep bidirectional transformers for language understanding[END_REF]. However, it must be taken into account that the resource requirements for techniques based on the computation of word embeddings are very high (Martinez-Gil & Chaves-Gonzalez, 2022).

Contribution over the state-of-the-art

Determining text readability based on a formal analysis of the structures and words used has been a recurring theme in the literature over the last few years. As a result, many metrics have been proposed to measure text readability. A common denominator of all these metrics is that a high score usually means the text is difficult to understand. In other words, a higher degree of study is needed to understand it. For this reason, many communication professionals often use tools to help them discern whether the text fits a given audience. However, none of these tools can do the professional's job automatically, which is why our contribution is essential.

To the best of our knowledge, this is the first time anyone has proposed automatically improving the readability of text without significantly altering the content or the text's form. In addition, we put this innovative method through its paces using a wide range of texts that varied in subject matter and level of readability. Furthermore, we provide the source code of the first implementation for anyone interested in experimenting with or improving the method.

Part I: Design and Implementation of a Functional Solution

In the following, we explain our proposal for text readability optimization using a method based on genetic algorithms. In this section, we outline the technical preliminaries, discuss the implementation, show an illustrative example of how our approach works in practice, and conduct an experimental study using real data and use cases that can help us get an idea of the performance of this approach in practice.

Technical Preliminaries

Our hypothesis is that we can find a set of synonyms to replace some words in the original text so that the value returned by the readability formula can be optimized. For example, if the readability formula rewards or penalizes long words, we have to find synonyms of less length. In reality, we only have to concern about understanding which formula best represents readability in our specific scenario and indicate it as a fitness function. The genetic algorithm will understand how to proceed. Thus, we are faced with a classical optimization problem.

We intend to act only on the vocabulary since it is one of the most critical parts of that language. It is widely assumed that vocabulary is the essential part of a language because, without vocabulary, it is impossible to compose any message [START_REF] Wilkins | Linguistics in language teaching volume 111[END_REF]. We do not act on proper nouns, prepositions, or other stop words to avoid distorting the original message.

While this problem can be solved by a brute-force search over the range of the words of a given text w 0 , w 1 , ..., w n , the GA method scales very well when dealing with large texts. In this case, a brute-force search would be prohibitively expensive. We could act on other aspects, such as the structure, but then we would risk distorting the original text's essence again.

Our idea is to find the combination of words (which will be encoded in the form of an individual) that optimizes the desired objective. The choice of the fitness function is effortless and has the advantage that the solution automatically identifies what kind of words lead to the optimization.

In this work, we work with three main sources of synonyms:

• WordNet [START_REF] Miller | Wordnet: a lexical database for english[END_REF], which is a thesaurus that has been manually compiled. It is probably one of the most widely used dictionaries in information systems and will give us several alternatives to substitute each candidate word. No surprises are to be expected in this library, except perhaps the substitution of words with a synonym that has a sense far from the original. In any case, we have a solution to this problem.

• wordvec [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF], which is an approach that calculates the vectors associated with each word according to a textual corpus of relevance. Once each vector has been computed, a computation process can be performed by which the N vectors most similar to a given one are identified. This way, synonyms of relevance are obtained for the word in question. Note that this process is computationally expensive.

• Web scraping [START_REF] Mitchell | Web scraping with Python: Collecting more data from the modern web[END_REF], which consists of obtaining the synonyms from some websites, usually specialized, so that we can shuffle several alternatives per candidate word. This method obtains many high-quality word candidates, but it should be used responsibly because it can cause problems on the server side if many hundreds or thousands of requests are made.

Therefore, the method is fine for experimentation, but it would be unreasonable to exploit it.

Implementation

The implementation of this novel approach is based on a classical optimization scheme using genetic algorithms. Algorithm 1 briefly explains in pseudo-code how the whole process is performed by adapting the classical structure of the genetic algorithm [START_REF] Forrest | Genetic algorithms[END_REF] where different operators capable of implementing selection, cross-over and mutation processes are considered in order to evolve a given population towards the desired objective.

Please note that before starting the evolution process, a pre-processing of the text must be done in order to identify the candidate words to be replaced by a synonym. We propose that all words are candidates except: proper names, stop words, and prepositions. The reason for this is that they are often words for which it is really difficult to find a synonym.

Algorithm 1 Optimizing Readability Using Genetic Algorithm 1: procedure ORUGA optimizedText ← correctErrorsIfNecessary (optimizedText)

13:

return optimizedText

In relation to the genetic algorithm itself, the parametric details of the solution will be discussed below, but it is possible to see how we implement it in the form of a classical evolutionary process.

This means that a population of individuals is selected randomly, and their readability score is calculated. We then proceed with an iterative process of selection, crossover, and mutation; the best individuals are passed from generation to generation until one of the stopping criteria is met: the highest possible has been reached (unlikely), or the number of iterations has been exhausted (very likely). Finally, at the end of the evolutionary process, we correct the text in case grammatical errors are produced by substituting a synonym that does not fit the tense and the form of the sentence in which it is framed. This way, we obtain a corrected readability score, which may vary slightly from the one derived automatically. In return, we ensure that the results are usable, or at least close to being usable.

Illustrative examples

Example 1 shows us how ORUGA works with written material about science extracted from Wikipedia. In fact, our aim is to observe how ORUGA behaves when trying to minimize the FKGL readability score using synonyms from the library WordNet. Let us remember that FKGL (or one of its variants) is probably the most widely used metric and its optimization brings advantages in several fields. Please note that the text to be treated can be of any length, but to facilitate the presentation to the reader, we have chosen (and will choose throughout this paper) one that contains only several sentences.

Example 1. Science

Original text Source: Wikipedia "The sea moderates the climate and has important roles in the water cycle, carbon cycle, and nitrogen cycle. Humans harnessing and studying the sea have been recorded since ancient times, and evidenced well into prehistory, while its modern scientific study is called oceanography. The most abundant solid dissolved in seawater is sodium chloride. The water also contains salts of magnesium, calcium, potassium, and mercury, amongst many other elements, some in minute concentrations. Salinity varies widely, being lower near the surface and the mouths of large rivers and higher in the depths of the ocean; however, the relative proportions of dissolved salts vary little across the oceans." FKGL score: 14.06.

ORUGA -minimizing the FKGL score -library Wordnet

The sea moderates the climate and has important part in the H2O cycle, C cycle, and N cycle. Humans harnessing and studying the sea have been taped since ancient times, and attested well into prehistory, while its modern scientific study is called oceanography. The most abundant solid fade out in brine is Na chloride. The H2O too contains salts of magnesium, calcium, potassium, and mercury, amongst many other elements, some in min concentrations. Salinity changes widely, being got down near the surface and the mouths of large rivers and higher in the depth of the ocean; however, the relative proportions of fade out salts change little across the oceans.

FKGL score: 11.85

As can be seen, ORUGA can optimize the textual input by first automatically identifying which words can be replaced by a synonym, and then undertaking a process of searching for synonyms that improve the results of the metric to be optimized. In this way, the impact on the initial message is minimal, although it is true that some synonyms can slightly distort the meaning of the text, and therefore final supervision by the user is required. However, there is no need to concern because this problem will be addressed later in the paper.

Let us look now at Example 2, which is a written text about the history of Austria that has been also extracted from Wikipedia, and we would like to to minimize the FKGL readability score using synonyms automatically obtained by web scraping. Once again, we can see how the genetic algorithm has acted intelligently to decrease the text readability score and therefore make the text accessible to more people. It is clear that the suitability of some words may be subject to debate, but the first objective of this research, i.e., to optimize the readability score, has been achieved. As we mentioned before, we will be concerned to outline a final product later in this paper. Finally, let us look at the opposite case, i.e., let us see if we can make a text more difficult to read without losing its essence. In Example 3, we have a text about sports also extracted from Wikipedia, and we do not want to make the text accessible to as many people as possible, but on the contrary, we want to increase the level of readability. We will now try a different metric, e.g., ARI.

Example As can be seen, after processing the fragment related to Real Madrid extracted from Wikipedia, the genetic algorithm selects synonyms that are much longer and more complicated to read to increase the ARI score. Although a use case consisting of making the text less accessible to people is hard to imagine, it may find application in some specific niches of learning, education, etc.

Experimental study

In this section, we explain the details of an empirical study that we have carried out to know the feasibility of our new method. To do so, we first established the conditions of the experiments by setting up an experimental setup. Secondly, we have run and obtained the raw results. Furthermore, thirdly, and lastly, we have proceeded with the analysis of the data obtained.

Experimental setup

Adjusting the parameters of the genetic algorithm differs from the focus of this work. Therefore, we have chosen a classical parameter setting, which has been shown to work quite well. Standard tuning of the parameters, e.g., through a grid search, is a possible line of future work. In the meantime, the parameters we have used for our experiments are the following: To test whether our approach can optimize text readability, we semi-randomly selected ten texts extracted from Wikipedia. These texts are classified into several categories engineering, geography, history, science, and sports. Some metrics, such as SMOG, require at least 30 sentences to apply their formula. For cases where we do not reach 30 sentences, we will duplicate the text until we reach that number of sentences. It should also be noted that depending on which readability category each use case represents. For example, magenta represents the highest difficulty (FKGL between 15 and 18), equivalent to an academic paper. Red represents medium-high difficulty (FKGL between 12 and 15). The black color represents a medium difficulty (FKGL between 9 and 12). Furthermore, the blue color represents a low-medium difficulty. It is estimated that up to 80% of the native English-speaking population could understand text with an FKGL between 6 and 9, which is what the blue value represents. Furthermore, every experiment was run on a standard computer with 32 GB of primary memory and an Intel Core i7-8700 processor running at 3.20 GHz on Microsoft Windows 10 64-bit. Most of the functionality has been implemented using the library PyGAD1 , an open-source Python library for building genetic algorithms.

• Population size {10,

Experiments

The first experiment is the one that is the most useful in practice. It consists of trying to minimize the readability of the ten proposed texts so that the processed text can reach the largest possible audience. To do that, we want to use readability metrics which estimate the readability of a text based on simple aspects such as syllable and word counts. We use the FKGL score since this metric, or some of its variants, has been used for decades on traditional texts, and it is still one of the most common and widely used traditional readability measures. Positive results have been obtained in all 100 experiments performed (ten runs for ten use cases).

In addition, minimum improvements, average improvements, and even maximum improvements have been achieved in the range between 0.77 and 2.73 points on the FKGL scale.

Fig 2 shows us the results obtained using the synonym calculation method using word2vec. As it is possible to see, the variance of the results is enormous, which means that using this library will make the results not very predictable. At the same time, as in the previous case, all 100 experiments were able to obtain readability improvements that ranged between 0.42 and 3.90-grade levels. Table 1 shows the summary results of the 300 experiments performed (100 for each synonym library). For WordNet, a median optimization of 1.63-grade levels is expected, very similar to Use case DCRF SMOG ARI FKGL 01/science 1.11 ± 0.17 2.03 ± 0.13 2.90 ± 0.27 2.53 ± 0.15 02/history 0.29 ± 0.12 0.71 ± 0.08 0.84 ± 0.05 0.90 ± 0.04 03/geography 0.65 ± 0.07 0.91 ± 0.04 1.17 ± 0.12 1.33 ± 0.04 04/sports 0.78 ± 0.14 0.42 ± 0.12 0.83 ± 0.05 0.93 ± 0.10 05/engineering 0.59 ± 0.06 0.60 ± 0.10 0.66 ± 0.10 0.75 ± 0.09 06/geography 0.52 ± 0.15 0.70 ± 0.10 0.77 ± 0.19 0.77 ± 0.18 07/engineering 1.03 ± 0.15 0.51 ± 0.03 1.12 ± 0.21 1.32 ± 0.01 08/history 0.77 ± 0.09 0.27 ± 0.06 0.44 ± 0.00 0.73 ± 0.17 09/sports 0.46 ± 0.06 1.06 ± 0.28 0.99 ± 0.12 0.81 ± 0.10 10/history 0.74 ± 0.04 0.65 ± 0.03 0.77 ± 0.13 0.93 ± 0.04 that achieved by web scraping. The median optimization using word2vec is the worst of the three libraries considered. Please note that we are not judging here the quality of the replacements, but the values to optimize the input text independently of the quality of the final result.

Table 2 shows a summary of all the results we have obtained. The texts have been randomly obtained from Wikipedia. The range of values shown indicates the minimum value that could be reached and the maximum value (for minimization and maximization problems respectively). We analyze the four formulas that we consider most representative, but the analysis of other formulas would not be a problem. When working with SMOG, we must be careful because the text to be analyzed requires at least 30 sentences. We have duplicated the text for these experiments so that these 30 sentences can be used.

Table 3 shows a summary of all the results we have obtained when maximizing the readability scores. As can be seen by comparing with the table above, it is much easier to increase the level of readability than to decrease it, i.e., it is easier to make a text difficult to read than the other way around.

Discussion

We have seen how it is possible to build a solution that optimizes the readability of texts of different natures. Moreover, such optimization is done respecting the content and the form of such texts, trying to minimize the impact of word replacements by synonyms that better fit the readability criteria of the different formulas we have studied. We have seen how optimization can occur in two ways. First, it can be done in such a way as to reduce the readability score, which will allow more people to understand the text perfectly. This is undoubtedly the most practical option in practice. Furthermore, secondly, it can be done to increase the readability score, allowing a smaller number of people to understand the processed text unambiguously. This option has less practical utility than can be discerned at first glance.

Based on the research we have carried out, possible improvements can be made. For example, a multi-objective optimization algorithm could simultaneously optimize the readability score by affecting as few words as possible. In this way, the impact of our method on the original text would be even more negligible. A solution front could allow the human operator to decide the trade-off between the score modification and the replaced words.

Finally, and as a limitation of our method, it can be observed that sometimes the processed text contains minor grammatical errors. This is because we have yet to use techniques that allow, for example, to choose the appropriate verb tense for the context. Here there are two alternatives. On the one hand, we can implement better methods for correcting grammatical errors to obtain a corrected readability score; on the other hand, we can give the user the option to edit or choose the word that best fits each moment.

Part II: Minimizing the impact on the form of the original text

While in Section 3, we have seen that it is possible to design a functional solution to optimize the text readability, we have also seen that the approach can be intrusive at times. That is, the replacement of many words by synonyms can lead to a distortion of the original message. For this reason, in this section, we focus on minimizing the impact of ORUGA on the original text by replacing as few words as possible. To do so, we will build a solution based on multi-objective optimization (MOO) that allows us to optimize readability and simultaneously minimize the number of replacements. This section comprises the technical preliminaries, the implementation, some illustrative examples, and an empirical study to test several texts of different natures.

Technical Preliminaries

We have already seen how in the field of text readability, there has been a great effort to build straightforward formulas that can be understood by people and have a good correlation to how easily a text can be read from a human perspective. Now we go one step further to obtain a higher quality result. MOO is a strategy in which two or more objectives are simultaneously optimized. This is the situation we find ourselves in, given that we want: on the one hand, to improve the readability of a text, and on the other hand, we want to reduce as much as possible the number of words that need to be replaced to improve readability, and thus to minimize the impact that our approach has on the original text form. Furthermore, MOO is useful when decisions must be made despite potential trade-offs between more than one orthogonal objective. Again, this is our situation because our goals of maximizing readability while simultaneously replacing the fewest possible words require us to pursue two completely different goals. In situations like this, different solutions can simultaneously fulfill all objectives. As a result, all optimal solutions ought to be regarded as equivalent merit without any external evaluation from a human operator [START_REF] Martinez-Gil | Semantic similarity controllers: On the trade-off between accuracy and interpretability[END_REF]. More formally, we can model a MOO problem as expressed in Equation 5.

min (s 1 ( x), s 2 ( x), . . . , s n ( x)) subject to x ∈ X (5)
In MOO, no solution addresses all objective functions simultaneously. As a result, the priority should be placed on finding solutions that cannot make any goals better without making at least one of the other goals worse. Therefore, a solution x 1 ∈ X is said to dominate another one x 2 ∈ X if the conditions expressed in Equation 6 are met.

s i ( x 1 ) ≤ s i ( x 2 ) ∀i ∈ {1, 2, 3, . . . , n} s j ( x 1 ) < s j ( x 2 ) ∃j ∈ {1, 2, 3, . . . , n} (6)
In this way, a solution x ∈ X is optimal if no solution might dominate it. An element x is said to dominate another element y if x is not worse than y concerning all the goals and is strictly better than y for at least one. The elements of the search space that are not dominated give rise to a Pareto front, which represents the best possible solutions to the orthogonal objectives.

Implementation

There are several implementations for MOO strategies [START_REF] Kukkonen | Gde3: The third evolution step of generalized differential evolution[END_REF]; [START_REF] Zhang | MOEA/D: A multiobjective evolutionary algorithm based on decomposition[END_REF]. It is beyond the scope of this paper to consider them all. However, we will look at one of the best ones, NSGA-II [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: NSGA-II[END_REF]. This strategy is summarized in Algorithm 2. Its mode of operation is based on the concepts of fronts and crowding distance.

NSGA-II adheres to the basic structure of a genetic algorithm but employs a different approach to mating and selection for survival. In the NSGA-II, the first step is to select individuals in a front-wise fashion. In this way, a situation will arise where it will be necessary to divide a front because it will not be possible for all individuals to survive.

The solutions are chosen according to the crowding distance for this particular splitting front.

Within the parameters of the objective space, the Manhattan Distance corresponds to the crowding distance. On the other hand, it is desired that the extreme points be maintained with each new generation, and as a result, an infinite crowding distance is assigned to them. Algorithm 2 shows us a possible implementation of this approach.

Algorithm 2 MOO Technique for Optimizing Text Readability 1: procedure ORUGA2-MOO return optimizedText NSGA-II is an example of a genetic algorithm, and it possesses the three characteristics listed below: It operates based on an elitist principle, which states that only the most privileged members of a population are permitted to be passed down to subsequent generations. In addition, it employs a mechanism specifically designed to preserve diversity (crowding distance). As a direct consequence of this, it can identify non-dominated solutions.

Illustrative examples

Since we are trying to optimize two orthogonal objectives simultaneously, it is impossible to offer a single solution. Nevertheless, we can put in the hands of the human operator a front of solutions ranging from a total optimization by modifying the most significant number of words to a minor optimization by touching a minimum number of words. It is up to the human operator to decide which solution to choose.

Example 4 shows a real trace that controls the number of words to be replaced using the MOO technique known as NSGA-II. The text on which it operates is about geography and has been extracted from Wikipedia. Once again, we must insist that although, in theory, it would be possible to edit the words manually to satisfy the criteria of a given metric, this approach is transparent and works automatically for any desired metric. Please note that the words in blue are candidates to be replaced by a synonym.

Example 4. Geography Source: Wikipedia Goal: Minimize the FKGL score by using Wordnet synonyms and minimize the words to be replaced using NSGA-II.

"Niagara Falls is a group of three waterfalls at the southern end of Niagara Gorge, spanning the border between the province of Ontario in Canada and the state of New York in the United States. The largest of the three is Horseshoe Falls, which straddles the international border of the two countries. It is also known as the Canadian Falls. The smaller American Falls and Bridal Veil Falls lie within the United States. Bridal Veil Falls is separated from Horseshoe Falls by Goat Island and from American Falls by Luna Island, with both islands situated in New York. Formed by the Niagara River, which drains Lake Erie into Lake Ontario, the combined falls have the highest flow rate of any waterfall in North America that has a vertical drop of more than 50 m (160 ft). During peak daytime tourist hours, more than 168,000 m3 (5.9 million cu ft) of water goes over the crest of the falls every minute." FKGL score: 10.72. But that open question will be addressed later in this paper.

Experimental study

This section will explain the specifics of an empirical study we conducted to determine whether this novel approach is feasible. To accomplish this, we initially prepared an experimental setup so that we could determine the parameters of the experiments. Second, we completed the test and collected the unprocessed data. We have moved forward with the analysis of the data that we have gathered, which brings us to our third and last point.

Experimental setup

As was the case in the preceding part, the meticulous fine-tuning of the MOO strategy's parameters will not be the primary focus of this work. As a result, following a brief preliminary study based on a scheme of traditional parameter settings, one configuration works quite well. As a direct consequence of this, the following is a list of the parameters that we used for our experiments:

• Population size {10, 15, 20}: 20

• Number of parents mating {10, 15, 20}: 20

• Number of genes: one per candidate word to be substituted by a synonym

• Fitness function: the user can choose among Equations 1, 2, 3, 4, words to be replaced

• Stop condition: {300, 600, 900}: 900 generations Furthermore, every experiment was run on a standard computer with 32 GB of primary memory and an Intel Core i7-8700 processor running at 3.20 GHz on Microsoft Windows 10 64-bit. Most of the functionality has been implemented using the library jMetalPy2 , an open-source Python library for designing and implementing MOO strategies [START_REF] Benítez-Hidalgo | jmetalpy: A python framework for multi-objective optimization with metaheuristics[END_REF].

Experiments

Now we will proceed with the experiments concerning minimizing the impact on the original message's form. While we focused previously on pure optimization, we focus here on minimizing the number of replaced words to affect how the message looks as little as possible.

In Figure 4, we can see a summary of the results obtained after our experiments. What we have done is try to minimize the readability score (FKGL) at the same time as the number of words to be replaced in the ten use cases we are using throughout this work. As can be seen, we always obtain a Pareto front of solutions which indicates that the fewer words replaced, the less optimization is carried out. However, it should also be noted that the fewer words replaced also means a more negligible impact on the form of the initial message. It should be noted that different colors have been used for the Pareto fronts as in the previous experiments. Each color represents the degree of difficulty of each case study.

Discussion

We have shown how it is possible to design a solution that enhances the readability of texts, and we implemented that solution through MOO techniques. In addition, this sort of optimization is carried out while paying attention to the form of the texts in question to minimize the impact of replacing words with synonyms that better fit the readability criteria of the various formulas we have researched.

As we explained earlier the paper, this kind of optimization can also occur in two distinct ways: it can be carried out to lower the readability score, making it possible for more people to comprehend the text altogether. Also, as a second possibility, it is possible to do so in order to improve the readability score, which will enable a lesser number of individuals to comprehend the processed text.

Although the solutions will always be presented as a Pareto front for human operator to choose his solution, it is also possible to define profiles: conservative, medium, and aggressive, which will opt for the conservative, medium, or more daring versions respectively without any question, without prejudice to the fact that it should be possible to manually edit a word that does not fit the context.

Part III: Preserving the essence of the original text

In Section 3, we have seen how it is possible to design and implement a functional solution to optimize the readability of any text. Although such a solution seems to work quite well, it cannot be considered fully automatic since a human user still has to evaluate whether any word used to replace original terms is not out of place in the context of the original message. In Section 4, we have used a MOO strategy to ensure that we only replace a minimum number of words in the original text in order to preserve its form, and we even go a step further and allow a human operator to decide the degree of impact of ORUGA on the form of the original text. In Section 5, we will address a remaining problem, which is to keep under control the semantic distance between the original text and the generated text so that a short distance guarantees that the original text has not been distorted, while a long-distance means that we have been able to optimize readability by a large amount, but at a high cost in terms of altering the meaning of the original text. The importance of this third and final part is that success in our strategy is what can guarantee that the solution is entirely unsupervised.

Technical Preliminaries

The additional element we will add in this part is to measure the semantic distance between the original text and the text to be delivered. In this way, we can control any significant change in the meaning of the message. This semantic distance will be the third objective in our MOO strategy.

In the literature, there are methods that allow us to determine the semantic distance between two pieces of text in a meaningful way, even when those pieces do not share any words. To do that, words are embedded as vectors using this method. It has been demonstrated to perform better than many of the methods considered to be state-of-the-art in the k-nearest neighbor's classification.

With the help of Word Mover's Distance (WMD) [START_REF] Kusner | From word embeddings to document distances[END_REF], and given pre-trained word embeddings, it is possible to automatically assess the semantic distance between two texts by computing the minimum distance that the embedded words of one text need to travel to reach the ones of another text. So, for example, we can use the WordNet library to calculate synonyms that allow us to optimize text readability. At the same time, we can use word2vec to supervise that the semantic between the generated text and the original text is minimized. We could use as a metaphor that it is an adversarial process.

The beauty of this approach is that the different synonym libraries now do not compete with each other but collaborate to try to measure (and therefore facilitate control) the semantic distance between the original text and the final text. Values close to zero will indicate that the meaning of the texts under consideration is practically equivalent, while distances approaching infinity indicate that the texts are incredibly different. Moreover, we do not have to concern about whether the genetic algorithm replaces a word with one or more words (e.g., 'considering' by 'taking into account') since the WMD is prepared for this contiguity, as it assumes by design that the texts will not have the same length. Since when using WMD, each word is matched against all other words, but weighted by a flow matrix T that ensures the semantic distance will be symmetric, even when an unequal number of words must be matched.

Implementation

In this work, we have decided to use WMD to facilitate the measurement of the semantic distance between the initial text and the text that will be delivered at the end of the process. This ensures that the synonyms used to replace candidate words are coherent. This choice is because WMD can measure the amount of semantic distance that separates two pieces of text by comparing the words that are important to each other. This is true even if the two pieces of text do not share any words.

In addition to that, the method makes use of a representation known as the bag-of-words representation. The idea behind this method is that it should be possible to figure out how far apart two different texts are by figuring out the best way to move the distribution of the source text and the text being targeted.

We can formally define our strategy, so that let d and d ′ be the embedding representation of two texts, and T ∈ R n×n where T ij ≥ 0 means how much of word i in d travels to word j in d ′ . Furthermore, the distance between i and j might be c(i, j) = x ix j . By c(i, j), we denote the cost of moving from one word to another. In order to transform d into d ′ , it is necessary to be sure that the flow from i is equivalent to d i so that j T ij = d i . In this way, the minimum cumulative cost of moving d to d ′ , given all these constraints, is provided by the solution shown in Equation 7.

arg min n i,j=1 T ij c(i, j) subject to n j=1 T ij = d i ∀i ∈ {1, 2, 3 • • • n} ∧ n i=1 T ij = d ′ j ∀j ∈ {1, 2, 3 • • • n} (7)
Therefore, we use a function that determines the distance between two texts as the cumulative sum of the minimum distance each word in one text must move in vector space to the closest word in the other text. Word embeddings derived from word2vec will be utilized for this work because of their capability to maintain critical aspects of the context in which a word is used.

WMD is used quite frequently these days to calculate semantic distances, and this is one of the reasons why. The only problem is that the complexity of computing the constrained minimum cumulative cost in the worst case is O(p3 log u), where u is the number of unique words in the text [START_REF] Skianis | Boosting tricks for word mover's distance[END_REF]. Therefore, when working with texts that contain a large number of unique words, WMD may perform poorly. However, there are some techniques that improve performance.

In the context of this work, we have used the library gensim 3 implementation of the WMD fed by the word embeddings from word2vec [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF]. In this way, what was previously a rival synonym library now becomes an adversarial library that helps keep semantic distance under control.

Illustrative examples

Example 5 provides us with information about engineering that was taken from Wikipedia. We are interested in observing how ORUGA operates while attempting to minimize the FKGL readability score, the number of words that need to be replaced, and the semantic distance between the original text and the text that has been processed. We are replacing the synonyms with the help of WordNet, and we are moving forward with the MOO with the help of NSGA-II. The ultimate goal is to ensure a very low risk of distortion of the original message that wanted to be communicated.

Example 5. Engineering

Original text Source: Wikipedia "Big data refers to data sets that are too large or complex to be dealt with by traditional data-processing application software. Data with many fields (rows) offer greater statistical power, while data with higher complexity (more attributes or columns) may lead to a higher false discovery rate. Big data analysis challenges include capturing data, data storage, data analysis, search, sharing, transfer, visualization, querying, updating, information privacy, and data source. Big data was originally associated with three key concepts volume, variety, and velocity. The analysis of big data presents challenges in sampling, and thus previously allowing for only observations and sampling. Thus a fourth concept, veracity, refers to the quality or insightfulness of the data." ARI score: 14.43. Minimize ARI score with the least risk of distorting the original message Big data bring up to data sets that are too big or complex to be dealt with by traditional data-processing application software. Data with many fields (rows) offer greater statistical power, while data with higher complexity (more attributes or columns) may lead to a higher false finding rate. Big data analysis challenges include capturing data, data storage, data analysis, search, sharing, transfer, visualization, querying, updating, information privacy, and data source. Big data was originally tied in with three key concepts volume, variety, and velocity. The analysis of big data presents challenges in sampling, and thus previously let for only observations and sampling. Thus a fourth concept, veracity, refers to the quality or acumen of the data. ARI score: 13.33 -▽ 7.62%

The example shows that we no longer operate as blindly as before. Now, we also minimize the words to be replaced and the semantic distance between the initial and the generated text. Therefore, the results are much more reasonable and can be relied upon to work in exploitation environments. The readability score optimization is less spectacular than before, but the risk of distorting the original message, both in form and content, is much more substantially reduced.

Experimental study

In this section, we have performed the empirical study to test this version of ORUGA. To do so, we designed the experiments through an experimental setup. We performed the experiments and collected the raw data. And finally, we proceeded with the analysis of the collected data.

Experimental setup

The accurate adjustment of the MOO strategy's parameters is not the primary focus here, as was the case with the previous parts of this research. One configuration works quite well after a brief preliminary study based on a conventional parameter-setting strategy. This came about as a result of what was mentioned above. The following is a list of the parameters that we have used:

• Population size {10, 15, 20}: 20

• Number of parents mating {10, 15, 20}: 20

• Number of genes: one per candidate word to be substituted by a synonym

• Fitness function: Equations 1, 2, 3, 4, words to be replaced, and WMD [START_REF] Kusner | From word embeddings to document distances[END_REF].

• Stop condition: {300, 600, 900}: 900 generations

Experiments

We are going to proceed with the experiments concerning minimizing the impact on the meaning of the original message. We focus now on being able to produce a result that can be put (or be close to being put into exploitation). To do this, we will conduct experiments to see if we can control the difference in meaning between the original message's content and the generated text.

Figure 5 shows us the summary of all the results obtained for the ten use cases that we have been studying throughout this research work. As can be seen, each use case, no matter how topical or challenging, corresponds to a good number of solutions ranging from the most conservative (the one that has the least risk of distorting the original message) to the most aggressive (the one that reduces the readability score more conclusively at the risk of distorting the original message).

According to previous experiments, each color represents a degree of difficulty.

Discussion

We have seen how it is possible to build a solution that enhances the readability of texts of very different natures and readability levels, and we implemented that solution. In addition, this sort of optimization is conducted while paying attention to both the content and the structure of the texts in question to minimize the impact of replacing words with synonyms that are a better fit for the readability criteria of the various formulas we have researched.

Throughout this research, we have seen how it is possible to use genetic algorithms to improve the readability of any text formulated in English. As we have explained earlier, optimization is bi-directional. That is, it can automatically increase or decrease the readability of the text. Once we established the basis for the optimization, we could control the number of words that could be replaced; we could also control that the semantic distance between the original text and the final text does not skyrocket. Therefore, our initial goals of building a solution that improves the readability of any text without significantly altering its form or content have been achieved.

Conclusion

In this research work, we have seen how ORUGA can automatically optimize the readability of a text by using genetic algorithms. We have shown that by automatically replacing some words of the text to be optimized by their synonyms, we can optimize the readability levels in the direction (minimize or maximize) we wish. Neither the content nor the form of the text is altered because a minimal impact on the transformation of the original text is sought through various additional MOO techniques. Although, in theory, analogous solutions could be built using neural language models, this approach has a significant advantage: it is unsupervised and requires no training.

An exhaustive empirical study has shown that we have successfully performed all experiments. In the first instance, these experiments consisted of processing texts of different natures (history, geography, sports, nature, and science) using three synonym libraries and using different readability metrics. In the second instance: designing a MOO solution to control the number of words to be replaced. We have tested different texts to assess and compare the feasibility of this approach. Furthermore, in the third instance: measuring and controlling the semantic distance between the original text and the one that will finally be outputted. For this, we have used a novel technique that uses a library of synonyms to control the results obtained with another library of different synonyms in an adversarial process.

The results demonstrate that our hypothesis about text readability optimization at the beginning of this paper is valid. Despite the success of this research, it is necessary to bear in mind that simple formulas are typically simpler to put into practice, which is a limitation of this body of work. These formulas have a fundamental inability to model the semantics of word usage in context, which is needed to capture richer ideas text difficulty.

As future work, a possible approach (yet computationally expensive) would be using a model of contextual embeddings such as BERT on a large dataset. Then, it should be necessary to store pairs of words and corresponding contextual representations and then use the nearest neighbors approach to identify synonyms that include the context. In this way, the impact of text processing will be even more limited.

  Example 2. History Original text Source: Wikipedia "Austria emerged from the remnants of the Eastern and Hungarian March at the end of the first millennium. Originally a margraviate of Bavaria, it developed into a duchy of the Holy Roman Empire in 1156 and was later made an archduchy in 1453. In the 16th century, Vienna began serving as the empire administrative capital and Austria thus became the heartland of the Habsburg monarchy. After the dissolution of the Holy Roman Empire in 1806, Austria established its own empire, which became a great power and the dominant member of the German Confederation. The defeat in the Austro-Prussian War of 1866 led to the end of the Confederation and paved the way for the establishment of Austria-Hungary a year later." FKGL score: 13.20 ORUGA -minimizing the FKGL score -web scraping Austria looms from the debris of the Eastern and Hungarian March at the end of the first millennium. Originally a margravate of Bavaria, it matured within a duchy of the Holy Roman Empire in 1156 and was next made an arch duchy in 1453. In the 16th century, Vienna lead plate as the command departmental central and Austria thus come the heartland of the Habsburg monarchy. After the divorce of the Holy Roman Empire in 1806, Austria settled its own empire, that come a great power and the dominant branch of the German Confederation. The defeat in the Austro-Prussian War of 1866 led to the end of the Confederation and brick the way for the founding of Austria-Hungary a year later. FKGL score: 11.35

•

  15, 20}: 20 • Number of parents mating {10, 15, 20}: 10 • Number of genes: one per candidate word to be substituted by a synonym • Fitness function: the user can choose among Equations 1, 2, 3, 4 Stop condition: {100, 200, 300}: 300 generations

Figure 1 :

 1 Figure 1: Results for the minimization of the FKGL score using WordNet

Fig 3

 3 Fig 3 shows us the results we have obtained by searching for synonyms with web scraping techniques. The results this time have a smaller variance than in the previous case. In addition, we have again obtained favorable results in all 100 experiments performed. The optimization achieved ranges between 1.02 and 4.20-grade levels.

Figure 2 :

 2 Figure 2: Results for the minimization of the FKGL score using word2vec

Figure 3 :

 3 Figure 3: Results for the minimization of the FKGL score using Web Scraping

Figure 4 :

 4 Figure 4: Non-dominated solutions for ten use cases obtained using NSGA-II

Figure 5 :

 5 Figure 5: Summary of the results obtained for the third (and final) version of ORUGA

  3. SportsOriginal text Source: Wikipedia "Real Madrid Club de Futbol, meaning Royal Madrid Football Club, commonly referred to as Real Madrid, is a Spanish professional football club based in Madrid. Founded in 1902 as Madrid Football Club, the club has traditionally worn a white home kit since its inception. The honorific title real is Spanish for Royal and was bestowed to the club by King Alfonso XIII in 1920 together with the royal crown in the emblem. Real Madrid have played their home matches in the Santiago Bernabeu Stadium in downtown Madrid since 1947. Unlike most European sporting entities,

Real Madrid members (socios) have owned and operated the club throughout its history." ARI score: 12.69.

ORUGA -maximizing the ARI score -web scraping

Real Madrid Club de Futbol, connotation Royal Madrid Football Club, frequently referred to as Real Madrid, is a Spanish professional football business established in Madrid. Founded in 1902 as Madrid Football Club, the business has consistently timeworn an alabaster home kit since its inception. The appellation title real is Spanish for Royal and was entrusted to the business by King Alfonso XIII in 1920 together alongside the aristocratic culmination in the emblem. Real Madrid have played their familiar matches in the Santiago Bernabéu Stadium in downtown Madrid afterward 1947. Unlike most European sporting entities, Real Madrid assemblage (socios) have owned and negotiated the business throughout its history. ARI score: 15.53

Table 1 :

 1 Summary of the results obtained using the different libraries of synonyms

	Library	Minimum Median Maximum
	WordNet	0.77	1.63	2.73
	word2vec	0.42	0.96	3.90
	Web scraping	1.02	1.61	4.20

Table 2 :

 2 Summary of the results obtained for the experiments performed w.r.t. minimization. The numerical values represent absolute improvements after using ORUGA

Table 3 :

 3 Summary of the results obtained for the experiments performed w.r.t. maximization. The numerical values represent absolute improvements after using ORUGA

	Use case	DCRF	SMOG	ARI	FKGL
	01/science 1.98 ± 0.16 1.30 ± 0.06 1.80 ± 0.08 2.09 ± 0.14
	02/history 1.85 ± 0.25 1.99 ± 0.09 3.88 ± 0.28 3.02 ± 0.08
	03/geography 2.38 ± 0.12 1.23 ± 0.08 4.44 ± 0.13 4.00 ± 0.44
	04/sports 2.09 ± 0.40 2.79 ± 0.07 4.63 ± 0.40 4.26 ± 0.04
	05/engineering 2.10 ± 0.43 2.16 ± 0.11 4.55 ± 0.10 4.23 ± 0.35
	06/geography 1.53 ± 0.21 1.81 ± 0.22 2.96 ± 0.04 2.90 ± 0.41
	07/engineering 1.49 ± 0.38 1.71 ± 0.04 3.87 ± 0.46 3.34 ± 0.16
	08/history 1.43 ± 0.18 3.09 ± 0.13 4.11 ± 0.63 3.70 ± 0.21
	09/sports 1.60 ± 0.21 2.29 ± 0.16 3.54 ± 0.28 2.56 ± 0.04
	10/history 2.06 ± 0.08 2.64 ± 0.04 3.99 ± 0.25 3.27 ± 0.52

  As it is possible to observe, minor changes can be made to the original text and still optimize readability. It is still an open question whether minor changes in form are not so minor in meaning.

	Words to be replaced FKGL expected
	5	10.43 (▽ 2.71%)
	6	10.28 (▽ 4.10%)
	7	10.13 (▽ 5.50%)
	8	9.98 (▽ 6.90%)
	9	9.91 (▽ 7.56%)
	10	9.84 (▽ 8.21%)
	11	9.76 (▽ 8.96%)
	12	9.68 (▽ 9.70%)
	13	9.61 (▽ 10.35%)

https://pypi.org/project/pygad/

https://jmetal.github.io/jMetalPy/

https://pypi.org/project/gensim/

Acknowledgments

The research reported in this paper has been funded by the Federal Ministry for Climate Action, Environment, Energy, Mobility, Innovation, and Technology (BMK), the Federal Ministry for Digital and Economic Affairs (BMDW), and the State of Upper Austria in the frame of SCCH, a center in the COMET -Competence Centers for Excellent Technologies Programme managed by Austrian Research Promotion Agency FFG.

Source code

The source code of this approach is published under MIT license in the following Github repository: https://github.com/jorge-martinez-gil/oruga.


Review of "500+ Verbs in UmoNhoN (Omaha). By Alice Saunsoci and Ardis Eschenberg"

International Journal of American Linguistics, 84-1, pp. 154-156 ---500+ VERBS IN UMONHON (OMAHA). By Alice Saunsoci and Ardis Eschenberg. CreateSpace Independent Publishing Platform, 2016. Pp. 276, $10.001 (paper). This book, co-written by the late Umoⁿhoⁿ speaker Alice Saunsoci and the linguist Ardis Eschenberg, is the first published book to be dedicated specifically to the verbal system of Umoⁿhoⁿ, a Siouan language referred to as "Omaha" in most anthropological and linguistic literature.

Since it is primarily intended for learners and tribal members, it avoids technical linguistic terms as much as possible and contains numerous sentences illustrating the uses of verbs in context.

The book begins with a short introduction to the spelling system and to the grammar of the language (parts 1 to 4). The main body of this book (part 5) includes more than 500 verb paradigms. Each verb is provided with imperative forms (except when the semantics do not allow it), and at least one example sentence. The main section is followed by indexes that list the verbs by Umoⁿhoⁿ and English alphabetical order, as well as by conjugation patterns (parts 6 to 8). This work is very useful for documenting and revitalizing the language given the importance and complexity of the Umoⁿhoⁿ verbal system. Umoⁿhoⁿ verbs can index two arguments, generally the agent and the patient, as in oⁿ-thá-noⁿ'oⁿ (1SGPATIENT-2AGENThear) 'You hear me'. The system is split intransitive, which means that some intransitive verbs, called "stative", use the patient markers of the transitive verbs to mark the subject (e.g. oⁿ-xtá 'I am sleepy'), while other intransitive verbs, called "active", use the agent markers of the transitive verbs to mark the subject (e.g. a-wáoⁿ 'I sing'). Finally, Umoⁿhoⁿ has a large number of conjugation classes. The authors divide the verbs into nine conjugation patterns, and one could further subdivide them.

In the forms provided by the book, we see that the second person subject of verb stems beginning with th-[ð] is marked by initial n-. In nineteenth century data from [START_REF] Dorsey | The ¢egiha language[END_REF][START_REF] Dorsey | Omaha and Ponca letters[END_REF], described in detail by [START_REF] Koontz | Preliminary Sketch of the Omaha-Ponca language[END_REF][START_REF] Koontz | Omaha verbal paradigms[END_REF], and also in [START_REF] Marsault | The verbal system of Omaha. Forms and functions of verbal prefixes[END_REF] for the verbs, there used to be variation between shn-(the older form), n-and hn-, which has disappeared in modern Umoⁿhoⁿ. On the other hand, the book shows a lot of variation in other areas, such as accent, vowel length and nasal harmony, apparently more than was recorded by Dorsey.

A particularly interesting fact revealed by the data in this book has to do with the numerous "Ablaut" verbs. Umoⁿhoⁿ, like other Siouan languages, has a category of verbs which undergo a final vowel alternation (from -e to -a), called "Ablaut" [START_REF] Rankin | On Mississippi Valley Siouan "Ablaut[END_REF]. One of the suffixes that historically triggers the Ablaut is -i, which marks plurality and proximate (i.e. main actor) 2 subjects. In nineteenth-century texts, most third person subjects were marked as proximate. In modern Umoⁿhoⁿ, the proximate/plural suffix -i has disappeared except with imperative plurals and in certain traditional speech styles, but the final vowel alternation remains. The authors explain that first SG and second persons correlate with the -e final vowel, while third and first person PL correlate with -a (p.25).

2 The proximate/obviative parameter in Umoⁿhoⁿ works in discourse somewhat like the well-documented Algonquian systems but lacks associated direct/inverse distinctions and does not serve a clear reference-tracking function, unlike those systems. For further description see [START_REF] Koontz | Proximate/Obviate in Omaha-Ponca[END_REF] and Eschenberg (2005, 78). This would mean that third person subjects of Ablaut verbs have an unchangeable -a final vowel based on person alone, and regardless of the proximate/obviative parameter and aspect. The negative suffix -azhi seems to be conditioned similarly. This suffix occurs with an initial -b-, an allomorph of proximate/plural -i, when the subject of the verb is 1PL or third person, and it takes an -m-whenever the subject of the verb is 1SG person.

Table 1 presents the person marker prefixes of the regular conjugational pattern (the "A pattern" in the authors' terminology). It also shows the distribution of the final vowel of Ablaut verbs, according to the statements on p.25, and the negation marker paradigm in the right column, albeit without the Ablaut vowels. It shows a nominative/accusative alignment of intransitive verbs according to verb ending and negation, in contrast with the split intransitivity of person markers. Most verbs in the book conform to the data given in Table 1.

The apparent double alignment can be checked with the stative verbs bíize "be dry" (p.41) for Ablaut and giúdoⁿ-bazhi "not feel well" (p.145) for negation.

PATIENT

Active Negative (all verbs) A G E N T 1SG 1PL 2 3SG 3PL 1S G wí-Σ-e a-Σ-e a-wá-Σ-e a-Σ-e Σ-m-azhi 1P L oⁿ-thí-Σ-a oⁿ-Σ-a oⁿ-wóⁿ-Σ-a oⁿ-Σ-a Σ-b-azhi 2 oⁿ-thá-Σ-e wa-thá-Σ-e tha-Σ-e wa-thá-Σ-e tha-Σ-e Σ-azhi 3 oⁿ-Σ-a wa-Σ-a thi-Σ-a Σ-a wa-Σ-a Σ-a Σ-b-azhi [Σ = verb stem] Stativ e oⁿ-Σ-e wa-Σ-a thi-Σ-e Σ-a Σ-a
Table 1: Alignment of prefixed person markers, final vowel alternation, and negation.

However, a closer look at the data in the book reveals that the Ablaut alternation is still controlled by the proximate/obviative parameter, animacy, aspect, and sometimes plurality.

For example, the third person form of stative verbs is written with a final -a in the In sum, this book provides learners and linguists with rich information about modern Umoⁿhoⁿ, and with a glimpse of the changes that have taken place over the previous century.

Presumably in order to help beginning learners, it avoids some grammatical detail, such as the

  multiply constrained -e/-a variation. Advanced learners and linguists may wish to use this volume in combination with other reference works in order to have a complete overview of the verb endings. JULIE MARSAULT, Université de la Sorbonne-Nouvelle -Paris 3 Laboratoire Mondes Iranien et Indien (MII) and BRYAN JAMES GORDON, Title VI Umoⁿhoⁿ Language and Culture Center, Umoⁿhoⁿ Nation Public School

Table above ,

 above but a final -e does occur in most example sentences (e.g. Ágthiⁿ-thoⁿ sábe 'The chair is black', p.34). Other verbs take an -e final vowel in interrogative sentences (e.g. Midé-a? 'Is she crawling?', p.85). On one occasion at least, an active perfective verb is shown with an -e final vowel, in agreement with the obviative article of its subject: Shóⁿge-kʰe t'é 'The horse died' (p.39). Moreover, the verbs 'to hate' (p.111) and 'to look for' (p.133) have 1SG>2PL forms 'I hate/looked for all of you' with an -a final vowel, evidence of the original presence of the -i plural suffix. Such data show that the old parameters are still operating, although they are not explained in this book. The authors do state that the -b on the 3SG negative is not obligatory but "more likely in conversational circumstances" (p.9).

We warmly thank Guillaume Jacques and Catherine Rudin for their corrections and comments.