John Samuel
email: john.samuel@liris.cnrs.fr

Sylvie Servigne
email: sylvie.servigne@liris.cnrs.fr

Gilles Gesquière
email: gilles.gesquiere@liris.cnrs.fr

Representation of Concurrent Points of View of Urban Changes for City Models

Cities evolve over time and their evolution is often studied using material objects and historical documents. Based on available evidence, researchers propose various hypotheses explaining the probable evolution, both imaginary and factual. Furthermore, city models are used to model and visualize 3D structures and semantic information of the cities. With the help of versioning of city objects, it is possible to represent temporal changes of city structures. And with the support for representing scenarios, it is possible to represent different possible sequences of urban changes. In this article, we formalize a set of rules for representation of concurrent points of view of researchers related to urban changes based on standard city model. The goal is to understand how the cities have evolved, what were the key changes and allow exchange between various hypotheses (or processes). We developed a proof-of-concept named U rbanCo 2 F ab based on these rules to demonstrate the highly potential use cases of our proposition.

Introduction

Cities are under constant evolution. In the study of understanding historical past of a city, it is important to understand not only the changes that occurred but also how these changes occurred. Historical documents like old photographs, paintings, postal cards etc. give a snapshot [START_REF] Peuquet | An approach for time-based analysis of spatiotemporal data[END_REF] or version [Van Ruymbeke et al., 2015] of the city at a particular instant or a period of time. Take for instance, a council meeting report describing the discussion on demolition of a building and an associated photograph that proves its actual demolition at a later period. But historical documents are not just confined to such factual elements of the urban past. They may also give an imagined view of the city by different actors. Though such imagined views like project plans may have never been implemented, their mere propositions in some cases may have left a lasting impact on the cities.

To understand and study these aspects, researchers are increasingly looking for solutions that can be used to model structural and semantic information concerning various city objects at different points of time. Geographical information systems (GIS), especially maps are now commonly used for navigational purposes, currently serving the main purpose of getting the most recent version of the city. But historians and urban planners require options to navigate through the historical timeline to comprehend several aspects of the urban fabric. They want to spatially and temporally annotate their document corpus in GIS along with several other domain-specific information before finally being able to pose complex queries and navigate or explore urban data through data visualization approach. In other words, a support for nD (or multidimensional) solutions that can represent and visualize the 3D (spatial), temporal as well as semantic information is required.

Collaboration among multiple actors is important in every scientific domain. Researchers and experts [Van Ruymbeke et al., 2017, Van Ruymbeke et al., 2018] propose, discuss and debate various hypotheses on probable urban evolution. Different actors base their decisions on facts available to them at a given moment of time. It is important to save these valuable discussions and the resulting hypotheses to get an overview of the various points of view concerning the study of urban changes. Projects proposed or imagined by different urban planners may or may not come to completion. Nevertheless, these projects give multiple alternate scenarios envisioned by the proposers in contrast to the existing reality. Thus we also need to be able to represent different proposed scenarios. Lessons from the past failed projects also serve as a guiding factor for the future projects of urban planners. This work here is focused on the past. Urban planning will require changes that are not provided here in order to have a focus on the urban changes in the past. Nevertheless, our work may be seen as a common ground for urban planning.

Finally, considering the ever-changing software landscape, one commonly discussed problem is the incompatability of past softwares in newer platforms. Hence there is an increasing demand for data-driven solutions based on standards (e.g standard city models) in order to promote data interoperability and data sharing.

Considering all these requirements, we introduce and formalize a new method to represent concurrent points of view in a 4D context in this article. Our proposed method lets multiple researchers propose and share various scenarios of the city evolution. Section 2 describes in detail the study of urban evolution and its various requirements. We take a look at several related works in section 3. Section 4 details versions and workspaces and also presents their formalization. We present U rbanCo 2 F ab in section 5 and briefly describe the proof of concept. Section 6 finally concludes the article and presents the future course of actions.

Study of Urban Evolution

As cities expand both vertically and horizontally, the study of urban evolution has taken prime importance in several research circles especially among the urban planners. As cities expand both vertically and horizontally, the study of urban evolution has taken prime importance in several research circles especially among the urban planners and historians. Lessons from the past serve as a guidance for the future project plans of a city. Urban evolution study involves several domains: geography, social science, urban planning, history etc. In our work, we are interested in representing this nD (or multimensional) urban evolution information: 3D structural, temporal and several domain-specific information. Precisely, our document corpus consists of old postal cards, aerial views, photographs, project plans (both successful and failed), municipal meeting notes. This corpus is currently used by us for selective case studies for the manual recreation of a building or a city sector at different points of time using standard city models.

Cities have their stories [Fields, 2012] to tell, right from the first human establishment to its current state. Even though it seems utopian to have a complete and continuous description of the urban changes, historical documents and anecdotes may be considered as witnesses or footprints of changes. Researchers study this urban evolution at various scales. While some of them focus on the changes of buildings [START_REF] Stefani | Time indeterminacy and spatio-temporal building transformations: an approach for architectural heritage understanding[END_REF] of historical importance, others take it to much larger scale of city sectors [Simon, 2012] or to the entire scale of the city [Renolen, 2000, Lefebvre et al., 2008, Rollier-Hanselmann et al., 2014, Billen et al., 2012] or to even larger space [START_REF] Harbelot | Continuum: a spatiotemporal data model to represent and qualify filiation relationships[END_REF], Chaturvedi et al., 2017] in a much more generic approach. They focus on changes in different features of city objects. Highly granular changes like on those on the level of buildings [START_REF] Stefani | Time indeterminacy and spatio-temporal building transformations: an approach for architectural heritage understanding[END_REF] take into consideration various possible transformations like annexation, union etc. of buildings, whereas those on a coarser level consider only the features of city objects like roads, buildings, bridges etc. without going into details.

City object features are used to describe 3D structural, temporal, semantic and thematic information concerning the objects. For any given city object, the feature values change during any given period of time. These could be structural changes, like the number of storeys of a building or they could be related to its use (e.g., administrative, religious use of a building, use of a bridge for vehicles, pedestrians etc.). It is interesting to observe the evolution of these changes in feature values for given city objects for the study of urban evolution. Such studies are usually based on available evidences like paintings, municipal council minutes, project plans, construction permits, aerial views, photographs etc. Researchers and domain experts propose, discuss, debate different possible scenarios of urban evolution and propose various hypotheses. They use these evidences [Simon, 2012, Samuel et al., 2016] to study the existence [START_REF] Hornsby | [END_REF]Egenhofer, 2000, Hallot andBillen, 2016] and non-existence (for e.g., destruction) of various city objects and to obtain a time duration for various features of city objects. These timelimited feature values of one or more city objects constitute a version [Van Ruymbeke et al., 2015, Chaturvedi et al., 2017, Van Ruymbeke et al., 2017]. However, there are also periods of time, where we do not have any evidence concerning the changes that may have occurred to these objects or the researchers may not be interested to know about these periods. Such gaps between two versions for the given objects is called a version transition [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF]. A sequence [Van Ruymbeke et al., 2017, Van Ruymbeke et al., 2018] of versions and version transitions arranged in a chronological order of time may describe one of the possible ways a city could have evolved. However, multiple people working on the study either in isolation or in collaboration may propose different possible scenarios of changes based on the evidences available to them. Therefore, all these scenarios may be considered in parallel before a consensus is made on the best possible scenario. This final consensus scenario may be used as a reference by all the researchers until some other changes are decided upon. However, it is very important to save both the consensus scenario along with other proposed scenarios to understand other points of views on the urban changes and if necessary, to make more future modifications to the consensus scenario.

A scenario may also contain imagined city versions for representing and understanding other possible urban project plans proposed in the past that did not come to completion because of socio-economic or political pressures. Researchers want to understand how the city may have looked like if the proposed project were carried out. Documents like abandoned project plans, construction permits can give another possible view, detailing how the city would have looked like if the concerned plan had been carried out. New project plans often influence the surrounding areas especially leading to price fluctuations, construction of new habitat zones, shopping complexes and transport lines. In some cases, even abandoned projects are known [START_REF] Samuel | Representation and Visualization of Urban Fabric through Historical Documents[END_REF] to have left some traces on the cities, like in the case of Givors and Terrenoire, two old industrial towns of France [START_REF] Périnaud | Exploration of the changing structure of cities: Challenges for temporal city models[END_REF]. Therefore, such an information of project influences on city infrastructure also forms a key constituent of urban evolution.

With the growing availability of different geographical information systems, the study of historical past has become a interdisciplinary field [START_REF] Gregory | Geographical Technologies and the Interdisciplinary Study of Peoples and Cultures of the Past[END_REF] and collaboration is important for discussing possible scenarios among stakeholders. In the past, researchers made use of physical models like plan-reliefs or virtual mockups for proposing their hypotheses. Physical models are limited both in scale and temporal dimension and virtual mockups are created using the software technology and expertise available at the particular time of development making them unusable with the advancement of backward-incompatible technologies. Hence during the last few years, a data-driven approach is being considered, where standards are promoted by international communities in order to represent domain-specific knowledge. The primary goal of these standards is to promote data interoperability and easier sharing and exchange. Thus we require a solution that can support collaborative effort of the researchers using international standards able to represent 3D, temporal and domain-specific information concerning the cities.

In this article, we focus on representing possible scenarios of changes of a city or one or more city objects during a given period time. We believe that by adopting an abstract view for a generic approach, we free ourselves from specific technologies. Nevertheless, such an approach can be implemented using various existing software solutions. Our proposed approach called U rbanCo 2 F ab is a method that aims to provide the ability to represent several possible scenarios of urban evolution using interoperable data standards. It is a generic approach that can be targeted for several ongoing processes based on city models. Our proposition can be built over several existing software solutions. U rbanCo 2 F ab can also be extended to represent future imagined versions, but this requires further study and is out of scope for this paper. But this work can be seen as a base for studies related to scenarios of future urban evolution.

Related Works

We are interesting in reconstructing virtual cities of the past, both hypothetical and existing using a document corpus consisting of old postal cards, photographs, aerial views, newspaper archives, municipal meeting notes etc. Photographs of a building, for example at different periods of time are currently used by us to manually build virtual models of the building using standard city models at discrete time intervals. When extended to more buildings in a city sector or town, we get an overview of how a city evolved both horizontally and vertically. Evolution of cities [Renolen, 2000, Lefebvre et al., 2008, De Roo et al., 2013, Rollier-Hanselmann et al., 2014, Harbelot, 2015] has been studied in several different ways. Spatio-temporal object model (STOM) [Renolen, 2000] considers objects like roads, parcels along with their spatial, temporal and attribute changes and models both object-level and version-level transitions. These transitions are modeled using spatial, temporal, relationship and attribute descriptors. With the help of version-level transitions, it is possible to represent when an object ceased to exist, is tranformed from one form to another, is split into two different objects etc. Similarly, with the object-level transitions, it is possible to represent when an object is deduced or annexed from another object. OH FET model [START_REF] Lefebvre | Understanding urban fabric with the oh fet model based on social use, space and time[END_REF] also considers this object-oriented approach by considering the change in functional (usage), spatial and temporal information of the individual objects of interest. Continuum [Harbelot, 2015], a much recent work considers spatio-temporal changes as one single entity and tracks the structural, temporal and geometrical changes altogether. Though these studies are able to represent the version of one or more city objects at a given point of time, they focus on giving one possible hypothesis of the urban evolution. Additionally they do not consider imagined versions of urban evolution. Our proposed approach takes into consideration the above works and further explores the possibility of representing concurrent hypotheses: both factual and imagined. Finaly, custom-built versions or scenario of urban evolution with some proprietary technology or softwares is not our goal. In an interdisciplinary field, it has become very important to be able to exchange data in an interoperable manner. Most of the above works [Renolen, 2000, Lefebvre et al., 2008, Stefani et al., 2010, Simon, 2012, Harbelot, 2015] are not based on any particular international standard. Nevertheless, these works form the basis for this proposed work.

An analogy of the proposed city object versions and scenarios can be made with the terminology used in management of software repositories. Software repositories (centralized and decentralized) [Otte, 2009] are commonly used in software development to promote parallel development by multiple programmers. Repositories and branches can be used by historians to suggest multiple possible historical successions of a city or city objects of interest. Yet current implementation of most of version control systems like GIT1 is primarily targeted for text files and cannot be easily used to represent and understand the historical changes of city object features and to even propose any future imagined changes on them. We are interested in obtaining the value of features of such city objects at different temporal points or intervals. The focus on textual line changes and a missing object model make the existing implementations of software repositories unsuitable for studying historical evolution using standard city models, especially to study changes in city features or city object features. [START_REF] Swierstra | The semantics of version control[END_REF] recently formalized the key concepts of a version control systems, though once again focusing on line based version control systems. Nevertheless, by reutilizing the associated terminology in version control systems, the learning curve of the researchers can be reduced.

Finally in order to support interoperable solutions, we may base our approach on CityGML [START_REF] Gröger | OGC city geography markup language (CityGML) encoding standard v2.0[END_REF] or city model [START_REF] Stadler | Making interoperability persistent: A 3d geo database based on citygml[END_REF]. CityGML is an international standard proposed by OGC2 for representing thematic, structural and semantic information of cities at different scales or levels of detail. It is also being currently used for the study of historical evolution [START_REF] Pfeiffer | Virtual leodium: from an historical 3d city scale model to an archeological information system[END_REF], Billen et al., 2012, Morel and Gesquière, 2014, Samuel et al., 2016, Chaturvedi and Kolbe, 2019]. The standard [Tegtmeier et al., 2014, Chaturvedi and[START_REF] Chaturvedi | [END_REF] is currently being used by diverse communities for integrating domain specific information to the underlying city model [START_REF] Gil | The backbone of a city information model (cim): Implementing a spatial data model for urban design[END_REF]. It permits these extensions by Application Domain Extensions (ADE) that allows not only to easily share the extension but also the associated data in an interoperable manner. Take for example, a recent work studies various actions in understanding urban modeling [START_REF] Sindram | Modeling of urban planning actions by complex transactions on semantic 3d city models[END_REF].

CityGML also considers the urban fabric from an object-oriented approach. In CityGML, for every city object, there is an associated information concerning its geometry and spatial position. CityGML 2.0 building model has two temporal information yearOfConstruction and yearOfDemolition for representing the year of construction and demolition respectively. However, this was very limited in scope since it could not be used to represent information on the real physical existence of other types of objects. With the latest proposed extension [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF]Kolbe, 2018] to CityGML (see Figure 1), it is now possible to add a temporal dimension to every feature of the city object, i.e., a time validity for the existence of an object. This extension permits to represent lifetime of city objects right from its construction to its demolition and various changes in between, like change of roof structure of a building or its usage. However, this extension focused mainly on the physical existence of city objects. [START_REF] Hallot | Enhancing spatio-temporal identity: States of existence and presence[END_REF] formalize the concept of existence of city objects and distinguish between existence and presence of objects. An object comes into existence as soon as a (semantic or spatial) relationship [START_REF] Hallot | Enhancing spatio-temporal identity: States of existence and presence[END_REF] is established between this object and other objects under consideration. In our study, this notion of existence is important since we are interested in representing not only the physical presence of objects, but also their existence in the form of formal project plans or a thought process. We represent the changes to the objects during their existence time by giving a temporal validity to their known feature through V ersionableAbstractF eature and V ersion (see Figure 1). The extension represents the features giving them a existence time validity and groups these versionable features in user-defined versions. The users can then define the transitions between the versions detailing through the transactions (Transaction) of the various changes that occurred in between. One of their suggestions was to make use of the attribute tag in the Version (see Figure 1) to create agent-specific versions for various purposes like proposing historical evolution or even future scenarios. This suggestion enabled searching specific versions created by the agents with a given tag name to find a proposed historical evolution. But this proposition is very limited for practical uses involving a large number of researchers and it also missed a formal specification. Additionally their proposition also did not provide any constraint rules on the overall proposed model. Nevertheless, the above work has been extended in a much recent work [START_REF] Samuel | Representation and Visualization of Urban Fabric through Historical Documents[END_REF] to represent document and their references to different city objects. Taking into account these two works, we want to explore the study of urban evolution by making use of an approach commonly used in version control systems.

GeoGig3 , previously GeoGit [START_REF] Clark | Rapid open geospatial userdriven enterprise (rogue) joint capability technology demonstration white paper[END_REF] is one of the currently available software solutions that tackles the problem of tracking geospatial data changes made by users. However, it is not designed to handle situations where the agents wish to track changes of historical and future urban data. Besides it cannot currently handle CityGML files (or other city models). We have not found any solution that can meet all our above requirements of representing concurrent points of view of urban evolution, factual as well as planned and support for interoperable city data models. In particular, we want to not only obtain forward and backward traversal of the urban changes but also be able to see other possible propositions. In this article, we formalize our requirements and also present U rbanCo 2 F ab to fully describe our requirements. We may have several technical possibilities, but in this paper, we propose a formal approach that can be derived to a technical specification dedicated to a software or a format (e.g., GML, JSON etc.)

Workspaces for Concurrent City Projects

In this section, we introduce the concept of W orkspace and its formalization. A workspace manages various scenarios of urban evolution proposed by agents (e.g., researchers, users, domain experts, enterprises etc.). Like [START_REF] Hallot | Enhancing spatio-temporal identity: States of existence and presence[END_REF], we consider a workspace consisting of one or more objects of interest and their associated period of existence. However, we wish to distinguish between the scenario that received a majority consensus and the scenarios that were proposed, debated or even abandoned. These scenarios, consisting of city object versions (both factual and imagined) enables representation of concurrent points of view for the study of historical urban evolution. We consider that every city object consisting of one or more geospatial features, each of which can be identified by an identifier [START_REF] Hornsby | Identity-based change: a foundation for spatio-temporal knowledge representation[END_REF]]. There could be multiple workspaces managed by independent groups working together in parallel. But in this article, we focus on formalizing a single workspace. An example workspace is given in Figure 2.

A workspace consists of two spaces: Consensus Space and Proposition Space. A space in a workspace lets a user create different scenarios of urban evolution. A Consensus Space is a mutually agreed upon space that can have only one scenario whereas the Propositions Space can have more than one scenarios. A scenario consists of one or more versions, where a version of urban evolution corresponds to the state of the city at a given instant of time (or time period). A scenario in our context is closely related to interpretative sequence proposed by [Van Ruymbeke et al., 2017, Van Ruymbeke et al., 2018], where the authors consider an interpretative sequence having multiple episodes (or versions). A version can be considered Existing if there is enough evidence for its materialized or physical existence [START_REF] Hallot | Enhancing spatio-temporal identity: States of existence and presence[END_REF] in the real world. [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF]. DocumentObject, Reference represented by white-colored boxes are extensions proposed by [START_REF] Samuel | Representation and Visualization of Urban Fabric through Historical Documents[END_REF] to represent document references to objects. Classes Version, VersionTransition represented by blue-colored boxes are our proposed changes to the proposition by [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF]. Classes Workspace, Space, ConsensusSpace, PropositionsSpace, Scenario, VersionType, TransitionType represented by green-colored boxes are newly proposed to support concurrent points of view in CityGML.

Imagined version corresponds to an imagined city (like in a urban plan) or a possible state (as proposed by a historian). Take for example, a photograph may be considered as sufficient evidence by a research group to call a version Existing and unimplemented project plans or mockups may be enough to call a version Imagined. Hence definition for Existing or Imagined versions is decided beforehand by a group based on the available categories of evidences. 'Transitions' between versions are used to represent the change from one state to the other. A transition [START_REF] Hornsby | Identity-based change: a foundation for spatio-temporal knowledge representation[END_REF] may signify a certain time period or point in time for which enough evidence on the city object(s) is not available. We also assume the ability to identify city objects [START_REF] Hornsby | Identity-based change: a foundation for spatio-temporal knowledge representation[END_REF] across different periods of time, i.e., we consider that it is possible to identify the objects that undergo changes. Take for example, we have two photographs (or videos) concerning the construction of a city building and its finished version, but we may not have any evidences on the stages of its development. This uncertain period is represented by a transition. As more evidence on intermediate states are obtained, it is possible to add new versions and transitions between them.

'Influence' is a special type of link between two versions in order to show that an imagined version (of the past) had some influence on a later version (Existing). This is used to represent situations where some project plans (like project plan for construction of a new highway) impact the city (like construction or destruction of houses).

A user would like to navigate in time to see the events at a given instant of time (both the past and the future with respect to that considered moment of time). As shown in Figure 2, the agent is at time T obs and navigates the past and the future with respect to this point. We did not show the transactions in Figure 2. Transactions include addition, modification or removal of features of city object(s).

The key objects required to represent workspaces are further detailed in corresponding UML classes in the model of Figure 1. It is based on the extension of the CityGML core and slightly modifies the previous work [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF] on the versioning of city objects. Yet the above model is not sufficient to specify the various constraint rules on each of the objects specified in the model. We now formalize workspaces using description logic, presenting both the key objects and the various constraint rules on them. It is important to note that on first look, it may seem that this work can be used immediately for imagining future scenarios starting from the current date. There are several questions that may require adjustments, especially with respect to transition types. Stating a statement on the current date like a future project influenced another future project is questionable. What evidences can be given to justify such a statement? These discussions are out of scope of this paper and will be presented in our future works.

Theoretical Preliminaries

We need to provide a formalized representation that can be mapped to several models that can manage city related information (e.g., CityGML). Additionally, we want to specify constraint rules on these models for representing a consistent city model. Current UML based model of CityGML (v2.0) doesn't specify the constraint rules. There are several ways of formalization like UML or description logic. We use description logic [START_REF] Baader | The Description Logic Handbook: Theory, Implementation, and Applications[END_REF] to formalize the notions of concurrent points of view of urban evolution given its capability to define both the concepts and the associated constraints rules. This choice is also considering the fact that it can be easily mapped to semantic web languages and to ensure mapping to other possible data representations or city models. Let be a top concept and ⊥ be a bottom concept and A, B, C, . . . be atomic ≥ nR (at-least number restriction)

≤ nR (at-most number restriction)

= nR (equal number restriction)

(1)

The interpretation of the above syntax is given by I = (∆ I , . I ), where ∆ I is called the domain of the interpretation and . I is an assignment of every atomic concept A to a subset of ∆ I and every atomic role R to a subset of ∆ I × ∆ I . φ corresponds to an empty set. Delta I \A I below corresponds to all elements present in Delta I excluding those in Delta A I .

I = ∆ I ⊥ I = φ (¬A) = ∆ I \A I (B C) I = B I ∩ C I (B C) I = B I ∪ C I (∀R.C) I = {a ∈ ∆ I |∀b.(a, b) ∈ R I → b ∈ C I } (∃R. ) I = {a ∈ ∆ I | ∃b.(a, b) ∈ R I } (∃R.C) I = {a ∈ ∆ I | ∃b.(a, b) ∈ R I ∧ b ∈ C I } (≥ nR) I = {a ∈ ∆ I |{b|(a, b) ∈ R I }| ≥ n} (≤ nR) I = {a ∈ ∆ I |{b|(a, b) ∈ R I }| ≤ n} (= nR) I = {a ∈ ∆ I |{b|(a, b) ∈ R I }| = n} (2)
With a given interpretation I, inclusion is defined in the following manner

B C, if and only if B I ⊆ C I (3)
Finally, equivalence is defined in the following manner

B ≡ C, if and only if B I = C I (4)
An equivalence is called a definition when the left side of the equation is an atomic concept (e.g., see definitions of T emporalInterval, T emporalP oint etc.)

Time

In order to consider precise instants or time intervals, we introduce temporal point T emporalP oint (a precise instant of the chosen timeline) and time interval T imeInterval (period between two instants of the chosen timeline) [Harbelot, 2015].

T emporalP oint

(5)

A time interval defined by [t s , t e ], where t s , t e ∈ T emporalP oint I correspond to start and end temporal points following strict ordering.

T imeInterval

T imeInterval ≡ (= 1hasStartingP oint.T emporalP oint)

(= 1hasEndingP oint.T emporalP oint) (6)
We require τ to refer to temporal points or a time interval (e.g. documents like photographs are momentary whereas videos, project plans etc. have a time duration).

τ ≡ T emporalP oint T imeInterval (7)
Temporal points and time intervals are disjoint.

T emporalP oint T imeInterval ⊥ (8) Meets shows that black colored temporal events are immediately followed by red-colored temporal events. Before corresponds to represent events when black colored temporal events are followed by red-colored temporal events but not immediately, i.e., there is a temporal gap of more than one instance of time between them. During shows that black colored temporal events occur at the same time as those of red-colored temporal events.

In order to specify various conditions like an instant (or a period) is immediately followed by another instant (or a period), occurred before another instant (period) or happened at the same instant (or during a given period), we introduce meets similarly like [Harbelot, 2015], bef ore and during respectively, inspired from [Allen, 1983] (See Figure 3).

meets I = {< T i , T i+1 > |i ∈ N}and                              if T i , T i+1 ∈ T emporalP oint ∀T i , T i+1 → succ(T i ) = T i+1 if ∀a, b ∈ T emporalP oint I if ∀I, I ∈ T imeInterval I if ∀(I, a) ∈ hasEndingP oint if ∀(I , b) ∈ hasStartingP oint → a = b (9) bef ore I = {< T i , T i+1 > |i ∈ N}and                              if T i , T i+1 ∈ T emporalP oint ∀T i , T i+1 → T i < T i+1 if ∀a, b ∈ T emporalP oint I if ∀I, I ∈ T imeInterval I if ∀(I, a) ∈ hasEndingP oint if ∀(I , b) ∈ hasStartingP oint → a < b (10) during I = {< T i , T i+1 > |i ∈ N}and                                        if T i , T i+1 ∈ T emporalP oint ∀T i , T i+1 → T i = T i+1 if ∀a, b, c, d ∈ T emporalP oint I if ∀I, I ∈ T imeInterval I if ∀(I, a) ∈ hasStartingP oint if ∀(I, b) ∈ hasEndingP oint if ∀(I , c) ∈ hasStartingP oint if ∀(I , d) ∈ hasEndingP oint → a ≥ c ∧ b ≤ d (11)

Versionable Features

In this section, we make use of the UML model given in [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF], which in turn is based on the city model [START_REF] Gröger | OGC city geography markup language (CityGML) encoding standard v2.0[END_REF] to define versionable abstract features.

Every feature is versioned by the duration of time interval. VersionableAbstractFeature is a time-stamped feature giving the agents the ability to specify the time duration (or validity) of the concerned feature. The relationship between versions and versionable features is shown with a graphical view in Figure 4. We consider two objects O1 and O2 composed of features like name, f unction, geometry and storeysaboveground and their changes in a particular period of time. As can be seen, whenever there is a change in some features like values, a version transition is created. Note the change in values for storeysaboveground and the resulting creation of versions and version transitions.

We introduce concepts N ame to define names and Agent to define agents responsible for creating or manipulation of instances.

In addition to an identifier [START_REF] Hornsby | Identity-based change: a foundation for spatio-temporal knowledge representation[END_REF], every feature also has a name. This identification of feature is important to track every change that occured to any given feature.

AbstractF eature ≡ (= 1hasN ame.N ame)

(= 1hasIdentif ier.Identif ier) (12)
We now introduce V ersionableAbstractF eature, that is an abstract feature with additional attributes to specify the existence of the feature.

V ersionableAbstractF eature AbstractF eature (13)

It has two properties hasExistenceT ime and hasT ransactionT ime for representing the time period or interval of the existence of an object and the transaction interval concerning the addition of a object in a data store (e.g., database transaction interval).

V ersionableAbstractF eature ≡ (= 1hasExistenceT ime.τ ) (= 1hasT ransactionT ime.T imeInterval) (14)
An abstract city object [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF] is a V ersionableAbstractF eature.

AbstractCityObject V ersionableAbstractF eature (15)

Physical Time Interval VF O1 1,0 VF O1 2,0 VF O1 2,3 VF O1 2,1 VF O1 3,0 VF O1 4,0 4. Storeys aboveground 3.Name 2. Function 1. Geometry V 0 V 3 V 1 V 2 VF O2 1,0 VF O2 2,0 VF O2 3,0 3. Name 2. Function 1. Geometry VF O2 3,1 VF O1 4,1 VF O1 4,2 VF O1 4,3

City Object Features

City Object 2 (O2) City Object 1 (O1)

VF O i,j: Versionable Feature I of Object O of counter j V i : Version i It is also possible to create groups of city objects. This CityObjectGroup inherits all the properties of AbstractCityObject. It also permits aggregation of city objects.

T 0 T 1 T 2 T k : Transition k

CityObjectGroup AbstractCityObject

CityObjectGroup ≡ (≥ 0hasAbstractCityObject.AbstractCityObject)

(= 1hasP arent.AbstractCityObject) (16)
It is possible to create city object groups of city object groups, the hierarchy of which is tracked by hasP arent. hasP arent is a transitive property. In order to prevent cycling of groups, the following condition is introduced (see also [START_REF] Gröger | OGC city geography markup language (CityGML) encoding standard v2.0[END_REF]):

∀o c ∀o p ∀o a (hasP arent(o c , o p ) ∧ hasP arent(o d , o a )) → o a = o c (17)
We introduce DocumentObject which is also considered as an abstract city object by [START_REF] Samuel | Representation and Visualization of Urban Fabric through Historical Documents[END_REF] and therefore inherits all its properties. A document object references other city objects (or another document, or collection of documents).

DocumentObject AbstractCityObject DocumentObject ≡ (≥ 0hasRef erence.AbstractCityObject) (18)
A document may concern another city object for a particular time instant (e.g., photos, newspapers) or an interval (e.g., videos), which is defined by the following definition of hasRef erence hasRef erence ≡ (= 1hasRef erenceT ime.τ )

Changes occur during the course of time and these changes are captured by transactions. There are three ways a new transaction may occur: new features are added, values of features may be changed or an old feature may be removed. Hence T ransactionV alue is used to represent these three types of transactions:

T ransactionV alue ≡ Insert Replace Delete (20)
A transaction [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF] is defined to capture these changes between two temporal geospatial features.

T ransaction ≡ (= 1hasT ransactionV alue.T ransactionV alue)

(≤ 1hasOldV ersionableAbstractF eature.V ersionableAbstractF eature) (≤ 1hasN ewV ersionableAbstractF eature.V ersionableAbstractF eature) (21)
Insert: When a previously unknown value for feature is now known, Insert is used.

∀t(hasT ransactionV alue(t, Insert)

∧hasOldV ersionableAbstractF eature(t, N U LL) ∧hasN ewV ersionableAbstractF eature(t, vf ) ∧vf = N U LL (22)
Note that N U LL can be used to signify unknown value or no value. Delete: When a previously known value for a feature is no longer valid and a new value is not available anymore, Delete is used. ∀t(hasT ransactionV alue(t, Delete)

∧hasOldV ersionableAbstractF eature(t, vf ) ∧hasN ewV ersionableAbstractF eature(t, N U LL) ∧vf = N U LL (23)
Replace: When a previously known value for a feature is no longer valid and a new value is available, Replace is used.

∀t(hasT ransactionV alue(t, Replace)

∧hasOldV ersionableAbstractF eature(t, vf 1 )

∧hasN ewV ersionableAbstractF eature(t, vf 2 ) ∧hasExistenceT ime(vf 1 , tm 1 ) ∧ hasExistenceT ime(vf 2 , tm 2 ) ∧bef ore(tm 1 , tm 2 ) ∧ vf 1 = vf 2 ) (24)

Version

A version is created by a user and is a collection of temporal geospatial features [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF], geospatial features with a timespan. There are two types of versions: Existing or Imagined. For every version, there may exist some supporting evidence.

VersionType ≡ Existing Imagined (25)
A version can be considered Existing based on the materialized evidence available to the user to prove the real physical existence. It is entirely left to the researchers in how they use the document evidences to decide whether a version is imagined or existing. A version may have user-defined tags.

Version V ersionableAbstractF eature

Version ≡ (= 1hasV ersionT ype.V ersionT ype) (≥ 0hasEvidence.DocumentObject) (≥ 0hasT ag.T ag) (≥ 1hasV ersionableAbstractF eature.V ersionableAbstractF eature)

(= 1hasCreator.Agent) (26)
The existence time of a version must be contained within the existence time of every versionable abstract feature contained in it.

∀v∀vf (hasV ersionableAbstractF eature(v, vf ) ∧ hasExistenceT ime(v, tm v ) hasExistenceT ime(vf, tm f ) → during(tm v , tm f )) (27)

Version Transitions

A version transition [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF] is a collection of transactions between two versions, i.e., it a collection of changes between two versions. There are two types of version transitions: Regular and Influence. Regular transitions are transitions used to represent the time period (or interval) between two consecutive versions.

Following condition ensures that an Influence transition type is allowed between two versions (for example, in Figure 2, a transition between V 9 to V 2), where the previous version is imagined and the new version is existing and also the imagined version must exist before the existing version.

∀vt(hasT ransitionT ype(vt, Inf luence)∧ hasP reviousV ersion(vt, v p ) ∧ hasN ewV ersion(vt, v n )∧ hasV ersionT ype(v p , Imagined) ∧ hasV ersionT ype(v n , Existing)∧ hasExistenceT ime(v p , tm 1 ) ∧ hasExistenceT ime(v n , tm 2 )) → bef ore(tm 1 , tm 2 ) (31) Following conditions ensure that a Influence transition type is allowed between two imagined versions having different existence times (one before the other) as in Figure 2, an example transition between V 13 to V 9.

Scenario

A scenario [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF] or an interpretative sequence [Van Ruymbeke et al., 2017, Van Ruymbeke et al., 2018] consists of a number of versions. ∀v 1 ∀v 2 (hasV ersion(b, v 1 ) ∧ hasV ersion(b, v 2 ) hasExistenceT ime(v 1 , tm 1 ) ∧ hasV ersion(v 2 , tm 2 ))

∧tm 1 = tm 2 → v 1 = v 2 (37)
No two version transitions in a branch can have the same existence time.

∀vt 1 ∀vt 2 (hasV ersionT ransition(b, vt 1 ) ∧ hasV ersionT ransition(b, vt 2 ) hasExistenceT ime(vt 1 , tm 1 ) ∧ hasExistenceT ime(vt 2 , tm 2 ))

∧tm 1 = tm 2 → vt 1 = vt 2 (38)
There exists only one version that is shared between the two transitions, i.e., the next version of a version transition is the same as previous version of another one. ∃vt 1 ∀vt 2 (hasV ersionT ransition(b, vt 1 ) ∧ hasV ersionT ransition(b, vt 2 )

hasN ewV ersion(vt 1 , v 1 ) ∧ hasP reviousV ersion(vt 2 , v 1 )) (39)
These conditions are necessary to ensure a single sequence of changes proposed by a scenario. Consensus Space has a scenario with all the versions having version type Existing.

ConsensusSpace Space

ConsensusSpace ≡ (= 1hasScenario.Scenario)

All the version types in a Consensus Space must be Existing. In section 4, we presented a new formalization to manage concurrent points of view of urban evolution. These rules pave way to manage all the possible use cases and are used to develop the U rbanCo 2 F ab command-line tool [START_REF] Samuel | Urbanco2fab: Comprehension of concurrent viewpoints of urban fabric based on git[END_REF]. It can represent concurrent points of view of the evolution of one or more city objects proposed by a group of users by ensuring the consistency of the underlying city data and its extensions by making use of rules. The command line application focuses on management of workspaces and is based on the above proposed rules and CityGML. CityGML uses identifiers to identify the city objects and uses XML data format. Every CityGML city object has a set of attributes and associated values. Thanks to the XML format and path query languages like XPath, it is possible to get the value of any attribute of a city object given its object identifier. Considering the close similarity between workspaces and current version control systems, we proposed the extensions [START_REF] Samuel | Urbanco2fab: Comprehension of concurrent viewpoints of urban fabric based on git[END_REF] required to implement U rbanCo 2 F ab using git version control system. To reduce the learning curve of U rbanCo 2 F ab command line tool, we reused the vocabulary of git like init, commit, push, pull, add, rm [START_REF] Samuel | Urbanco2fab: Comprehension of concurrent viewpoints of urban fabric based on git[END_REF].

∀v(ConsensusSpace(c) ∧ hasScenario(c, b) ∧ hasV ersion(b, v) ∧hasV ersionT ype(v, t v )) → t v = Existing (
As described above in section 3, current implementations of GIT mainly targets line based changes. In our case, we are interested to know the city objects that underwent a change between two versions along with the changes in their attribute values. In order to work with CityGML files (XML files), we needed to modify the way differences between two changes of a file. U rbanCo2F ab command line tool, developed using python library Pygit24 uses git to store both the CityGML files and the key metadata of versions, version transitions, scenarios and workspace. A user writes to a CityGML file the values of different attributes of relevant city objects with their identifiers. Then the user commits a version (using the command urbanco2fab commit [START_REF] Samuel | Urbanco2fab: Comprehension of concurrent viewpoints of urban fabric based on git[END_REF]) assigning a physical existence time for a given version. The identifiers of a (git) commit are used to identify versions. User can continue creating new versions for specifying changes to city objects. To see the changes between any two versions, the classical git diff tool is not very useful since it will show the lines that changed. However, urbanco2fab diff makes use of the git diff to not only identify these lines but also the city objects that underwent changes. Thanks to this, the user can see the object (identifiers) as well as the attribute value changes (replace, insert etc.)

There are three major metadata files in U rbanCo2F ab: workspace.json, scenarios.json and versions.json. Recall that the identifier of a commit in GIT is a unique hash value generated taken into account the transaction time, the commit message, the author and the diff. A version transition is identified by two version identifiers, i.e., if id 1 and id 2 are two identifiers of a commit (or a version), a possible version transition can be identified by id 1 -id 2 . The version metadata 1950 1957 1958 1960 1961 1962 1965 1967 1970 1972 Figure 5 shows the output of urbanco2fab viz. It shows two scenarios in workspace: one consensus and one proposition scenario. The 6-character identifier is the version identifier (6 first letters of hash created following a urbanco2fab commit). Internally, U rbanCo2F ab uses pygit2 to generate version identifiers. The consensus scenario has five versions 30f25c, 055e5c, d6db0a, 968e1a, b41f43 and the proposition scenario scenario2 has three versions 30f25c, 47b779, b41f43. Thanks to the constraint rules presented in section 4, it is possible to verify validity of a version, a version transition and a scenario. These rules are used to reject cases like when a user tries to create scenarios with versions having the same physical existence times etc. Study of urban evolution of a city helps not only to understand its history but also to obtain valuable lessons from the past for its future plans. The work started by [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF] to represent temporal evolution of city objects was enhanced in this article to represent concurrent possible hypotheses of urban evolution. Our new contributions on Workspace, Scenario, Version, Version Transition and Versionable Features enable researchers to represent, store and navigate multiple parallel hypotheses on the evolution of a city. Based on these enhancements and the initial proposal from [START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF], we defined a complete set of rules in order to describe the urban evolution. We developed a proof of concept U rbanCo 2 F ab by making use of the formalization rules linked with real city models. Analogous to existing control systems and their well-known options, we tend to reduce the learning curve of the end users of our proposal. Our next goal is to fully integrate our solution to the current 3D visual environment so that users can easily visualize the urban past. Figure 6 shows the current 3D visualization tool called UDV [START_REF] Gaillard | Urban data visualisation in a web browser[END_REF]. Additonal work is needed to link UDV with our current proposal on U rbanCo 2 F ab to allow complete navigation in 4D urban environment. This will be completed by providing a graph-based visual interactive tool that can guide the users in the concurrent views of city lifecycle. Another objective will be to manage additional rules for rights management on the data related to workspaces and versions.

Fig. 1 :

 1 Fig. 1: UML model for representing concurrent points of view in CityGML. Grey boxes are existing classes of the CityGML core. Classes VersionableAbstractFeature, TransactionValue, Transaction represented by yellow-colored boxes are classes proposed to represent versioning of city objects[START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF]. DocumentObject, Reference represented by white-colored boxes are extensions proposed by[START_REF] Samuel | Representation and Visualization of Urban Fabric through Historical Documents[END_REF] to represent document references to objects. Classes Version, VersionTransition represented by blue-colored boxes are our proposed changes to the proposition by[START_REF] Chaturvedi | Managing versions and history within semantically enriched 3d city models[END_REF]. Classes Workspace, Space, ConsensusSpace, PropositionsSpace, Scenario, VersionType, TransitionType represented by green-colored boxes are newly proposed to support concurrent points of view in CityGML.

Fig. 2 :

 2 Fig.2: Workspace for the study of historical evolution. There is one workspace with the consensus space and propositions space. A consensus space has only one scenario whereas the propositions space has multiple scenarios. Each scenario consists of many versions and transitions in between. There are two types of versions: Existing and Imagined. Two types of transitions are also shown: Regular transition (or simply Transition) and Influence. The agent is at time T Obs and navigates through the time to study both the past and future with respect to T Obs .

Fig. 3 :

 3 Fig.3: Different time constraints: Dots represent temporal points and line represents time intervals. Three terms are introduced: Meets, Before, During. Meets shows that black colored temporal events are immediately followed by red-colored temporal events. Before corresponds to represent events when black colored temporal events are followed by red-colored temporal events but not immediately, i.e., there is a temporal gap of more than one instance of time between them. During shows that black colored temporal events occur at the same time as those of red-colored temporal events.

Fig. 4 :

 4 Fig. 4: Versions and versionable features. Box with yellow and orange colored strokes correspond to the features of object O 2 and O 1 . A version can be defined as a set of stable version features of objects during the defined time interval of the version. The space between two consective versions corresponds to a version transition.

  ransaction.T ransaction) (= 1hasP reviousV ersion.V ersion) (= 1hasN ewV ersion.V ersion) (= 1hasT ransitionT ype.T ransitionT ype) (= 1hasCreator.Agent)

  ∀vt(hasT ransitionT ype(vt, Inf luence)∧ hasP reviousV ersion(vt, v p ) ∧ hasN ewV ersion(vt, v n )∧ hasExistenceT ime(v p , tm 1 ) ∧ hasExistenceT ime(v n , tm 2 )) → bef ore(tm 1 , tm 2 ) (32)The time limits of the version transition must be greater than or equal to the end time of old version and the start time of the new version ∀vt(hasT ransitionT ype(vt, Inf luence)∧ hasP reviousV ersion(vt, v p ) ∧ hasN ewV ersion(vt, v n )∧ hasV ersionT ype(v p , Imagined) ∧ hasV ersionT ype(v n , Imagined)∧ hasExistenceT ime(v p , tm 1 ) ∧ hasExistenceT ime(v n , tm 2 )∧ hasExistenceT ime(v p , tm)) → meets(tm 1 , tm) ∧ meets(tm, tm 2 ) (33)

  Scenario ≡ (≥ 1hasV ersion.V ersion) (≥ 0hasV ersionT ransition.V ersionT ransition) (= 1hasT ransactionT ime.T imeInterval) transitions present in a scenario also must have their one previous and next version existing in the scenario. ∀vt(hasV ersionT ransition(b, vt)∧ hasP reviousV ersion(vt, vt p ) ∧ hasN ewV ersion(vt, vt n )) → hasV ersion(b, vt n ) ∧ hasV ersion(b, vt p ) (35)For any two versions present in the scenario, there must exist a version transition.∀v 1 ∀v 2 ∃vt(hasV ersionT ransition(b, vt)∧ hasV ersion(b, v 1 ) ∧ hasV ersion(b, v 2 ) ∧hasP reviousV ersion(vt, v 2 ) ∧ hasN ewV ersion(vt, v 1 )) (36)There must not be any existence time overlap between any two versions or any two version transitions.

  44) A workspace consists of one Consensus Space and one Propositions Space. It has an owner. Consensus Space andPropositions Space must share at least one common version (i.e., the starting point). ∃v bc , ∃v bp (ConsensusSpace(c) ∧ hasScenario(c, b c ) ∧ hasV ersion(b c , v bc ) P ropositionsSpace(p) ∧ hasScenario(p, b p ) ∧ hasV ersion(b p , v bp )) → v bc = v bp (47) 5 U rbanCo 2 F ab: Collaborative Comprehension of Urban Fabric

Fig. 5 :

 5 Fig. 5: Example of workspace and output of urbanco2fab viz showing one consensus scenario (scenario1) and one proposition scenario (scenario2). 6 first letters of hash created following a urbanco2fab commit are used to identify the different versions

Fig. 6 :

 6 Fig. 6: UDV: Application to visualize and navigate 3D cities

  4.7 Workspace for concurrent points of viewA workspace has two spaces: Consensus Space and Propositions Space. Both these spaces contain scenarios detailing the changes occuring in a given place or time through a sequence of versions. A Consensus Space is the reference space used by the researchers in a group and there is a consensus among them about its contents. A Consensus Space has only one scenario whereas thePropositions Space can have zero or more scenarios. Contrary to the Consensus Space, a Propositions Space is used by agents to propose alternate scenarios.Propositions Space has zero or more scenarios. A scenarios inPropositions Space may have different type of versions having version type Existing or Imagined.

	Space	(40)
	Space ≡ (≥ 1hasT ransaction.T ransaction) (= 1hasCreator.Agent)	(41)
	PropositionsSpace Space PropositionsSpace ≡ (≥ 0hasScenario.Scenario)	(42)

https://git-scm.com/

http://www.opengeospatial.org/

http://geogig.org

http://pygit2.org/

Acknowledgements

This work was performed within the framework of the LABEX IMU (ANR-10-LABX-0088) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). We would like to thank Clémentine Périnaud, Vincent Jaillot, Eric Boix, Frédéric Pedrinis and Jérémy Gaillard for their feedback. We would also like to thank anonymous reviewers for their valuable feedback, thanks to which we we were able to improve our work.


Yanlin Wu

Olivier Monfort

Wenbo Dong

Marcello Brigante
email: marcello.brigante@uca.fr

Gilles Mailhot

Enhancement of iron-mediated activation of persulfate using catechin: from generation of reactive species to atenolol degradation in water

Keywords: Pollutant degradation, sulfate radical, hydroxyl radical, iron reduction Highlights

Persulfate (PS) activation reaction, which forms sulfate radical (SO 4

•-), can be used to degrade organic pollutants in water. However, a drawback of this reaction is that the regeneration of ferrous ions requires a high concentration of hydrogen peroxide (Fenton-like reaction) or use of UV radiation. Catechin (CAT), a non-toxic antioxidant of natural origin from tea, is used in this work to improve the sulfate radical-mediated degradation of atenolol (ATL, a model pollutant) in water using relatively low concentrations of reactive chemical species (less than 100 µM).

To the best of the author's knowledge, the direct effect of CAT on the oxidation state of iron, which is promoted by the reduction of ferric into ferrous ions with the enhancement of SO 4

•formation in the presence of PS, is demonstrated for the first time. The enhancement versus inhibition effect of CAT and the chemical mechanism of the iron-based activation process are explained. Results show that UVA radiation, which is representative of solar light, accelerates the 2 initial degradation of ATL by more than 30% through ferric iron photolysis. Finally, a reaction mechanism leading to the formation of hydroxyl radicals (HO • ) and SO 4 •-is proposed considering the implication of different activation/reaction chemical steps.

Introduction

The Fenton process based on the Fe(II/III) redox cycle in the presence of hydrogen peroxide was described for the first time in 1894 [START_REF] Fenton | LXXIII.-Oxidation of tartaric acid in presence of iron[END_REF] and has been used for the degradation of a wide range of organic contaminants. In the last decades, many works focusing on the modified Fenton-like process have been proposed to stabilize and generate additional Fe(II) species and improve the removal efficiency of organic contaminants in water [START_REF] Kaur | Photo-induced oxidation of ceftriaxone by persulfate in the presence of iron oxides[END_REF][START_REF] Li | Photochemical transformation of aminoglycoside antibiotics in simulated natural waters[END_REF][START_REF] Romero | Enhancement of Fenton and photo-Fenton processes at initial circumneutral pH for the degradation of the β-blocker metoprolol[END_REF][START_REF] Tian | Heterogeneous Fenton-like degradation of ofloxacin over a wide pH range of 3.6-10.0 over modified mesoporous iron oxide[END_REF]. These modified reactions, such as ferric ion (Fe(III)) photoreduction or complexation with organic ligands, have also been used for persulfate (PS) activation to generate additional Fe(II) and sulfate radical (SO 4

•-) [START_REF] Bi | Degradation of oxytetracycline with SO 4 under simulated solar light[END_REF][START_REF] Jiang | Bicarbonate-activated persulfate oxidation of acetaminophen[END_REF][START_REF] Wu | Sulfate radical photogeneration using Fe-EDDS: Influence of critical parameters and naturally occurring scavengers[END_REF]. Furthermore, the reaction mechanism was becoming increasingly clear, and the concentration of ferrous iron in water was found to be the most critical parameter.

Therefore, researchers investigated different technologies, such as reaction in acidic media (Velo [START_REF] Gala | Comparative study of oxidative degradation of sodium diatrizoate in aqueous solution by H 2 O 2 /Fe 2+ , H 2 O 2 /Fe 3+ , Fe (VI) and UV, H 2 O 2 /UV, K 2 S 2 O 8 /UV[END_REF], use of irradiation [START_REF] Giannakis | Solar photo-Fenton disinfection of 11 antibiotic-resistant bacteria (ARB) and elimination of representative AR genes. Evidence that antibiotic resistance does not imply resistance to oxidative treatment[END_REF][START_REF] Guerra | Oxidation mechanisms of amoxicillin and paracetamol in the photo-Fenton solar process[END_REF], presence of organic ligands [START_REF] Luca | Study of Fe(III)-NTA chelates stability for applicability in photo-Fenton at neutral pH[END_REF][START_REF] Huang | Assessment of the Fe(III)-EDDS complex in Fenton-like processes: From the radical formation to the degradation of Bisphenol A[END_REF][START_REF] Wang | Hydroxyl and sulfate radicals activated by Fe(III)-EDDS/UV: Comparison of their degradation efficiencies and influence of critical parameters[END_REF], and reduction conditions [START_REF] Nazari | Degradation of 4-chlorophenol in aqueous solution by sono-electro-Fenton process[END_REF][START_REF] Wu | Kinetics and mechanism of degradation of chitosan by combining sonolysis with H 2 O 2 /ascorbic acid[END_REF], to enhance the Fe(II) formation/regeneration.

Antioxidant agents, such as polyphenolic compounds, are known for their anti-aging, anti-carcinogenetic, and anti-atherosclerotic properties [START_REF] Brown | Health effects of green tea catechins in overweight and obese men: a randomised controlled cross-over trial[END_REF]. Green tea is rich in polyphenolic compounds, especially (+)-catechin (CAT) (Yang et al., 2018). CAT has catecholate groups that easily chelate Fe 3+ , which makes it susceptible to undergo light-induced ligand oxidation and Fe 3+ reduction [START_REF] Barbeau | Photochemistry of organic iron(III) complexing ligands in oceanic systems[END_REF][START_REF] Barbeau | Photochemical cycling of iron in the surface ocean mediated by microbial iron(III)-binding ligands[END_REF]. Dong et al. already used another polyphenolic compound (gallic acid), which played an important role on Fe(II) formation/regeneration and promoted the efficiency of H 2 O 2 /Fe(III) system in the degradation of methyl orange [START_REF] Dong | Promoted discoloration of methyl orange in H 2 O 2 /Fe(III) Fenton system: Effects of gallic acid on iron cycling[END_REF]. However, we believe that studies assessing the mechanism of radical generation and reactivity through iron reduction have not been reported.

Atenolol (ATL), a widely used pharmaceutical which exhibits toxicity on freshwater species and inhibition on human embryonic cell growth, was selected as the target pollutant [START_REF] De | Occurrence of pharmaceuticals in a water supply system and related human health risk assessment[END_REF]. ATL is also considered a recalcitrant pollutant due to its slow biodegradation and high persistence under sunlight in water [START_REF] Yamamoto | Persistence and partitioning[END_REF]. Under chlorination or UV treatment, ATL leads to the fast formation of products with high toxicity in water [START_REF] Dellagreca | Unusual products of the aqueous chlorination of atenolol[END_REF][START_REF] Diniz | Ecotoxicity of ketoprofen, diclofenac, atenolol and their photolysis byproducts in zebrafish (Danio rerio)[END_REF].

In the present work, the mechanism of SO 4 •-generation in the Fe(III)/PS system, as well as the formation of Fe(II) and ATL degradation, was investigated for the first time using CAT.

Interestingly, as a non-toxic extract from green tea, CAT shows high stability and solubility in water, which makes it a good candidate for contaminant removal application. The effect of CAT, Fe(III), and PS concentrations on the degradation efficiency of ATL was also studied, and the role of oxidative radicals as well as the second-order reaction rate constants with generated radicals (HO • /SO 4 •-) was elucidated. An activation and reactivity system, in which CAT plays a key role, was proposed to assess the enhancement versus inhibition role of antioxidant agents as reduction species for iron but also as radical scavengers in water. Finally, the effect of solar spectrum UVA radiation on the CAT-mediated persulfate activation system was evaluated.

Materials and methods

Chemicals

Sodium persulfate (Na 2 S 2 O 8 , PS), Atenolol (ATL), (+)-catechin (CAT), Ferrozine, isopropanol

(2-Pr), and tert-Butanol (t-BuOH) were obtained from Sigma-Aldrich. Ferric perchlorate (Fe(ClO 4 ) 3 ) was obtained from Fluka. Perchloric acid (HClO 4 ) and sodium hydroxide were used to adjust the pH of the solutions. All chemicals were utilized without further purification. All solutions were prepared in milli-Q water (18.2 MΩ cm). Unless otherwise stated, all experiments were performed at pH 3.3 to maintain soluble iron in water (homogeneous reactivity).

Experimental Procedure

All experiments in the absence of light (dark) were conducted in a brown bottle at ambient temperature (298 ± 2 K). A total of 50 mL mixture was magnetically stirred during the reaction, and samples were withdrawn at fixed intervals. The samples were then analyzed using UV-vis spectroscopy and high-performance liquid chromatography (HPLC-UV) (section 2.3). A total of 10 µM of ATL was used in all the experiments. The effect of different concentrations of CAT, PS, and iron was investigated at pH approximately 3.3. Irradiation experiments were conducted in a homemade photoreactor equipped with four UVA lamps (TLD 15W/05, Philips, Netherlands) located on the top of the solution. The emission spectrum of the lamp is shown in Fig. S1.

Quantitative analysis of ATL and iron

The ATL concentration in the samples was determined using ultra-performance liquid chromatography (UPLC) (Waters, USA) with C18 column (BEH, 100 mm × 2.1 mm × 1.7 μm), and the mobile phase was an ammonium acetate (0.01 M)/methanol solution with 70:30 (v/v). The flow rate was 0.25 mLmin -1 , and the detection wavelength was 224 nm. The CAT concentration was determined by HPLC (Waters, USA) with C18 column (Agilent, 250 mm × 4.6 mm × 5 μm), and the mobile phase was an acetonitrile/formic acid (0.5%) solution with 25:75 (v/v). The flow rate was 0.6 mL min -1 , and the detection wavelength was 279 nm. Fe(II) was quantified using a colorimetric method based on ferrozine complexation [START_REF] Stookey | Ferrozine -a new spectrophotometric reagent for iron[END_REF].

Second-order kinetic constants determination

Two different methods were used to determine the second-order rate constant of ATL and CAT with sulfate and hydroxyl radicals (SO 4 •-and HO • ), respectively. For HO • , the transient absorption spectroscopy was adopted to investigate the reactivity with CAT and ATL. In this approach, a laser flash photolysis (LFP) system using an excitation wavelength of 266 nm coupled with UV-vis detection could follow the radical absorption signal decay or its formation in the presence of different CAT and ATL concentrations. Similar experimental procedures and conditions were already detailed in previous works, and only a brief description is provided in the SM section [START_REF] Huang | UVA-UVB activation of hydrogen peroxide and persulfate for advanced oxidation processes: Efficiency, mechanism and effect of various water constituents[END_REF][START_REF] Wu | Sulfate radical photogeneration using Fe-EDDS: Influence of critical parameters and naturally occurring scavengers[END_REF].

For the reactivity between SO 4 •-and ATL, the formation of a new transient species absorbed around 450 nm close to the signal of SO 4

•-interfered with the kinetic decay (Fig. S2). Hence, a different method using a competition kinetic approach under steady-state irradiation (UVA) in the presence of Bisphenol A (BPA) was used to determine the reactivity constant between SO 4

•-and ATL. Meanwhile, the reactivity constant between SO 4

•-and CAT of the transient-state absorption of SO 4 •-could be directly investigated.

Results and discussion

Reactivity of hydroxyl and sulfate radicals with ATL and CAT

The reactivity between ATL and CAT with generated radicals (SO 4 •-/HO • ) was determined to assess the effect of different reaction pathways during the Fenton-like reaction. For the reactivity between SO 4 •-and CAT, a solution containing 10 mM of PS was used to generate SO 4 •-under UVA irradiation (R1). BPA was used as a reference compound, and no direct photolysis under UVA irradiation was observed [START_REF] Huang | UVA-UVB activation of hydrogen peroxide and persulfate for advanced oxidation processes: Efficiency, mechanism and effect of various water constituents[END_REF]. A competition kinetic approach considering the decays of ATL and BPA concentrations during times (R2 and R3) was used to determine the second-order rate constant (R2 and R3) following Eq. 1.

k  = (1.65 ± 0.25) × 10 9 M -1 s -1 .
Other constants with HO • were determined using chemical competition reactivity in the presence of thiocyanate anion (SCN -), which led to the formation of di-thiocyanate radical anion (SCN 2 •-) followed at 470 nm using LFP experiments (see SM for experimental procedure and Fig. S3).

CAT was found to be approximately twice more reactive with SO 4

•-and HO • than ATL (Table 1).

The high reactivity of CAT toward electron transfer reaction (main reactive pathway of SO 4 •-) is attributed to the presence of two lone electron pairs on the phenolic groups. This high affinity with radical species also suggests a possible scavenging effect of CAT (i.e., negative contribution) during the ATL degradation experiments.

Reactivity between Fe 3+ and CAT

UV-vis spectroscopy was used to investigate the possible reactivity between CAT and ferric ions (Fe 3+ ) in the solution. A total of 100 µM CAT solution was found to be stable in dark condition at least five days. The spectroscopic analysis of solutions at different pH is presented in Fig. S4.

From pH 2.5 to 6.0, no significant differences in the UV-vis spectra of CAT were observed, and the same absorption maximum at 279 nm was found (ε 279 = (3610 ± 70) M -1 cm -1 ). A bathochromic shift (from 279 nm to 290 nm) was observed when the pH increased from 7.8 to 11.3, and a shoulder appeared at 320 nm at a high pH. This redshift corresponded to the deprotonation of phenolic groups on CAT occurrence at high pH values (pKa approximately 9.0).

In the presence of 100 µM of CAT at pH 3.3, the UV-vis spectrum of 100 µM solution of ferric ions was strongly modified (Fig. 1); no additional absorption was observed at wavelengths higher than 300 nm. The UV-vis spectrum of the solution indicated the absence of CAT in the solution, whereas no spectroscopic contribution of Fe 3+ was observed. Moreover, the UV-vis spectrum of solution demonstrated a slight bathochromic shift compared with that of pure CAT. This effect was due to the possible electron transfer from the phenolic groups of CAT to Fe 3+ , leading to the formation of quinone groups as previously observed during selective oxidation of CAT [START_REF] Tanaka | Oxidation of tea catechins: Chemical structures and reaction mechanism[END_REF]. No significant differences between the spectra of Fe 3+ and Fe 2+ in the presence of CAT were observed (Fig. 1 insert).

The concentration of Fe 2+ in the solution was monitored during the mixture of 100 µM of Fe 3+

with different CAT concentrations to clarify the interaction mechanism between CAT and Fe 3+ . As reported in Figure 2A, the formation of a significant amount of Fe 2+ from Fe 3+ solution (100 µM)

was strongly correlated to the initial CAT concentration. The plot of ratios between [Fe 2+ ] and [Fe tot ] as function of initial CAT/Fe 3+ concentrations ([CAT]/[Fe 3+ ]) reported in Figure 2B indicated the significant formation of Fe 2+ . Fe 2+ immediately reached a plateau in all experiments.

This finding suggests that Fe 3+ was quantitatively converted into Fe 2+ following a reaction with a stoichiometry (R4) of 1 mole of CAT with 2 moles of Fe 3+ . To explain the ferrous ions generation, we can consider that semiquinone and quinone (CAT ox ) might stepwise be formed with each step being a single electron transfer from the two phenolic groups.

(R4)

Effect of CAT on the modified PS activation process

ATL degradation

The reactivity of CAT (5 µM) in the solution containing 50 and 100 µM of Fe 3+ and PS, respectively, was investigated by monitoring the degradation of ATL and the formation of Fe 2+

during the reaction (Fig. 3). No ATL degradation was observed after 60 min in blank experiments, that is, using ATL + PS, ATL + Fe 3+ , ATL + CAT, ATL + PS + CAT, and ATL + Fe 3+ + CAT; meanwhile, only 10% degradation could be determined in the system Fe 3+ + PS (Fig. 3). However, in Fe 2+ + PS system, a fast ATL initial degradation rate ( d ATL R ) was be observed during the first 10 min (2.51±0.50 × 10 -7 M min -1 ) and followed by a plateau. ATL (30%) was degraded in Fe 2+ + PS system after 60 min of reaction. This reactivity could be explained by considering the formation of SO 4

•-through the well-known PS activation reaction (R5). The plateau was due to the fast reactivity of Fe 2+ in the system, while no additional Fe 3+ could be converted back to Fe 2+ without a reducing agent. When 50 µM of Fe 3+ was previously mixed with 5 and 100 µM of CAT and PS, respectively, a similar trend was observed for the first 10 min ( d ATL R = 2.12 ± 0.44 × 10 -7 M min -1 ), whereas ATL concentration continued to decrease by up to 52% of the initial concentration after 60 min (Fig. 3).

The enhancing effect observed in the presence of CAT could be explained by observing the Fe 2+ formation during the reaction (insert Fig. 3). As expected, approximately 10 µM of Fe 2+ was observed when 50 µM of Fe 3+ was mixed with 5 µM of CAT (R4), and Fe 2+ concentration remained stable during its time in the ATL + Fe 3+ + CAT system. However, when 100 µM of PS was present in the solution (ATL + Fe 3+ + CAT + PS), Fe 2+ could activate PS for SO 4 •-formation (R5), thereby leading to enhance ATL degradation (R6).

(R5) (R6)

The higher efficiency in the presence of CAT/Fe 3+ /PS than that of Fe 2+ /PS highlighted the role of CAT for the regeneration of Fe 2+ during the process and its capability to activate the cycle between Fe 2+ and Fe 3+ .

Antagonist role of CAT and oxidant species occurrence

Although CAT could enhance SO 4 •-formation via Fe 2+ generation, it could also scavenge generated radicals (Table 1), thus partially inhibiting the ATL degradation. The stability of CAT in the presence of Fe 3+ , ATL, and PS is reported in Figure 4A. No direct reaction between CAT and ATL was observed. Meanwhile, slight CAT oxidation occurred in the presence of PS (approximately 25% after 1 h). However, approximately 75% of CAT was degraded in the presence of Fe 3+ after 60 min (with a pseudo-first-order decay kˋ= 8.4 ± 1.3 × 10 -2 min -1 ) due to the oxidation corresponding to the formation of Fe 2+ through electron transfer reaction (R4).

Complete degradation of CAT was achieved in the Fe 3+ +PS system after 10 min (kˋ= 2.7 ± 0.5 × 10 -1 min -1 ) due to the reaction of generated SO 4 •-with CAT. When ATL was observed in the Fe 3+

+ PS system, CAT degradation slightly decreased (kˋ= 2.3 ± 0.1 × 10 -1 min -1 ) due to the competitive reaction of SO 4 •-with ATL. Therefore, finding the optimal concentration of CAT for efficient wastewater treatment and assessment of positive versus negative effect on modified activation of PS is crucial.

ATL degradation was monitored using different CAT concentrations (from 0 to 25 µM) in the presence of 50 µM of Fe 3+ and 100 µM of PS (Fig. 4B). When the CAT concentration was raised up to 5 µM, the pseudo-first-order decay of ATL (kˋA TL ) increased by approximately two orders of magnitude (from 2.3 × 10 -3 to 1.6 × 10 -1 min -1 ) (R5) through the formation of Fe 2+ (R4) due to PS activation. The ATL degradation rate at 60 min was enhanced from 10% to 52% with CAT concentration up to 5 µM. When the CAT concentration was raised to 25 µM, the kˋA TL decreased to 8.6 × 10 -3 min -1 , and ATL degradation rate decreased to 32%. This negative effect observed at high CAT concentrations was attributed to the reactivity between CAT (or its oxidation products)

and SO 4

•-, which competed with ATL degradation. Given the second-order rate constants reported in Table 1, the initial ATL and CAT concentrations, and the similar reactivity of CAT oxidation products (reasonably quinone derivatives), the SO 4 •-selectivity on each reactive species in solution ( ) can be estimated as follows:

, where [X] was the initial concentration of reference compounds, and is the second-order rate constant with SO 4 •-. was calculated from the sum of the contribution of the initial concentration of all reactive species in the solution (i.e., CAT, PS, and ATL) with the second-order rate constant of SO 4 •-. Under adopted experimental conditions reported in Figure 4B, when CAT concentration was 5 µM, approximately 57% of SO 4 •-reacted with ATL while 43% reacted with CAT. However, in the presence of 25 µM of CAT, only 21% of SO 4 •-reacted with ATL and up to 79% reacted with CAT.

In all experiments, less than 0.5% of SO 4 •-was scavenged by PS due to the low reactivity constant ( = 1.2 × 10 6 M -1 s -1 ) [START_REF] Neta | Rate constant for reactions of inorganic radicals in aqueous solution[END_REF].

UVA effect on modified PS activation system

The effect of UVA irradiation on ATL degradation is reported in Figure 5 using different systems.

No ATL degradation was observed under UVA with or without CAT (blank experiments not reported in Figure 5). However, approximately 10% and 35% of ATL degradation could be achieved after 60 min using either 100 µM of PS or 50 µM of Fe 3+ , respectively. This process could be attributed to the UVA-mediated formation of SO 4

•-(PS photolysis) (R7) and HO • (iron-aqua complex photolysis) (R8) in the solution. A redox cycle including HO • and SO 4

•enhanced the ATL degradation with the presence of PS and Fe 3+ in the solution. The ATL degradation extent was increased from 52% to 80% in the presence of UVA in the system containing 10 µM of ATL mixed with 5 µM of CAT, 50 µM of Fe 3+ , and 100 µM of PS.

(R7) (R8) Thus, high efficiency was observed in the presence of light. This finding indicates the presence of an important complementarity between the formation of Fe 2+ through Fe 3+ reduction by UVA radiation and CAT.

Radical species involvement

Scavenging experiments were performed by using isopropanol (2-Pr) and tert-butanol (t-BuOH) to assess the involvement of different radical species during ATL degradation in the presence of Fe 3+ and PS. Meanwhile, 2-Pr was used as a quencher of HO • and SO 4

•-(

• 2-Pr,HO k = 1.9 × 10 9 M -1 s -1 , 4 2-Pr,SO k  = 6.9 × 10 7 M -1 s -1 ), and t-BuOH selectively reacted with HO • rather than with SO 4 •-due to differences between reactivity constants of the two radicals ( • , BuOH HO k = 6.0 × 10 8 M -1 s -1 and 4 , BuOH SO k  = 8.4 × 10 5 M -1 s -1 ) [START_REF] Buxton | Critical review of rate constants for reactions of hydrated electrons, hydrogen atoms and hydroxyl radicals (°OH/O°-) in aqueous solution[END_REF][START_REF] Neta | Rate constant for reactions of inorganic radicals in aqueous solution[END_REF]. A concentration of 10 mM of each scavenger was adopted to trap specific radical species (in the case of (t-BuOH) efficiently also considering the possible competition effect of CAT in the solution.

The effect of 2-Pr and t-BuOH was compared when 10 µM of ATL was used in the presence of 5 µM of CAT, 50 µM of Fe 3+ , and 100 µM of PS at pH = 3.3. No significant difference in ATL degradation was observed with t-BuOH (for both system kˋ approximately 1.2 ± 0.1 × 10 -2 min --1 ) (Figure 6A). By contrast, the ATL degradation was completely inhibited using 2-Pr, indicating that only SO 4

•-was generated under dark conditions. Under UVA irradiation (Fig. 6B), the ATL degradation was partially inhibited with t-BuOH (kˋ without scavengers = 3.2 ± 0.3 × 10 -2 min -1 and kˋ with t-BuOH = 1.8 ± 0.2 × 10 -2 min -1 ). However, almost no degradation could be observed in the presence of 2-Pr. Considering the reactivity constants of radical with ATL and scavengers, approximately 77% and 23% of ATL degradation under UVA were attributed to SO 4 •-and HO • , respectively. The generation of the two radicals was considered an asset for the degradation of water containing different kind of pollutants.

Conclusions

Ferrous iron was the key parameter in PS activation processes, and many efforts have been made

in the direction of formation/regeneration of reactive species under different conditions. For the first time, the present work investigated the use of CAT, a non-toxic and natural antioxidant, on the

Figure captions Figure 1 :

 captions1 Figure captions

Figure 2 :

 2 Figure 2: (A) Formation of Fe 2+ from 100 µM of Fe 3+ using different CAT concentrations for 1

Figure 3 :

 3 Figure 3: Degradation of ATL (10 µM)using different solution in which 5 µM of CAT are mixed

Figure 4 :

 4 Figure 4: CAT stability (A) by monitoring its degradation under different conditions (10µM ATL,

Figure 5 :

 5 Figure 5 : Effect of UVA radiation on the ATL (10 µM) degradation in different solutions

Figure 6 :

 6 Figure 6: Scavenging experiments using 10 mM of 2-Pr ort-BuOH under dark (A) and UVA (B)

ACKNOWLEDGMENTS

Authors acknowledge financial support from National Natural Science Foundation of China (NSFC 21607116), the Region Council of Auvergne Rhône Alpes, and the "Fédérationdes Recherchesen Environnement" through the CPER "Environment" founded by the Region AURA, the French government, the FEDER from the European Community and PRC program CNRS/NSFC n°270437, and the CAP 20-25 I-site project.

of eight selected pharmaceuticals in the aquatic environment: Laboratory photolysis, biodegradation, and sorption experiments. Water Res. 43, 351-362. Yang H., Xue X., Li H., Apandi S.N., Tay-Chan S.C., Ong S.P., et al., 2018. The relative antioxidant activity and steric structure of green tea catechins -A kinetic approach. Food Chem. 257, 399-405.

reduction capability of Fe 3+ into Fe 2+ in a modified PS activation process (Fe 3+ /CAT/PS).

An optimal concentration of CAT (5 µM) was utilized for systems containing 50 µM of Fe 3+ and 100 µM of PS to limit the competitive reaction with generated radicals and target pollutant (ATL).

Under such low concentration conditions, the high degradation extent of 10 µM ATL could be achieved in the dark after 60 min (approximately 50%). CAT was complementary to PS in the reduction/oxidation cycle of Fe(III)/Fe(II). Under UVA irradiation, the modified PS activation process was enhanced and reached almost 80% of ATL degradation. Moreover, the only reactive species involved in the dark conditions was the SO 4 •-. Meanwhile, HO • also contributed up to approximately 25% of the total radical generation under UVA. Moreover, products from waste green tea leaves were proven useful in Fe(III) reduction to produce Fe(II). This work strengthened the possible use of waste (tea leaves) for water application treatments.