Статті в журналах з теми "Weighted k-out-of-n systems"

In this paper, we consider the optimal design of the binary weighted k-out-of-n system. The binary weighted k-out-of-n: G system works if and only if the total utility of all working components is at least k. In the design process, we need to evaluate system reliability repetitively. The universal generating function (UGF) approach is used for this purpose when the system size is small or moderate. When the size of the system is large, the recursive approach is used, which is more efficient. Two optimal models are formulated. One is to minimize the expected total cost while guaranteeing the system reliability higher than a pre-specified value; the other is to maximize the system reliability with the constraints on total system cost. Genetic algorithms (GA) and Tabu Search (TS) methods are both used to solve the proposed optimization models. Since the key to a good TS algorithm is usually quite problem-specific policies and memory structures, there is no existing general TS tool available. Therefore more details of the TS approach used in this paper are discussed than the GA approach. The results obtained with these two methods are compared. The results illustrate that both methods are powerful tools for solving these kinds of problems. However TS is more efficient than GA in computation. The materials in this paper have been published in 19.

It seems there is a scope to study how we can find the fuzzy reliability of two-stage weighted-k-out-n. This paper studies the fuzzy reliability of two-stage weighted-k-out-of-n model with components in common. Algorithms are developed to calculate the system fuzzy reliability, and generate the minimal cuts and minimal paths of two-stage weighted-k-out-of-n systems. Fuzzy reliability bounds for systems with s-dependent component failures are investigated based on the generated minimal cuts and minimal paths. Two types of two-stage weighted-k-out-of-n models, the Series Weighted (SW)-k-out-of-n model, and the Parallel Weighted (PW)-k-out-of-n model, can be applied to investigate fuzzy reliability issues in network applications, such as the project management, and the shortest path problems. Examples are provided to demonstrate the developed models and algorithms of systems having components following different type of membership functions.

Recently many popular reliability systems are being extended to weighted systems where weight associated with each component refers to load/capacity of that component. The simplest k-out-of-n system extended under this concept is known as weighted-k-out-of-n system. A weighted-k-out-of-n: G(F) system consists of n components each one having a positive integer weight wi, i = 1, 2, …, n such that the total system weight is w and the system works (fails) if and only if the accumulated weight of working (failed) components is at least k. In this paper, we introduce the concept of Weighted Markov Bernoulli Trial (WMBT) {Xi, i ≥ 0} and study the distribution of [Formula: see text], the total weight of successes in the sequence of n WMBT and conditional distribution of [Formula: see text] given that uth trial results in failure/success. We refer the distribution of [Formula: see text] as Weighted Markov Binomial Distribution (WMBD). Further we discuss application of WMBD and conditional WMBD in evaluation of reliability, Birnbaum reliability importance (B-importance) and improvement potential importance of weighted-k-out-of-n: G/F system. The numerical work is included to demonstrate the computational simplicity of the developed results. Further we compare our study with the existing results in terms of efficiency and find that our results are efficient for large values of k.

For the weighted k-out-of-n system with statistically dependent component lifetimes, we have a discussion on the system performance through investigating the ordering properties of the total system weight with respect to component weight vector. Applications of the present ordering results to signature of coherent systems are presented as well.

We apply the algebraic reliability method to the analysis of several variants of multi-state k-out-of-n systems. We describe and use the reliability ideals of multi-state consecutive k-out-of-n systems with and without sparse, and show the results of computer experiments on these kinds of systems. We also give an algebraic analysis of weighted multi-state k-out-of-n systems and show that this provides an efficient algorithms for the computation of their reliability.

In modern systems, not only the number and the position of the functioning or the failed components are the main factors that keep the system into the functioning state or transform it into failure state, but the contribution or the working probability of the component is also a very important one. This contribution is usually called the component weight. In this paper, the reliability and the failure functions of the consecutive weighted k-out-of-n: F linear and circular system, the weighted f-out-of-n: F system, the weighted (n,f,k) linear and circular system and the weighted linear and circular system are obtained.

The reliability of a weighted-[Formula: see text]-out-of-[Formula: see text] system that consists of three-state components is studied. The system is assumed to comprise [Formula: see text] three-state components, namely, perfect functioning, partial working, and complete failure and functions if the total weight of all the working components is at least [Formula: see text]. Reliability expressions are presented when the times spent by components in perfect functioning and partial working states are dependent with a given joint distribution. Sufficient conditions are also provided to compare the expected total weights of two systems.

Reliability evaluation has a vital importance at all stages of processing and controlling modern engineering systems. In most of these modern systems the components have different contributions to the system, which are defined as weights. Among the other weighted systems, a linear consecutive-weighted-k-out-of-n:F system consists of n components, where each component has its own weight and reliability. The system fails if and only if the total weight of the failed consecutive components is at least k. The aim of this paper is to study the reliability of linear consecutive-weighted-k-out-of-n:F system consisting of independent & nonidentical and nonhomogeneous Markov dependent components. Exact formulae are provided for computing the reliability for above mentioned cases. Approximation formulae for the reliability are also presented.

A notable reliability model is the binary threshold system (also called the weighted-k-out-of-n system), which is a dichotomous system that is successful if and only if the weighted sum of its component successes exceeds or equals a particular threshold. The aim of this paper is to extend the utility of this model to the reliability analysis of a homogeneous binary-imaged multi-state coherent threshold system of (m+1) states, which is a non-repairable system with independent non-identical components. The paper characterizes such a system via switching-algebraic expressions of either system success or system failure at each non-zero level. These expressions are given either (a) as minimal sum-of-products formulas, or (b) as probability–ready expressions, which can be immediately converted, on a one-to-one basis, into probabilities or expected values. The various algebraic characterizations can be supplemented by a multitude of map representations, including a single multi-value Karnaugh map (MVKM) (giving a superfluous representation of the system structure function S), (m+1) maps of binary entries and multi-valued inputs representing the binary instances of S, or m maps, again of binary entries and multi-valued inputs, but now representing the success/failure at every non-zero level of the system. We demonstrate how to reduce these latter maps to conventional Karnaugh maps (CKMs) of much smaller sizes. Various characterizations are inter-related, and also related to pertinent concepts such as shellability of threshold systems, and also to characterizations via minimal upper vectors or via maximal lower vectors.

A field intercomparison was conducted at the Acqua Alta Oceanographic Tower (AAOT) in the northern Adriatic Sea, from 9 to 19 July 2018 to assess differences in the accuracy of in- and above-water radiometer measurements used for the validation of ocean colour products. Ten measurement systems were compared. Prior to the intercomparison, the absolute radiometric calibration of all sensors was carried out using the same standards and methods at the same reference laboratory. Measurements were performed under clear sky conditions, relatively low sun zenith angles, moderately low sea state and on the same deployment platform and frame (except in-water systems). The weighted average of five above-water measurements was used as baseline reference for comparisons. For downwelling irradiance ( E d ), there was generally good agreement between sensors with differences of <6% for most of the sensors over the spectral range 400 nm–665 nm. One sensor exhibited a systematic bias, of up to 11%, due to poor cosine response. For sky radiance ( L s k y ) the spectrally averaged difference between optical systems was <2.5% with a root mean square error (RMS) <0.01 mWm−2 nm−1 sr−1. For total above-water upwelling radiance ( L t ), the difference was <3.5% with an RMS <0.009 mWm−2 nm−1 sr−1. For remote-sensing reflectance ( R r s ), the differences between above-water TriOS RAMSES were <3.5% and <2.5% at 443 and 560 nm, respectively, and were <7.5% for some systems at 665 nm. Seabird-Hyperspectral Surface Acquisition System (HyperSAS) sensors were on average within 3.5% at 443 nm, 1% at 560 nm, and 3% at 665 nm. The differences between the weighted mean of the above-water and in-water systems was <15.8% across visible bands. A sensitivity analysis showed that E d accounted for the largest fraction of the variance in R r s , which suggests that minimizing the errors arising from this measurement is the most important variable in reducing the inter-group differences in R r s . The differences may also be due, in part, to using five of the above-water systems as a reference. To avoid this, in situ normalized water-leaving radiance ( L w n ) was therefore compared to AERONET-OC SeaPRiSM L w n as an alternative reference measurement. For the TriOS-RAMSES and Seabird-HyperSAS sensors the differences were similar across the visible spectra with 4.7% and 4.9%, respectively. The difference between SeaPRiSM L w n and two in-water systems at blue, green and red bands was 11.8%. This was partly due to temporal and spatial differences in sampling between the in-water and above-water systems and possibly due to uncertainties in instrument self-shading for one of the in-water measurements.

Minimum tillage reportedly reduce erosion, avoid soil degradation and improve crop productivity. This study aimed to determine how tillage operations may affect either nutrient accumulation or nutrient losses by erosion. The study was, carried out from December, 2000 to March, 2001, in the watershed of the Caetés River, in Rio de Janeiro State, Brazil (22º25'43"S, 43º25'07"W). The experiment was set up in sandy clay Kandiudult soil, 60% slope, under cucumber (Cucumis sativus L.) crop. Soil samples were collected before planting and after harvest, on 22.0 X 4.0 m Greeoff plots. After each rainfall, fine sediments carried by runoff were deposited into two collecting tanks in a row, installed at the end of each plot, and were later dried, weighed and stored for analyses. Treatments (n = 4) were characterized by different tillage systems: (i) downhill plowing followed by the burning of crop residues (DPB); (ii) downhill plowing with no burning of the crop residues (DPNB); (iii) animal traction contour plowing, with strips of guinea grass planted at a spacing of 7.0 m (AT); and (iv) minimum tillage (MT). Samples of the soil-plowed layer were collected before planting and after harvest, between the rows and from the plants. Total concentration of Ca, Mg, K and P were determined after extraction with nitric perchloride digestion. Labile P and exchangeable K were extracted with the Mehlich 1 extractant solution. The MT system reduced losses of both exchangeable bases (15%) and P (8%), and affected the distribution of labile and organic P. Crop residues left on soil surface in the MT system, resulted in increased organic matter content. Downhill plowing, the most used tillage operation in the region, resulted in the greatest losses of Ca, Mg, K, and P.

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.

AbstractThe performance of civil infrastructure systems is vital in supporting a community’s functionalities. Reliability assessment of these systems is a powerful approach to evaluate whether the system performance is desirably safe under the impacts of resistance degradation and non-stationary loads. A k-out-of-n system is a widely-used logic model for a system with n components, which survives (works) if at least k components work. Its special cases include a series or a parallel system. Furthermore, a weighted k-out-of-n system has components with positive integer weights and the system survives if the total weight of working components reaches the predefined threshold k. This paper proposes a method for estimating the time-dependent reliability of both ordinary and weighted k-out-of-n systems, taking into account the effects of resistance deterioration, resistance correlation and load non-stationarity, for which a mathematical solution is derived. The applicability of the proposed method is illustrated through reliability evaluation of a representative k-out-of-n system.

AbstractThis paper proposes and explores an extension of the usual k-out-of-n systems, where the components of the system are assumed to play different roles in determining its failure and with not necessarily i.i.d. components lifetimes. The theoretical reliability framework is compared with the standard weighted k-out-of-n systems, and it is actually adopted for the development of a financial derivative model whose outcome depends on the crossing of some predefined barriers of a set of assets. More precisely, such a derivative is presented as a coherent system whose components are the assets of the basket.

Persistent and ever-changing threat of terrorism has led to the evolution of security systems in the air transportation industry. Passenger and checked-baggage screening prior to boarding an aircraft has become a priority for the airport security system. We propose a two-stage screening system by integrating the passenger prescreening and a multi-level checked-baggage screening. Based on the concept of the weighted k-out-of-n system, we introduce an integrated weighted alarm security screening system for a multi-level baggage screening system, where the system alarms when the total weight of its working levels is greater than a predefined system alarm threshold. To improve the security and efficiency of aviation systems, two optimization models are formulated to enhance the detection of possible threats in the passenger and baggage screening with consideration of the system life cycle cost. The optimal solutions of the threshold values are obtained for screening technologies and passenger classes to achieve the maximum security and efficiency. Numerical analysis is implemented to demonstrate the effectiveness of the proposed two-stage screening system.

This article reflects on part of a three-year battle over the redevelopment of an iconic Melbourne music venue, the Palace-Metro Nightclub (the Palace), involving the tactical use of Facebook Page data at trial. We were invited by the Save the Palace group, Melbourne City Council and the National Trust of Australia to provide Facebook Page data analysis as evidence of the social value of the venue at an appeals trial heard at the Victorian Civil Administration Tribunal (VCAT) in 2016. We take a reflexive ethnographic approach here to explore the data production, collection and analysis processes as these represent and constitute a “data public”.Although the developers won the appeal and were able to re-develop the site, the court accepted the validity of social media data as evidence of the building’s social value (Jinshan Investment Group Pty Ltd v Melbourne CC [2016] VCAT 626, 117; see also Victorian Planning Reports). Through the case, we elaborate on the concept of data publics by considering the “affordising” (Pollock) processes at play when extracting, analysing and visualising social media data. Affordising refers to the designed, deliberate and incidental effects of datafication and highlights the need to attend to the capacities for data collection and processing as they produce particular analytical outcomes. These processes foreground the compositional character of data publics, and the unevenness of data literacies (McCosker “Data Literacies”; Gray et al.) as a factor of the interpersonal and institutional capacity to read and mobilise data for social outcomes.We begin by reconsidering the often-assumed connection between social media data and their publics. Taking onboard theoretical accounts of publics as problem-oriented (Dewey) and dynamically constituted (Kelty), we conceptualise data publics through the key elements of a) consequentiality, b) sufficient connection over time, c) affective or emotional qualities of connection and interaction with the events. We note that while social data analytics may be a powerful tool for public protest, it equally affords use against public interests and introduces risks in relation to a lack of transparency, access or adequate data literacy.Urban Protest and Data Publics There are many examples globally of the use of social media to engage publics in battles over urban development or similar issues (e.g. Fredericks and Foth). Some have asked how social media might be better used by neighborhood organisations to mobilise protest and save historic buildings, cultural landmarks or urban sites (Johnson and Halegoua). And we can only note here the wealth of research literature on social movements, protest and social media. To emphasise Gerbaudo’s point, drawing on Mattoni, we “need to account for how exactly the use of these media reshapes the ‘repertoire of communication’ of contemporary movements and affects the experience of participants” (2). For us, this also means better understanding the role that social data plays in both aiding and reshaping urban protest or arming third sector groups with evidence useful in social institutions such as the courts.New modes of digital engagement enable forms of distributed digital citizenship, which Meikle sees as the creative political relationships that form through exercising rights and responsibilities. Associated with these practices is the transition from sanctioned, simple discursive forms of social protest in petitions, to new indicators of social engagement in more nuanced social media data and the more interactive forms of online petition platforms like change.org or GetUp (Halpin et al.). These technical forms code publics in specific ways that have implications for contemporary protest action. That is, they provide the operational systems and instructions that shape social actions and relationships for protest purposes (McCosker and Milne).All protest and social movements are underwritten by explicit or implicit concepts of participatory publics as these are shaped, enhanced, or threatened by communication technologies. But participatory protest publics are uneven, and as Kelty asks: “What about all the people who are neither protesters nor Twitter users? In the broadest possible sense this ‘General Public’ cannot be said to exist as an actual entity, but only as a kind of virtual entity” (27). Kelty is pointing to the porous boundary between a general public and an organised public, or formal enterprise, as a reminder that we cannot take for granted representations of a public, or the public as a given, in relation to Like or follower data for instance.If carefully gauged, the concept of data publics can be useful. To start with, the notions of publics and publicness are notoriously slippery. Baym and boyd explore the differences between these two terms, and the way social media reconfigures what “public” is. Does a Comment or a Like on a Facebook Page connect an individual sufficiently to an issues-public? As far back as the 1930s, John Dewey was seeking a pragmatic approach to similar questions regarding human association and the pluralistic space of “the public”. For Dewey, “the machine age has so enormously expanded, multiplied, intensified and complicated the scope of the indirect consequences [of human association] that the resultant public cannot identify itself” (157). To what extent, then, can we use data to constitute a public in relation to social protest in the age of data analytics?There are numerous well formulated approaches to studying publics in relation to social media and social networks. Social network analysis (SNA) determines publics, or communities, through links, ties and clustering, by measuring and mapping those connections and to an extent assuming that they constitute some form of sociality. Networked publics (Ito, 6) are understood as an outcome of social media platforms and practices in the use of new digital media authoring and distribution tools or platforms and the particular actions, relationships or modes of communication they afford, to use James Gibson’s sense of that term. “Publics can be reactors, (re)makers and (re)distributors, engaging in shared culture and knowledge through discourse and social exchange as well as through acts of media reception” (Ito 6). Hashtags, for example, facilitate connectivity and visibility and aid in the formation and “coordination of ad hoc issue publics” (Bruns and Burgess 3). Gray et al., following Ruppert, argue that “data publics are constituted by dynamic, heterogeneous arrangements of actors mobilised around data infrastructures, sometimes figuring as part of them, sometimes emerging as their effect”. The individuals of data publics are neither subjugated by the logics and metrics of digital platforms and data structures, nor simply sovereign agents empowered by the expressive potential of aggregated data (Gray et al.).Data publics are more than just aggregates of individual data points or connections. They are inherently unstable, dynamic (despite static analysis and visualisations), or vibrant, and ephemeral. We emphasise three key elements of active data publics. First, to be more than an aggregate of individual items, a data public needs to be consequential (in Dewey’s sense of issues or problem-oriented). Second, sufficient connection is visible over time. Third, affective or emotional activity is apparent in relation to events that lend coherence to the public and its prevailing sentiment. To these, we add critical attention to the affordising processes – or the deliberate and incidental effects of datafication and analysis, in the capacities for data collection and processing in order to produce particular analytical outcomes, and the data literacies these require. We return to the latter after elaborating on the Save the Palace case.Visualising Publics: Highlighting Engagement and IntensityThe Palace theatre was built in 1912 and served as a venue for theatre, cinema, live performance, musical acts and as a nightclub. In 2014 the Heritage Council decided not to include the Palace on Victoria’s heritage register and hence opened the door for developers, but Melbourne City Council and the National Trust of Australia opposed the redevelopment on the grounds of the building’s social significance as a music venue. Similarly, the Save the Palace group saw the proposed redevelopment as affecting the capacity of Melbourne CBD to host medium size live performances, and therefore impacting deeply on the social fabric of the local music scene. The Save the Palace group, chaired by Rebecca Leslie and Michael Raymond, maintained a 36,000+ strong Facebook Page and mobilised local members through regular public street protests, and participated in court proceedings in 2015 and February 2016 with Melbourne City Council and National Trust Australia. Joining the protesters in the lead up to the 2016 appeals trial, we aimed to use social media engagement data to measure, analyse and present evidence of the extent and intensity of a sustained protest public. The evidence we submitted had to satisfy VCAT’s need to establish the social value of the building and the significance of its redevelopment, and to explain: a) how social media works; b) the meaning of the number of Facebook Likes on the Save The Palace Page and the timing of those Likes, highlighting how the reach and Likes pick up at significant events; and c) whether or not a representative sample of Comments are supportive of the group and the Palace Theatre (McCosker “Statement”). As noted in the case (Jinshan, 117), where courts have traditionally relied on one simple measure for contemporary social value – the petition – our aim was to make use of the richer measures available through social media data, to better represent sustained engagement with the issues over time.Visualising a protest public in this way raises two significant problems for a workable concept of data publics. The first involves the “affordising” (Pollock) work of both the platform and our data analysis. This concerns the role played by data access and platform affordances for data capture, along with methodological choices made to best realise or draw out the affordances of the data for our purposes. The second concerns the issue of digital and data literacies in both the social acts that help to constitute a data public in the first place, and the capacity to read and write public data to represent those activities meaningfully. That is, Facebook and our analysis constitutes a data public in certain ways that includes potentially opaque decisions or processes. And citizens (protesters or casual Facebook commenters alike) along with social institutions (like the courts) have certain uneven capacity to effectively produce or read public protest-oriented data. The risk here, which we return to in the final section, lies in the potential for misrepresentation of publics through data, exclusions of access and ownership of data, and the uneven digital literacies at each stage of data production, analysis and sensemaking.Facebook captures data about individuals in intricate detail. Its data capture strategies are geared toward targeting for the purposes of marketing, although only a small subset of the data is publicly available through the Facebook Application Programming Interface (API), which is a kind of data “gateway”. The visible page data tells only part of the story. The total Page Likes in February 2016 was 36,828, representing a sizeable number of followers, mainly located in Melbourne but including 45 countries in total and 38 different languages. We extracted a data set of 268,211 engagements with the Page between February 2013 and August 2015. This included 45,393 post Likes and 9,139 Comments. Our strategy was to demarcate a structurally defined “community” (in the SNA sense of that term as delineating clusters of people, activities and links within a broader network), by visualising the interactions of Facebook users with Posts over time, and then examine elements of intensity of engagement. In other words, we “affordised” the network data using SNA techniques to most clearly convey the social value of the networked public.We used a combination of API access and Facebook’s native Insights data and analytics to extract use-data from that Page between June 2013 and December 2015. Analysis of a two-mode or bipartite network consisting of users and Posts was compiled using vosonSML, a package in the R programming language created at Australian National University (Graham and Ackland) and visualised with Gephi software. In this network, the nodes (or vertices) represent Facebook users and Facebook Posts submitted on the Page, and ties (or edges) between nodes represent whether a user has commented on and/or liked a post. For example, a user U might have liked Post A and commented on Post B. Additionally, a weight value is assigned for the Comments ties, indicating how many times a user commented on a particular post (note that users can only like Posts once). We took these actions as demonstrating sufficient connection over time in relation to an issue of common concern.Figure 1: Network visualisation of activity on the Save the Palace Facebook Page, June 2013 to December 2015. The colour of the nodes denotes which ‘community’ cluster they belong to (computed via the Infomap algorithm) and nodes are sized by out-degree (number of Likes/Comments made by users to Posts). The graph layout is computed via the Force Atlas 2 algorithm.Community detection was performed on the network using the Infomap algorithm (Rosvall and Bergstrom), which is suited to large-scale weighted and directed networks (Henman et al.). This analysis reveals two large and two smaller clusters or groups represented by colour differences (Fig. 1). Broadly, this suggests the presence of several clusters amongst a sustained network engaging with the page over the three years. Beyond this, a range of other colours denoting smaller clusters indicates a diversity of activity and actors co-participating in the network as part of a broader community.The positioning of nodes within the network is not random – the visualisation is generated by the Force Atlas 2 algorithm (Jacomy et al.) that spatially sorts the nodes through processes of attraction and repulsion according to the observed patterns of connectivity. As we would expect, the two-dimensional spatial arrangement of nodes conforms to the community clustering, helping us to visualise the network in the form of a networked public, and build a narrative interpretation of “what is going on” in this online social space.Social value for VCAT was loosely defined as a sense of connection, sentiment and attachment to the venue. While we could illustrate the extent of the active connections of those engaging with the Page, the network map does not in itself reveal much about the sentiment, or the emotional attachment to the Save the Palace cause. This kind of affect can be understood as “the energy that drives, neutralizes, or entraps networked publics” (Papacharissi 7), and its measure presents a particular challenge, but also interest, for understanding a data public. It is often measured through sentiment analysis of content, but we targeted reach and engagement events – particular moments that indicated intense interaction with the Page and associated events.Figure 2: Save the Palace Facebook Page: Organic post reach November—December 2014The affective connection and orientation could be demonstrated through two dimensions of post “reach”: average reach across the lifespan of the Page, and specific “reach-events”. Average reach illustrates the sustained engagement with the Page over time. Average un-paid reach for Posts with links (primarily news and legal updates), was 12,015 or 33% of the total follower base – a figure well above the standard for Community Page reach at that time. Reach-events indicated particular points of intensity and illustrates the Page’s ability to resonate publicly. Figure 2 points to one such event in November 2015, when news circulated that the developers were defying stop-work orders and demolishing parts of The Palace. The 100k reach indicated intense and widespread activity – Likes, Shares, Comments – in a short timeframe. We examined Comment activity in relation to specific reach events to qualify this reach event and illustrate the sense of outrage directed toward the developers, and expressions of solidarity toward those attempting to stop the redevelopment. Affordising Data Publics and the Transformative Work of AnalyticsEach stage of deriving evidence of social value through Page data, from building public visibility and online activity to analysis and presentation at VCAT, was affected by the affordising work of the protesters involved (particularly the Page Admins), civil society groups, platform features and data structures and our choices in analysis and presentation. The notion of affordising is useful here because, as Pollock defines the term, it draws attention to the transformative work of metrics, analytics, platform features and other devices that re-package social activity through modes of datafication and analysis. The Save the Palace group mobilised in a particular way so as to channel their activities, make them visible and archival, to capture the resonant effects of their public protest through a platform that would best make that public visible to itself. The growth of the interest in the Facebook Page feeds back on itself reflexively as more people encounter it and participate. Contrary to critiques of “clicktivism”, these acts combine digital-material events and activities that were to become consequential for the public protest – such as the engagement activities around the November 2015 event described in Figure 2.In addition, presenting the research in court introduced particular hurdles, in finding “the meaningful data” appropriate to the needs of the case, “visualizing social data for social purposes”, and the need to be “evocative as well as accurate” (Donath, 16). The visualisation and presentation of the data needed to afford a valid and meaningful expression of the social significance the Palace. Which layout algorithm to use? What scale do we want to use? Which community detection algorithm and colour scheme for nodes? These choices involve challenges regarding legibility of visualisations of public data (McCosker and Wilken; Kennedy et al.).The transformative actions at play in these tactics of public data analysis can inform other instances of data-driven protest or social participation, but also leave room for misuse. The interests of developers, for example, could equally be served by monitoring protesters’ actions through the same data, or by targeting disagreement or ambiguity in the data. Similarly, moves by Facebook to restrict access to Page data will disproportionately affect those without the means to pay for access. These tactics call for further work in ethical principles of open data, standardisation and data literacies for the courts and those who would benefit from use of their own public data in this way.ConclusionsWe have argued through the case of the Save the Palace protest that in order to make use of public social media data to define a data public, multiple levels of data literacy, access and affordising are required. Rather than assuming that public data simply constitutes a data public, we have emphasised: a) the consequentiality of the movement; b) sufficient connection over time; and c) affective or emotional qualities of connection and interaction with public events. This includes the activities of the core members of the Save the Palace protest group, and the tens of thousands who engaged in some way with the Page. It also involves Facebook’s data affordances as these allow for the extraction of public data, alongside our choices in analysis and visualisation, and the court’s capacity and openness to accept all of this as indicative of the social value (connections, sentiment, attachment) it sought for the case. The Senior Member and Member presiding over the case had little knowledge of Facebook or other social media platforms, did not use them, and hence themselves had limited capacity to recognise the social and cultural nuances of activities that took place through the Facebook Page. This does not exclude the use of the data but made it more difficult to present a picture of the relevance and consequence of the data for understanding the social value evident in the contested building. 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