A Methodological Approach on Disused Public Properties in the 15-Minute City Perspective

: Accessibility and Walkability represent, today, some of the most striking challenges contemporary cities are facing, particularly in light of the goals from UN Agenda 2030, aimed at a sustainable city, and particularly in terms of a livable, healthy and inclusive city. This can be also performed thanks to a set of high quality public services and a set of important and central services and infrastructures. These principles, however, are constrained by an overall, general fragmentation affecting many urban areas, particularly as an outcome of the vehicular accessibility needs. Scholars have debated through the years on the nature of cities and on the preference for centrality of services compared to the distribution of services towards dispersed neighborhood units. Recently, a need for a wider, minimum set of services that is easily reachable to most citizens is ﬁlling the scholars and city mayors’ agendas in order to improve urban performances. This is also coupled with a huge surge in the heritage of abandoned urban items coming from previous periods of time and alternative uses. The aim of this research is to evaluate the role of abandoned urban assets—particularly big-size buildings and compounds and their areas—to facilitate the implementation of the concept of a 15-minute city, a city that is capable of granting a wider social equality and access to main urban services to citizens and city users. To do this, we developed a set of indexes, capable of detecting porosity, crossing and attractiveness. This latter index in particular represents a combined index that can be used to improve the accessibility of pedestrians in urban central locations. In the present research, we decided to limit the analysis to a subset of disused public buildings in the historic center of a sample city, as Cagliari (Sardinia, Italy). This was done in order to understand if and in which terms they can contribute, after their redevelopment, to the development of the 15-minute city, as well as reducing the “enclave–effect: they are, at present, playing in the historic urban fabric.


Introduction
Public spaces have always been at the center of reflection and practice of disciplines that deal with the city and central places. Evaluating these spaces in relation to the new forms assumed by contemporary territories and cities increasingly "fragmented" by numerous abandoned buildings-such as large factories, hospitals, etc.-and by the need to reduce the health risk from COVID-19 is not easy and nonetheless requires an interdisciplinary approach. The economic transition process, from the old to the new economy [1], has produced non-negligible effects on the territory, modifying both the productive and the organizational structure of our cities and determining phenomena of dismissal of a significant number of buildings. Since the 1980s, the decommissioning of industrial areas and most of the buildings and large public infrastructures that made up the nineteenth-century city, and the first half of the twentieth century, which have • Movement: railway stations and public transport, ports, parking; • Welfare: schools, parks, hospitals, chemist's, churches; • Trade: food and other.
The traditional central locations in cities have evolved and changed in time ( Figure 1). After the early stage of industrialization (Square, Market, Church, Hospital, etc.), other locations became increasingly important in the following stages, summing up new places such as factories and schools, railway and bus stations and, more recently, universities, leisure (in the broad sense) and temporary locations.
Moreover, the current and tangible condition of the central places of the recent past has been their numerous disposals, with the associated phenomena of urban enclaves. Many of these divestments are often found incorporated in the urban environment or even in the historic center characterized by a strong materiality and stylistic mix [18]. The emerging need to adopt sustainable urban development models, based on the protection of the environment and natural resources [19] and the fight against indiscriminate land use [20], have brought attention to the compact city model [21]. This grows internally by recovering abandoned areas to respond to the new demands of the contemporary world-new forms of production and work: industry 4.0, social housing, co-working, smart community and health-wellness. The health crisis is transforming, and will transform, the conception of central places in cities. Indeed, architects and urban planners are looking for new visions [22][23][24][25][26] capable of orienting the urban development for the future. The spread of the epidemic has in fact put cities to a severe test, highlighting a series of new criticalities, which can also be overcome through the implementation of innovative strategies to reinvent and readjust abandoned buildings. At first, greater attention to the environment and to the quality of life in general, is followed by a more intense use of innovative technologies to which to delegate the control of the territory [27,28] and at the same time plan a new mobility-individual and public-with a view to smart mobility. Among these is the 15-minute city [29][30][31][32], which derives from the concept of "neighborhood unit", developed for the first time in 1923, as a proposal for an arrangement to build new residential districts. The current health situation in fact forces us to redesign our lives and the places where we live. Today more than ever, a smart city must be a safe city, ensuring constant analysis of vulnerability and adequacy also in terms of accessibility of services and/or central places. A mix of functions is needed, capable of improving the supply of services and therefore the quality of life, to alleviate the vehicular congestion of the central city-and therefore pollution-and to reduce commuting phenomena. To do this, pedestrian accessibility to central locations facilitated by urban porosity plays a fundamental role, resulting from the recovery of abandoned buildings that currently constitute "enclaves", which could represent strategic nodes in the 15-minute city network [33,34], through a renewed sense of common good from anti-commons to commons [35]. The objective of this research is to evaluate if and in what way the disused real estate assets can represent a facilitating element for reaching the 15-minute city. This was possible by developing suitable indexes, following analyzes on the centrality of the places.
The rest of the paper is organized as follows: 1. Literature review (Section 2) 2. The concept of "public city". Risks and opportunity of divestment (Section 3); 3. Methodology and data (Section 4); 4. Results and Discussion (Section 5); 5. Conclusions and Future Development (Section 6). The spread of the epidemic has in fact put cities to a severe test, highlighting a series of new criticalities, which can also be overcome through the implementation of innovative strategies to reinvent and readjust abandoned buildings. At first, greater attention to the environment and to the quality of life in general, is followed by a more intense use of innovative technologies to which to delegate the control of the territory [27,28] and at the same time plan a new mobility-individual and public-with a view to smart mobility. Among these is the 15-minute city [29][30][31][32], which derives from the concept of "neighborhood unit", developed for the first time in 1923, as a proposal for an arrangement to build new residential districts. The current health situation in fact forces us to redesign our lives and the places where we live. Today more than ever, a smart city must be a safe city, ensuring constant analysis of vulnerability and adequacy also in terms of accessibility of services and/or central places. A mix of functions is needed, capable of improving the supply of services and therefore the quality of life, to alleviate the vehicular congestion of the central city-and therefore pollution-and to reduce commuting phenomena. To do this, pedestrian accessibility to central locations facilitated by urban porosity plays a fundamental role, resulting from the recovery of abandoned buildings that currently constitute "enclaves", which could represent strategic nodes in the 15-minute city network [33,34], through a renewed sense of common good from anti-commons to commons [35]. The objective of this research is to evaluate if and in what way the disused real estate assets can represent a facilitating element for reaching the 15-minute city. This was possible by developing suitable indexes, following analyzes on the centrality of the places.
The rest of the paper is organized as follows: 1. Literature review (Section 2) 2.
The concept of "public city". Risks and opportunity of divestment (Section 3); 3.
Conclusions and Future Development (Section 6).

Literature Review
The need to contain the spread of the SarsCov-2 virus and, at the same time, to restart the economic system has brought the issues of pedestrianism and urban micro mobility back to the center of the political and scientific debate [36][37][38]. Among the consequences, we can recall the backlash suffered by public transport [39] and the return to the use of the car, which aggravated the already critical conditions of the urban environment in major cities [40]. Walkability, cycling and micro-mobility are therefore at the center of the new mobility supply, which finds wide collective consensus in the main national and international metropolitan cities [41]. Furthermore, these represent the fastest and cheapest solution-both for the public and the private sector-for urban travel, favoring healthy lifestyles and the distancing of health security.
The new choices on urban mobility go in the direction of improving walkability and encouraging micro-mobility, creating infrastructures for electric vehicles, and also in order to improve air quality. In fact, during the lockdown, it was possible to evaluate how bad air quality in the megalopolis-Po Valley, London, Paris, Shanghai and New York etc.-was related to the spread of the virus [16,42]. The health emergency has brought to light the link between the morphological and functional characteristics of urban contexts and the impacts of public health, opening new scenarios on the theme of "Urban Health", within the complex phenomena of urbanization and land take that characterizes contemporary Italian cities in particular [43][44][45]. Within this scenario, the fundamental role of public space is confirmed, not only the open one of squares, parks and promenades, but also that of large disused public buildings that await urban regeneration interventions. In this sense, one of the most interesting good practices is the Spanish design "Superblocks" developed in Barcelona: the "Street hierarchy model" [46], which allocates the urban space previously used by cars in areas destined for cycle-foot traffic [47]. Specifically, the objectives of the "Superblocks" model were: regeneration of public spaces; promotion of biodiversity with urban green; promotion of social cohesion; promotion of the circular economy; and integration of governance processes and sustainable mobility. The theory of the "Walkable City" [48][49][50] is in fact based on the concepts of sustainable mobility such as coherence, continuity, balance, safety, comfort, accessibility, efficiency and attractiveness of places, as key characteristics to promote transport choices capable of promoting correct styles of life [51]. Furthermore, also according to the UN (2020) [52], the promotion of walkability and micro-mobility is necessary in European cities to facilitate the transition towards a sustainable future and better air quality, in line with the ASI approach, "Avoid", "Shift" and "Improve":

•
Avoiding the need for transport: planning more compact cities with proximity services; • Shifting towards other modes of transport: pedestrian and micro-mobility cycle; • Improving the means of transport: technologically improve means of transport so that they are energy efficient and with low polluting emissions.
In this context, it is therefore necessary and crucial to regenerate the public space (outdoor) through the use of qualitative and quantitative standards [53], which represent the urban context and are supportive to promote healthy lifestyles such as walkability. In fact, making cities more pedestrian means improving the network of public spaces (indoor and outdoor), the mix of land use, in order to create healthier, safer, more comfortable and attractive places. Urban walkability thus represents a strictly functional action to achieve more general and common goals for all cities: accessibility, well-being, air quality and urban microclimate [54]. In addition, the urban walkability represents a general aim that can also be achieved through bottom-up and transitory actions of tactical urbanism. In fact, the temporary use is emerging in the disciplinary debate as a short-term response to the needs of reuse and redevelopment of buildings or major parts of the city [55]. These initiatives, often promoted by the local community, guarantee a spontaneous use of abandoned places, where social innovation and creativity [56] stimulate definitive urban regeneration projects for the future.

The Concept of "Public City". Risks and Opportunity of Divestment
The current conception of "public places" is a result of a process of stratification of meanings that took place over time in Western cities [57]. Public places were born with the first human settlements, with the affirmation of a proprietary system that did not exist in primitive society. Since then, they have always been the representation of the value system supported by the ruling power and by the hegemonic classes of each society. Public infrastructures, architecture and open spaces built for institutional, civil and religious functions testify the political and social organization of peoples in different historical moments. This network of the so-called "collective themes" [58] can be understood as the common foundation of the European cities and their democratic society. Over the course of time, this consolidated model evolved in order to respond to the demands of the new economic system based on globalization, which has generated significant changes in the urban structure and organization. Today, the complexity of urban dynamics makes it difficult to classify public places in a univocal way and asks to go beyond the rigid public-private dichotomies [59]. The contemporary city is characterized by hybrid public spaces in terms of form, ownership, functions and uses, users and relationship within the context.
In Italy too, this process is evident in all of its phases. The "public city" is no longer identified only with the social housing assets and with the urban planning standards of the 1960s -which are currently being updated [60]-but consists of a series of functions and services of public interest offered and managed also by the private subjects [61]. It is within this renewed conceptual framework that the adaptive reuse of obsolete, abandoned and underused buildings and spaces should arise, particularly those belonging to various public bodies, within a comprehensive strategy of sustainable development. The public real estate assets can represent an extraordinary opportunity to achieve the main public policy objectives. Among these, a renewed approach to the urban landscape leads to a reinterpretation of public properties as strategic nodes of urban and territorial networks able to ensure better levels of permeability and connectivity [62].
These aspects are progressively becoming fundamental elements of urban governance and planning in the city of Cagliari, case study in this paper. Cagliari is an Italian city of over 150,000 inhabitants, located on the southern coast of Sardinia. Capital of the Sardinia Region and an Italian Metropolitan City since 2016, Cagliari has established itself as the most important cultural, economic, political and administrative center of the island. Its economy is mainly based on the tertiary sector. Like too many other cities in Europe and in the world, Cagliari has been affected by phenomena of disposal and potential abandonment of a significant number of public assets. This process testifies the evolution of the urban and economic growth, which led to close important public services, industrial and business activities, to optimize the use of buildings thanks to the digital transformation of the Public Administration system, but also to divest military and civil defense assets thanks to the general conditions of peace reached globally [63]. The system of buildings, open spaces and green areas belonging to the State, the University and other public bodies and organizations ( Figure 2) constitutes a considerable component of the existing city, not only in quantitative, but also in qualitative terms, by virtue of the historical, cultural, architectural and environmental values recognized, which make this asset an important resource for the future. This is also at the center of research on how to foster a process of conversion [64]. At the moment, in the historic center there are important public properties such as the former Buoncammino Prison (001 B_ing), the former Tobacco Factory (003 B_ing) and the San Giovanni di Dio Hospital (002 B_ing), true icons of the city of Cagliari [65], for which it is necessary to define new uses. An important aspect to consider is that there is a significant degree of fragmentation of these components of the urban fabric, due not only to their different owners, which determines different types of use and accessibility of spaces, but also to the presence of fences and other physical elements that prevent a connection between them. As a matter of fact, although characterized by big areas compared to the surrounding disused fabric, the main public complexes involved in the process of disposal in the historic city appear as a sequence of "enclaves" rather than as a network of nodes and centralities: the tendency of inhabitants and city users is to circumnavigate, rather than cross. This issue has been faced by the Plan for the Historic Center of Cagliari (PHC) drawn up in 2015 [66] and subsequently by the participatory process launched to draft the Metropolitan Strategic Plan (MSP) of the Metropolitan City of Cagliari (MCC), which confirmed the prominent role of public real estate assets for the sustainable development of the city [31]. More specifically, the PHC defines strategies to guide a coordinated program of future interventions on the public city, aimed at improving the potential relationship between the existing-and often abandoned-open spaces and green areas, cultural heritage and monumental sites, which could enhance its historical value and urban relevance.
Sustainability 2021, 13, x FOR PEER REVIEW 6 of 20 accessibility of spaces, but also to the presence of fences and other physical elements that prevent a connection between them. As a matter of fact, although characterized by big areas compared to the surrounding disused fabric, the main public complexes involved in the process of disposal in the historic city appear as a sequence of "enclaves" rather than as a network of nodes and centralities: the tendency of inhabitants and city users is to circumnavigate, rather than cross. This issue has been faced by the Plan for the Historic Center of Cagliari (PHC) drawn up in 2015 [66] and subsequently by the participatory process launched to draft the Metropolitan Strategic Plan (MSP) of the Metropolitan City of Cagliari (MCC), which confirmed the prominent role of public real estate assets for the sustainable development of the city [31]. More specifically, the PHC defines strategies to guide a coordinated program of future interventions on the public city, aimed at improving the potential relationship between the existing-and often abandoned-open spaces and green areas, cultural heritage and monumental sites, which could enhance its historical value and urban relevance. On the other hand, the ongoing MSP promotes urban regeneration actions aimed at stimulating a sense of belonging and community, through a participatory process to bring out the real needs and preferred methods to use public buildings and spaces, according to the characteristics of the neighborhood.

Role of Public Real Estate Assets in the Metropolitan Strategic Plan
The Metropolitan City of Cagliari started in late 2019 (September) a participatory process aimed at the realization of the MSP, in order to face important challenges for the metropolitan area. The debate on the future development of the territory has highlighted principles and approaches to be considered in dealing with environmental, economic and social issues. More precisely, at the core of the discussion on the quality of the urban environment and of the "Urban Fabric" were the concepts of the "public city", mixed with that of the private city and of the-often disused-military enclaves. The stakeholders understood the public city as a complex network of public buildings, open spaces, green areas and mobility infrastructures, currently fragmented, but with great potential to assume a predominant role in post-COVID-19 lifestyles. As a matter of fact, it is important On the other hand, the ongoing MSP promotes urban regeneration actions aimed at stimulating a sense of belonging and community, through a participatory process to bring out the real needs and preferred methods to use public buildings and spaces, according to the characteristics of the neighborhood.

Role of Public Real Estate Assets in the Metropolitan Strategic Plan
The Metropolitan City of Cagliari started in late 2019 (September) a participatory process aimed at the realization of the MSP, in order to face important challenges for the metropolitan area. The debate on the future development of the territory has highlighted principles and approaches to be considered in dealing with environmental, economic and social issues. More precisely, at the core of the discussion on the quality of the urban environment and of the "Urban Fabric" were the concepts of the "public city", mixed with that of the private city and of the-often disused-military enclaves. The stakeholders understood the public city as a complex network of public buildings, open spaces, green areas and mobility infrastructures, currently fragmented, but with great potential to assume a predominant role in post-COVID-19 lifestyles. As a matter of fact, it is important to consider that contemporary society is characterized by a reduction of the private sphere and a growing propensity towards the use of collective, public or semi-public spaces.
The public participatory discussion has led to a listing of opportunities and weaknesses as synthetized here (Figure 3). Establishing an intermediate local government layer such as the MCC is seen as an important administrative and institutional target for defining strategic policies on the public city on a metropolitan scale, integrating the PREM (Public Real Estate Management) issue within the standard, more general public policies on economic, social and environmental nature, as well as those related to health. Within this scenario, it can be said that the public asset (buildings and areas) represents a cross-cutting theme, which will play an important role in pursuing the sustainable development objectives. It is an opportunity to improve the provision of socio-recreational and sports facilities, also through new forms of shared management between municipalities, institutions, private investors and citizens. It is retained that higher ranks of accessibility of the public real estate are important to foster sustainable urban development, and also limiting land take. to consider that contemporary society is characterized by a reduction of the private sphere and a growing propensity towards the use of collective, public or semi-public spaces. The public participatory discussion has led to a listing of opportunities and weaknesses as synthetized here (Figure 3). Establishing an intermediate local government layer such as the MCC is seen as an important administrative and institutional target for defining strategic policies on the public city on a metropolitan scale, integrating the PREM (Public Real Estate Management) issue within the standard, more general public policies on economic, social and environmental nature, as well as those related to health. Within this scenario, it can be said that the public asset (buildings and areas) represents a crosscutting theme, which will play an important role in pursuing the sustainable development objectives. It is an opportunity to improve the provision of socio-recreational and sports facilities, also through new forms of shared management between municipalities, institutions, private investors and citizens. It is retained that higher ranks of accessibility of the public real estate are important to foster sustainable urban development, and also limiting land take. Within this perspective, the contemporary urban dynamics led the authors to develop a research methodology aimed at defining indexes of porosity, crossing and attractiveness, and a composite index referred to as the Walkable City.

Methodology: Porosity, Crossing and Attractiveness Indexes and a Composite Index
It is important to underline that the methodology adopted was tested on a limited set of data-as the main locations in the study area are considered privileged candidates for redevelopment and revitalization operations, with the intention, in future research developments, to extend the analysis over the entire urban and metropolitan territory.
The research in particular was based on the development of a set of indexes, considered useful and interesting to evaluate the capacity of a sample of abandoned buildings Within this perspective, the contemporary urban dynamics led the authors to develop a research methodology aimed at defining indexes of porosity, crossing and attractiveness, and a composite index referred to as the Walkable City.

Methodology: Porosity, Crossing and Attractiveness Indexes and a Composite Index
It is important to underline that the methodology adopted was tested on a limited set of data-as the main locations in the study area are considered privileged candidates for redevelopment and revitalization operations, with the intention, in future research developments, to extend the analysis over the entire urban and metropolitan territory.
The research in particular was based on the development of a set of indexes, considered useful and interesting to evaluate the capacity of a sample of abandoned buildings acting as potential public spaces. In doing so, we proposed a set of indexes based on such a capacity, linking together the concept of centrality and therefore considering the quantity and quality of a set of central services and activities in close proximity to this selected subset. Distances from places have been considered from the studies on centrality. In this case, the 15-minute walk, corresponding to about 1200 m, considered by several sources to be those necessary to consider an area as having essential services, were used to define "service" areas around the places.
These service areas were drawn running a "service area" algorithm from the centroids of the selected locations and were expressed in terms of walking distances from the points. Such areas, shaped as irregular polygons drawn from the urban road network on the territory, subsequently serve to collect and count, within them, the data relating to some activities that can be defined as central. Centrality is expressed in the most recent sense of the term. It is worth noting that at the present stage of the research, no distance-decay function was implemented when collecting and counting activities and services from the selected points of origin. This consideration of the central activities located within a defined distance from the selected places led to reasoning in two different directions. On the one hand, there is the need to focus on evaluating the centrality and diversity (or variety) of activities present. It is, in fact, not sufficient to focus on the plain number of "central" activities located within a certain distance from the point, but it is also important to focus on the variety and diversity. It is different, from the user perspective, to find an area of the city characterized by a huge number of bank and insurance company branches, that could be defined as a "financial district", rather than an area characterized by a vibrant mix of differentiated activities [65]. On the other hand, there is the more articulated need to understand the current role of urban voids in order to bring real interruptions, cracks in the urban territory, and to evaluate, instead, their potential role as central places in the event of their opening. These aspects constitute one of the main challenges to the city of Cagliari and to contemporary cities in general. For this reason, the authors have proposed specific indicators to support walkability in contexts characterized by urban enclaves. In particular, the proposal of indexes definable as porosity, crossing and attractiveness, and a composite index, are functional for the reduction of the urban enclave effect previously described. It should be noted that the quantitative definition of the indexes refers to the case of the historic center of Cagliari and is the result of the assessment of the context of the Strategic Plan of the Metropolitan City of Cagliari (2020). Particularly important, in the computation of the different indexes, will be the setup of weights.
Please note that both the single indexes as defined in the following lines (PI, CI and AI) will hold appropriate weights, and also the composite index WBBI will be realized further weighting on the previous indexes.
In this regard, the following indexes (Ii) were defined for each public property: (1) Porosity index (PI): the weighted coverage ratio, between the building area and the pertinent free land area. The PI was calculated as in the formula: where Rc = the ratio, in percentage, between covered area referred to the building, built or buildable, and the land area of reference, and p p is a weight to be attributed to the ratio Rc, so that: In particular, if Rc ⇒ 0 then the weight p p ⇒ 1 (linear decreasing function) according to an inverse relationship and is closely related to the conditions of the reference context.
In other words, as Rc decreases, the weight p p increases in order to appreciate the empty surfaces included in the building areas functional to walkability (see case study, Paragraph 4.2).
(2) Crossing index (CI): The crossing index specifies the level of crossability that characterizes each public property and that allows people to reach different parts of the city. This index, in fact, depends on the architectural morphology of the building, in particular on the number of crossings and paths that connect the various entrances to the property. The CI was calculated as in the formula: where Nc = number of crossings that unfold between two accesses and that allows us to relate more urban portions and p c is a weight to be attributed to the Nc, so that: In particular, if Nc ⇒ n then the weight p c ⇒ 1 (linear increasing function) according to a direct relationship, and is closely related to the conditions of the reference context.
In other words, as Nc increases, the p c weight increases in order to appreciate the crossings included in the functional areas for walkability (see case study, Paragraph 4.2).
(3) Attractiveness index (AI) refers to both the number and the variety of central places found within a 15-minute travel range from the analyzed property compendium. Therefore, for the calculation of this index, the Simpson diversity index was taken as a reference, which allows us to give weight to the diversity of urban boundary functions. The Simpson diversity index, used in statistics in the case of populations with a finite number (in the case of index D) of elements: where Nj indicates the number of j-th "species" where λ corresponds to the Simpson concentration index in the case of finite population.
The Simpson index finds a wide application in ecology to represent environmental ecological diversity and by analogy it has been transposed to the urban context [67,68], or to the diversity of central places. Specifically, it refers to the diversity of central locations. These indexes constitute the first set proposed by the authors of a big data set under development, representative in quantitative terms of the intrinsic and extrinsic walkability of large-scale disused public assets.
(4) Walkable Big Buildings Index (WBBI). The indexes PI, CI and AI were integrated by the authors into a composite index Walkable Big Buildings Index (WBBI) experienced in the historic center of the city of Cagliari. In particular, the WBBI is the sum of the weighted (p k ) indexes (PI, CI, AI), where the sum of weights is 1. To distinguish this index from the others, a one hundred basis was used. The WBBI was calculated as in the formula: where ∑ n k=1 p k = 1 and I i = PI, CI, AI, . . . where i = 1, 2, 3, . . . n In other words, each index I i is weighted in relation to the intrinsic and extrinsic characteristics of the abandoned buildings and the relative conditions of the reference urban context in order to appreciate the potential (big disused buildings) functional walkability (see case study, Paragraph 4.2). In this sense, the plans of the historic centers constitute the main reference basis for the evaluation of the context to support the definition of the weights (p k ).

Data and Study Area
On the basis of a first survey of the public real estate assets present in the city of Cagliari, with particular reference to its historic center, the authors have undertaken an activity of collecting and processing data relating to the main public buildings that have been abandoned. Among these, the disused public complexes 001 B_ing, 002 B_ing and 003 B_ing were selected, among the most representative in terms of areas-valium and architectural stylistic dimensions. On the other hand, although located within the historic city center, characterized by an articulated system of central places, they limit the reach of the city in 15 minutes due to the persistent "enclave effect". It refers to a larger area of the disused building, as a result of the previous and/or subsequent urban infrastructures favored by the past effect of central location of the to-date abandoned buildings (Figure 4).

Data and Study Area
On the basis of a first survey of the public real estate assets present in the city of Cagliari, with particular reference to its historic center, the authors have undertaken an activity of collecting and processing data relating to the main public buildings that have been abandoned. Among these, the disused public complexes 001 B_ing, 002 B_ing and 003 B_ing were selected, among the most representative in terms of areas-valium and architectural stylistic dimensions. On the other hand, although located within the historic city center, characterized by an articulated system of central places, they limit the reach of the city in 15 minutes due to the persistent "enclave effect". It refers to a larger area of the disused building, as a result of the previous and/or subsequent urban infrastructures favored by the past effect of central location of the to-date abandoned buildings (Figure 4). This is a critical issue, also confirmed by the smart community that animates Strava's digital platform. This platform shows the densest areas, i.e., those most crossed by the community of users of the popular app for sports activities-for example running, cycling, etc.-to testify a "practicability" of walking in a broad sense. The Figure 4 shows the enclave effect and consequently how a greater and better accessibility of these spaces would facilitate the walkability, and therefore the desired goal, of the 15-minute city, as confirmed in the occasion of the health crisis.
The authors then proceeded to identify the central locations within the historic center of Cagliari with reference to the three previously selected real estate compendia, included in the relative 15-minute isochrones. For this evaluation, the OSMR1 algorithms referred to Google maps were used ( Figure 5). In particular, the isochrones have been used to define areas where activities are located. Activities were searched through the homonymous search engine embedded into Google Maps. The principle used is that of the Minimum Bounding Rectangle (MBR), as the extent of the polygon derived by the most extreme coordinate values of isochrones computed over each location. Figure 5 shows the extreme coordinates of the three MBR computed over the relative 15-min isochrones for each building. Within each area, the following central locations have been identified, divided into the three categories previously defined (Table 1). This is a critical issue, also confirmed by the smart community that animates Strava's digital platform. This platform shows the densest areas, i.e., those most crossed by the community of users of the popular app for sports activities-for example running, cycling, etc.-to testify a "practicability" of walking in a broad sense. The Figure 4 shows the enclave effect and consequently how a greater and better accessibility of these spaces would facilitate the walkability, and therefore the desired goal, of the 15-minute city, as confirmed in the occasion of the health crisis.
The authors then proceeded to identify the central locations within the historic center of Cagliari with reference to the three previously selected real estate compendia, included in the relative 15-minute isochrones. For this evaluation, the OSMR1 algorithms referred to Google maps were used ( Figure 5). In particular, the isochrones have been used to define areas where activities are located. Activities were searched through the homonymous search engine embedded into Google Maps. The principle used is that of the Minimum Bounding Rectangle (MBR), as the extent of the polygon derived by the most extreme coordinate values of isochrones computed over each location. Figure 5 shows the extreme coordinates of the three MBR computed over the relative 15-min isochrones for each building. Within each area, the following central locations have been identified, divided into the three categories previously defined ( Table 1).
The authors then proceeded to evaluate the PI, CI and AI and WBBI indexes: The assessment of PI and CI required the determination of the following weights resulting from the evaluation of the reference urban context of the historic center of Cagliari. For the three abandoned buildings obtained the following PI after identifying the specific weights: The assessment of PI and CI required the determination of the following we sulting from the evaluation of the reference urban context of the historic center of For the three abandoned buildings obtained the following PI after identifying the weights:  The following PI is therefore derived ( Table 2). For the three abandoned buildings, the following CI were after obtained with specific weights: The following CI is therefore derived (Table 3). In particular, for the AI index, the Simpson index was applied, in agreement with Borruso (2006) [66], transposing by analogy a typical index used to represent ecological diversity to the diversity of central locations, as reported in Table 4.  Finally, the evaluation of the WBBI required the determination of the weights for each index that composes it. In particular we considered p k = 0.3 for PI, p k = 0.4 for CI and p k = 0.3 for AI (Table 5), justified by the necessary role of "crossing" to reduce the enclave effect of large abandoned building dimensions. Below is a summary table of the calculation of the three indexes, starting from the input data referring to the abandoned real estate complexes selected in the historic urban area, Figure 6.   The results of the proposed method were presented and discussed in sections 5 and 6.

Results and Discussion
In this paper we wanted to represent a first synthesis of ongoing research relating to the identification of functional indexes to improve pedestrian accessibility in the urban area in the desired 15-minute city through PI (Porosity index), CI (Crossing Index) and AI (Attractiveness index), a combined WBBI index (Walkability Big Building Index).
The evolution of central locations and the consequent divestments of real estate assets together with the recent health emergency have highlighted the importance of acting in favor of an agile and healthy city. This research work made it possible to systematize the extensive literature on walkability and biodiversity indices, adapting it to the city with enclaves. According to the authors, this constitutes the original contribution of the method proposed and applied to the historic center of the city of Cagliari. This is a first application that will have the possibility of being improved and better represented during the future phases of strategic planning, particularly for the determination of the weights of the proposed indexes. In particular, these indexes make it possible to relate intrinsic elements (PI and CI) with extrinsic elements (AI) of a given decommissioned real estate asset with bigsized dimensional characteristics. This is in order to act in the redevelopment of abandoned assets to obtain maximum walkability, knowing that the ideal reference benchmark is given by squares and urban parks. In fact, PI, CI = 1 and AI = 1 (WBBI = 100) occur in an open space, which can be crossed in several directions and with a relative diversified attractiveness.
The assessment of the indexes shows that each abandoned building has the following WBBIs: 32.4 for 001 B_ing; 51.1 for 002 B_ing and 44.3 for 003 B_ing. In particular, the lowest WBBI (22.4) corresponds to 001 B_ing (former prison), although it has the highest index of AI = 0.85. The highest WBBI (51.1) corresponds to 002 B_ing (former hospital), which has the largest enclave. Each WBBI, in fact, must be interpreted in relation to its enclave and in general to the extrinsic characteristics (AI). In doing so, WBBI can support decisions in order to evaluate the intervention priorities aimed at making urban contexts, today characterized as enclaves, walkable. The results of the proposed method were presented and discussed in Sections 5 and 6.

Results and Discussion
In this paper we wanted to represent a first synthesis of ongoing research relating to the identification of functional indexes to improve pedestrian accessibility in the urban area in the desired 15-minute city through PI (Porosity index), CI (Crossing Index) and AI (Attractiveness index), a combined WBBI index (Walkability Big Building Index).
The evolution of central locations and the consequent divestments of real estate assets together with the recent health emergency have highlighted the importance of acting in favor of an agile and healthy city. This research work made it possible to systematize the extensive literature on walkability and biodiversity indices, adapting it to the city with enclaves. According to the authors, this constitutes the original contribution of the method proposed and applied to the historic center of the city of Cagliari. This is a first application that will have the possibility of being improved and better represented during the future phases of strategic planning, particularly for the determination of the weights of the proposed indexes. In particular, these indexes make it possible to relate intrinsic elements (PI and CI) with extrinsic elements (AI) of a given decommissioned real estate asset with big-sized dimensional characteristics. This is in order to act in the redevelopment of abandoned assets to obtain maximum walkability, knowing that the ideal reference benchmark is given by squares and urban parks. In fact, PI, CI = 1 and AI = 1 (WBBI = 100) occur in an open space, which can be crossed in several directions and with a relative diversified attractiveness.
The assessment of the indexes shows that each abandoned building has the following WBBIs: 32.4 for 001 B_ing; 51.1 for 002 B_ing and 44.3 for 003 B_ing. In particular, the lowest WBBI (22.4) corresponds to 001 B_ing (former prison), although it has the highest index of AI = 0.85. The highest WBBI (51.1) corresponds to 002 B_ing (former hospital), which has the largest enclave. Each WBBI, in fact, must be interpreted in relation to its enclave and in general to the extrinsic characteristics (AI). In doing so, WBBI can support decisions in order to evaluate the intervention priorities aimed at making urban contexts, today characterized as enclaves, walkable.
In particular, we have intended to evaluate the possibilities of making the "central places" of the past, such as ancient factories, hospitals etc., accessible in pedestrian terms in a logical and flexible network, where the "walkability" can renew the quality of life and, at the same time, reduce health risk from COVID-19. The vast literature on walkability and abandoned public properties, as well as the recent radical changes induced by the health emergency, have prompted the authors to evaluate this first specific set of indexes: porosity, intersection and attractiveness, from whose combination the index WBBI is derived.

Conclusions and Future Development
The analysis of the study context deriving from the evaluations of the Metropolitan Strategic Plan of Cagliari, and also in the light of the current pandemic health emergency, allowed us to deepen the role of the disused public properties in the direction of the desired "15-minute city". The geographic-ecological approach developed led to the proposal of a first set of three indexes PI, CI, AI-related to porosity, crossing and attractivity-and a composite index-WBBI related to walkability-coherent with the complex theoretical framework aggravated by the current health emergency situation. The proposed indexes, and in particular the combined WBBI index, respond to the need for analytical frameworks that support decision-making processes [69,70], identifying and measuring the environmental variables of the urban system that influence individual behavior and collective walking practices.
In particular, the methodological framework addresses the main aspects central to the quality of the walkable public space: the combination of contextualized qualitative and quantitative indicators, and the combination of indicators that measure the intrinsic and extrinsic attributes of disused public building areas, in particular of big dimensions and extensions. The proposed approach allows us to represent the quality of the public space and therefore its potential in the 15-minute city.
The methodological framework will be subject to participatory evaluation in the strategic co-planning of the metropolitan city of Cagliari, through decision-making techniques based on the Analytical Hierarchy Process (AHP) to involve stakeholders in complex decisions relating to the selection and prioritization of environmental variables and relevant indexes [71]. Finally, the methodological approach proposed can constitute a relevant framework to support the decision-making processes of urban walkability policies [70][71][72][73] in the context of a renewed social cohesion.
The future development of the methodological framework will address several aspects, hereby highlighted on the limited set of sample buildings and areas analyzed.
One research direction will lead to tackling the criticalities that emerged during this initial research, particularly in terms of the definition of weights and a broader analysis of the activities to consider as central. This will be done also incorporating a distance decay correction in the weights being used for the computation of the indexes. The set of the disused buildings considered as potential candidates for reuse will be also broadened to cover a wider extension of the urban fabric for a wider social inclusion.
Another direction of research will deal with the application of such methods to other already existing and working public buildings and areas in the same city, in order to compare the potential of the reusable buildings and areas to play again a new central, urban role. In particular, through a specific action foreseen in the Strategic Plan of the metropolitan city of Cagliari, called "Strategic projects of participatory redevelopment", it will be possible to reactivate urban functions also with tactical urbanism initiatives able to stimulate the 15-minute city.
A wider extension of the research will deal with the realization of a complete database of the disused buildings and areas in the Metropolitan City of Cagliari, with a possible comparison with other urban areas, regarding indexes and potential urban functions. Data Availability Statement: Not applicable (a small sample of an on-going building dataset was used).

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Glossary PI = Porosity index. It is the weighted coverage ratio, between the building and the pertinent free land surface CI = Crossing Index. It specifies the level of crossability that characterizes each public property and that allows people to reach different parts of the city. It depends on the architectural morphology of the project, in particular on the number of crossings and paths that connect the various entrances to the property. AI = Attractiveness Index. It refers to both the number and variety of central places found within a 15-minute travel range from the analyzed property compendium. WBBI = Walkability Big Building. It is a combined index given by the sum of the weighted indexes (PI, CI, AI). MCC = Metropolitan City of Cagliari PREM = Public Real Estate Management MSP = Metropolitan Strategic Plan PHC = Plan of the Historic Center