Dag Øivind Madsen

SWOT ANALYSIS: A MANAGEMENT FASHION PERSPECTIVE

Keywords: SWOT analysis, management idea, management fashion, strategy tool 1. INTRODUCTION 1.1

SWOT analysis has over a period spanning several decades enjoyed considerable popularity in the business community. In this paper management fashion theory is used as a theoretical lens to understand the history and evolution of SWOT as a management idea. The analysis shows that SWOT's evolution pattern diverges in several respects from that of other comparable management ideas. The findings from the analysis have several implications for research on SWOT and, more generally, management ideas and fashions.

Stanford

Other commentators have a slightly different take on the emergence of SWOT. For instance, according to Hindle (2008, p. 181) "Wikipedia credits the technique to Albert Humphrey, an academic at Stanford University, who based it on an analysis of Fortune 500 companies that he carried out in the 1960s and 1970". In a 2005 Stanford Research Institute newsletter Humphrey looks back on his work with SWOT at Stanford [START_REF] Humphrey | SWOT analysis for management consulting[END_REF]. However, [START_REF] Friesner | History of SWOT analysis[END_REF] argues that "the crediting to Humphrey as the creator of SWOT cannot be supported."

Other influences

Others point elsewhere when trying to pinpoint the inception of SWOT. A less common attribution is to strategic management thinker Igor Ansoff [START_REF] Turner | Tools for Success: A Manager's Guide[END_REF], cited in King, 2004), while [START_REF] Koch | SWOT does not need to be recalled: It needs to be enhanced[END_REF] notes the importance of various less well-known contributions made during the 1980s and early 1990s. The influential strategy scholar Jay Barney also draws on SWOT in his widely cited article on firm resources (Barney, 1991, p. 100). [START_REF] Panagiotou | Bringing SWOT into focus[END_REF] Harvard Business School and professor Kenneth Andrews 1960s Hill and Westbrook (1997, p. 47) Harvard Business School professors in the 1960s 1960s [START_REF] Haberberg | Swatting SWOT: Strategic Planning Society[END_REF], cited in King, 2004) Albert Humphrey at Stanford University 1960s and 1970s Hindle (2008, p. 181); [START_REF] Humphrey | SWOT analysis for management consulting[END_REF] Igor Ansoff 1960s and 1970s [START_REF] Turner | Tools for Success: A Manager's Guide[END_REF], cited in King, 2004) Various contributions by Weihrich, Dealtry, Wheelen and Hunger 1980s and 1990s Koch (2000) cites [START_REF] Dealtry | Dynamic SWOT Analysis[END_REF], [START_REF] Weihrich | The TOWS matrix-A tool for situational analysis[END_REF] and [START_REF] Wheelen | Strategic Management and Business Policy[END_REF]

Summary

This brief historical review has shown that SWOT does not have a clear genealogy. There is not much consensus on how SWOT emerged, both in terms the actors spearheading SWOT or the exact time period in which it occured. However, Harvard Business School seems to have played a pivotal role as the birthplace of SWOT. The important role played by the network around Harvard Business School has also been suggested in studies of other management ideas such as Activity Based Costing [START_REF] Jones | The ABC bandwagon and the juggernaut of modernity[END_REF] and Balanced Scorecard [START_REF] Cooper | Popularizing a Management Accounting Idea: The Case of the Balanced Scorecard[END_REF][START_REF] Qu | A sociological analysis of the rise and dissemination of management accounting innovations: Evidence from the balanced scorecard[END_REF].

Furthermore, the strong position of the strategic planning school provided fertile ground for the early emergence and popularization of SWOT. In addition, SWOT fit almost like a glove with the "zeitgeist" in the fields of strategic management and corporate planning. As [START_REF] Kieser | Rhetoric and myth in management fashion[END_REF] argues, timing plays an important role in determining the success of prospective fashions. A management idea must hit the "nerve of today's managers" (Kieser, 1997, p. 61). Management ideas which fit well with the current "zeitgeist" with stand a greater chance of becoming fashionable. The next section follows up on this point by analyzing the key characteristics of SWOT which determine its "fashion potential".

KEY CHARACTERISTICS

In this section the key characteristics of the SWOT idea are analyzed drawing on theories about popular management ideas [START_REF] Kieser | Rhetoric and myth in management fashion[END_REF][START_REF] Røvik | Moderne organisasjoner[END_REF][START_REF] Røvik | The secrets of the winners: Management ideas that flow[END_REF]. The analysis focuses on four characteristics which influence a management idea's "ability to flow" [START_REF] Røvik | The secrets of the winners: Management ideas that flow[END_REF]: (1) catchy label, (2) promises of performance improvements, (3) interpretive space, and (4) universal applicability. The extent to which SWOT exhibits these four characteristics influences SWOT's fashion potential.

Catchy label

The first characteristic is related to how a management idea is labelled. Popular management ideas are typically labelled in a catchy way, using a three-letter acronym [START_REF] Grint | JIT, BSCs and TLAs: Managerial waves or drownings?[END_REF][START_REF] Røvik | Moderne organisasjoner[END_REF]. In the case of SWOT, the short-form acronym is usually preferred instead of the long-form term Strength-Weaknesses-Opportunities-Threats, since the latter arguably is too long and not very catchy. In this way, SWOT differs from many other well-known management ideas which are known by far longer labels (e.g. Customer Relationship Management and Knowledge Management). However, it should be noted that in these cases three-letter or two-letter acronyms (CRM and KM, respectively) are often used to simplify. Another interesting aspect of the SWOT label is that it is frequently used as a verb. For example, in the literature we can find expressions such as "to SWOT something" or "SWOTing" (Pickton & Wright, 1998, p. 106). The SWOT acronym has also been reworked and remixed in different ways. For example, there are multiple variations of the SWOT acronym including USED and TOWS [START_REF] Weihrich | The TOWS matrix-A tool for situational analysis[END_REF], WOTSUP and SOFT (Panagiotou, 2003, p. 9), as well as SORF analysis [START_REF] Shadfar | Application of SORF Analysis in Formulating Businesses Strategies[END_REF].

Performance improvements

Another characteristic of popular management ideas is that performance improvements are promised to potential adopters of the concept [START_REF] Røvik | Moderne organisasjoner[END_REF][START_REF] Ten Bos | Fashion and utopia in management thinking[END_REF]. In the case of SWOT, these promises and claims are not as strong as in the cases of other management ideas. As mentioned in Section 2, there is not a seminal work or bestselling management guru books about SWOT, nor is the idea closely associated with a particular consulting firm or software vendor. [START_REF] Seidl | General strategy concepts and the ecology of strategy discourses: a systemic-discursive perspective[END_REF] refers to SWOT as an example of a relatively simple strategy tool, while Pickton and Wright (1998, p. 104) go even further and write that "SWOT analysis is supremely simple". Kay et al. (2006, p. 43) point out that this simplicity is appealing to managers: "And for a busy manager, confronted by endless everyday pressures and unused to stand back to think about longer-term issues, it is a particularly useful list." In a similar vein, [START_REF] Hindle | Guide to management ideas and gurus[END_REF] notes that SWOT can be a "handy mnemonic", i.e. a managerial memory aid.

Moreover, the SWOT framework is "seductive" to managers since it offers a generic solution: "the promise of uniformity may appeal to those with the task of developing strategies for businesses with increasingly diverse markets" (Hill & Westbrook, 1997, p. 51). To this point, Thomas (1998, p. 10) argues that "…the repetition of phrases and words, without even struggling to understand and define them, will allow managers to control the destiny of their organizations. This is the very principle of myth that Horkheimer and Adorno write of."

Despite its simple and appealing nature, SWOT has received its fair share of criticism. Both academics and practitioners have questioned the usefulness of the approach [START_REF] Hill | SWOT analysis: it's time for a product recall[END_REF][START_REF] Hussey | Company analysis: determining strategic capability[END_REF][START_REF] Piercy | Making SWOT analysis work[END_REF]. For example, critics have noted the high degree of subjectivity, as well the simplistic and mechanistic nature of the SWOT matrix [START_REF] Pickton | What's swot in strategic analysis?[END_REF]. To this point, Pickton and Wright (1998, p. 102) note that "a too simplistic adoption of the SWOT activity can lead to damaging consequences".

Defenders of SWOT point out that the idea should be seen as more of a generic framework and template. As pointed out by Kay et al. (2006, p. 43) "SWOT is simply a list. It conveys no information in itself, but is a way of helping us to think about the information we already have." In a similar vein, Hindle (2008, p. 182) writes that "the process of doing the analysis is more important and revealing than the results of the analysis themselves. The journey is more important than the destination." In other words, these authors point out that SWOT can increase performance by facilitating "strategizing activities" (cf. [START_REF] Jarzabkowski | Strategizing: The challenges of a practice perspective[END_REF][START_REF] Whittington | The work of strategizing and organizing: for a practice perspective[END_REF].

Interpretive space

The third characteristic of popular management ideas is that they have a wide room for interpretation, so-called "interpretive space" [START_REF] Benders | What's in a fashion? Interpretive viability and management fashions[END_REF][START_REF] Clark | The fashion of management fashion: A surge too far?[END_REF][START_REF] Giroux | It was such a handy term': Management fashions and pragmatic ambiguity[END_REF]. In the case of SWOT a number of researchers have highlighted the "ambiguous" [START_REF] Hill | SWOT analysis: it's time for a product recall[END_REF] and "open nature and unstructured method of SWOT" (Panagiotou, 2003, p. 9). The interpretive space means that SWOT can easily be understood and "translated" [START_REF] Czarniawska | Translating organizational change[END_REF] in different ways and combined and blended with other management ideas. For example, Panagiotou (2003, p. 9) notes that "others have incorporated current available models such as Kaplan and Norton's Balanced Score Card with SWOT". As will be shown in Sections 3.4 and 5.3, SWOT has been successfully re-interpreted and "travelled" to other contexts.

Universal applicability

The fourth characteristics exhibited by popular management ideas is that they are presented as universally applicable [START_REF] Strang | Institutional conditions for diffusion[END_REF] and can be used in organizations across the board [START_REF] Røvik | Moderne organisasjoner[END_REF]. This is clearly the case in the context of SWOT as it is presented as a generic solution [START_REF] Hill | SWOT analysis: it's time for a product recall[END_REF] which can be applied at different levels, from the individual/personal level to the international level. For example, [START_REF] Hindle | Guide to management ideas and gurus[END_REF] notes that SWOT analysis can be used to assess the competitive advantages and disadvantages of countries. Moreover, as the fictional character Jared explains on the TV show Silicon Valley, you can basically SWOT anything [START_REF] Youtube | SWOT -Silicon Valley -S02E06[END_REF].

SWOT's fashion potential

The analysis of the key characteristics of the SWOT idea shows that it exhibits several of the characteristics of popular management ideas. These characteristics are the so-called "secrets of the winners" [START_REF] Røvik | The secrets of the winners: Management ideas that flow[END_REF], i.e. the winning formula of management ideas with a high fashion potential. To sum up the analysis, the SWOT acronym is very catchy, and can even be used as a verb. Over time, SWOT has become a standard part of "management speak" and the vocabulary of just about every management consultant. In addition, SWOT analysis is featured in most textbooks on strategic management or marketing. When it comes to performance enhancements, SWOT does not score as highly as most other management ideas. This is because its generic nature makes it more of an "organizing framework" [START_REF] Kay | The history of strategy and some thoughts about the future[END_REF] or "handy mnemonic" [START_REF] Hindle | Guide to management ideas and gurus[END_REF]. However, the flipside of being more of a simple organizing framework is that it very seductive and appealing to busy managers.

When it comes to the third aspect, the room for interpretation is considerable, mainly due to SWOT's open, unstructured and flexible nature. The interpretive space makes it easy to combine SWOT with other management ideas in new "mashups". In addition, different variations of SWOT have been introduced such as TOWS, SOFT and USED. Finally, SWOT is presented as an universal solution which can easily be overlayed on nearly any problem, not only those faced by business organizations, but also individuals or nation-states. As will be discussed in more detail in Section 6, SWOT has been adapted to usage not only at the industry level, but also the individual or the inter-country level.

THE SUPPLY-SIDE OF SWOT

Thus far the paper has focused on the historical emergence of SWOT, and on analyzing the key characteristics which give SWOT a considerable potential as a fashionable idea. Management ideas which become fashions tend to exhibit most of these characteristics [START_REF] Benders | Tricks and Trucks? A Case Study of Organization Concepts at Work[END_REF]. However, only exhibiting these characteristics is usually not enough. Benders (1999, p. 625) points out that fashion setters promote and market management ideas to fashion consumers such as managers. For a management idea to become fashionable, it is important that supply-side actors create awareness and knowledge about the idea so that it reaches a critical mass of adopters. In turn, this may trigger bandwagon effects where other managers are pressured to adopt in order to keep up with their peers [START_REF] Benders | Tricks and Trucks? A Case Study of Organization Concepts at Work[END_REF][START_REF] Benders | Hitch-hiking on a hype: Dutch consultants engineering re-engineering[END_REF].

The SWOT fashion arena

This sub-section takes a closer look at the supply-side of SWOT, i.e. the actors promoting and propagating SWOT to managers and organizations on the demand-side of the market. In the literature on management fashions, these groups of actors (e.g. consulting firms, management gurus and business media) are referred to as the "fashion-setting community" [START_REF] Abrahamson | Management Fashions[END_REF] or "fashion arena" [START_REF] Jung | Consultants in the Management Fashion Arena[END_REF][START_REF] Klincewicz | Management fashions: Turning best-selling ideas into objects and institutions[END_REF][START_REF] Madsen | The Role of the Management Fashion Arena in the Cross-National Diffusion of Management Concepts: The Case of the Balanced Scorecard in the Scandinavian Countries[END_REF]. Table 3 provides an overview of the role of most relevant fashion-arena actors in the case of SWOT. The activities of each of the actor groups will be discussed in greater detail in the subsequent sub-sections.

Consultants

Consulting firms are typically viewed as the most central actor in the management fashion arena [START_REF] Jung | Consultants in the Management Fashion Arena[END_REF]. However, in the case of SWOT, consultants have been relatively passive, at least when compared to the important role of consultants in the popularization of management ideas such as the Balanced Scorecard [START_REF] Ax | Bundling and diffusion of management accounting innovationsthe case of the balanced scorecard in Sweden[END_REF][START_REF] Madsen | The Role of the Management Fashion Arena in the Cross-National Diffusion of Management Concepts: The Case of the Balanced Scorecard in the Scandinavian Countries[END_REF]. A possible reason for limited role of consultants this is that SWOT is difficult to commercialize and market because of its simplicity and its nature as an "organizing framework". Another reason could be that consultants would like to be seen as offering more "sophisticated solutions" to clients. Pickton and Wright (1998, p. 104) have noted that SWOT can be difficult to pitch as a sophisticated tool: "At its most basic, carrying out a `SWOT' is a `low-grade' form of analysis which causes some people to question whether it is truly analysis at all."

SWOT is not a solution which is typically advertised on large consulting firms' webpages. Internet searches reveal that relatively few large consulting firms market SWOT as a "stand-alone solution". However, this does not mean that consultants do not draw on tools such as SWOT analysis in actual client projects. It is likely that SWOT analysis is one of many tools in a consultant's repertoire which is drawn on in actual projects (cf. [START_REF] Heusinkveld | Consultants and organization concepts[END_REF].

Software firms

Software firms provide technical solutions which help in the implementation of management ideas [START_REF] Klincewicz | Management fashions: Turning best-selling ideas into objects and institutions[END_REF]. Overall, software firms have been relatively passive in the SWOT fashion arena.

Although there are some SWOT-related tools such as Creately, Gliffy, Grapholite, SmartDraw, SWOT Analysis Generator and SWOT Map (BusinessNewsDaily, 2015), the number of available tools is relatively low compared to plethora of software packages made for the Balanced Scorecard [START_REF] Marr | Weighing the Options-Balanced Scorecard Software[END_REF][START_REF] Marr | Automating the balanced scorecardselection criteria to identify appropriate software applications[END_REF] and Knowledge Management [START_REF] Klincewicz | Management fashions: Turning best-selling ideas into objects and institutions[END_REF]. However, as a whole, the SWOT software market can be characterized as being relatively small.

Business media

Different types of business media such as book publishers and professional magazines usually play important roles in the diffusion of management ideas [START_REF] Sahlin-Andersson | The expansion of management knowledge: Carriers, flows and sources[END_REF]. In the context of SWOT, business media actors have played a limited role. There are several reasons for this. One reason could be the generally low newsworthiness of SWOT analysis. After all, SWOT has been around since the 1950/60s. Book publishers and editors of professional magazines etc. tend to seek out new ideas (cf. [START_REF] Nijholt | Handling management ideas: Gatekeeping, editors and professional magazines[END_REF]. Another reason is that SWOT does not lend itself to long expositions and the management bestseller format. It can be difficult to write long books about a relatively simple and straightforward tool such as SWOT. However, as Table 4 shows there are some shorter e-books and handbooks about SWOT.

Management gurus

Management gurus are often closely associated with fashionable management ideas [START_REF] Jackson | Management Gurus and Management Fashions[END_REF]. However, management gurus have not played a very active role in the popularization of SWOT. Although a number of prominent management thinkers took part in the emergence of SWOT from the 1950s to 1980s (cf. e.g. [START_REF] Friesner | History of SWOT analysis[END_REF], in recent years it is hard to point to a specific management guru who has been closely associated with SWOT. One possible reason for this is that it is difficult to command high speaking fees because of the relatively simple nature of SWOT. In addition, since SWOT has been around for a long time, there is a high level of knowledge and awareness in the management community.

Conference/seminar organizers

The conference/seminar scene play a central role in the fashionization of management ideas [START_REF] Kieser | Rhetoric and myth in management fashion[END_REF][START_REF] Madsen | How do managers encounter fashionable management concepts? A study of balanced scorecard adopters in Scandinavia[END_REF]. In the same way that it is difficult for management gurus to command high speaking fees for talking about SWOT, it is difficult for professional conference and seminar organizers to sell expensive seats in conferences/seminars about SWOT. There is simply a limited market for conferences/seminars centered around a simple and well-known tool such as SWOT. However, this is not to say that there are not any events where SWOT is a topic. For example, SWOT is a crowd-pleaser since it is simple and easy to understand: "the ubiquitous SWOT analysis is a favourite of short management courses and marketing consultants that require a tool that can easily be understood by all participants" (Gunn & Williams, 2007, p. 210-211). Internet searches reveal that SWOT analysis workshops are held in different parts of the world. In addition, SWOT is frequently used as an "organizing framework" for conferences, e.g. where SWOT Analysis is used to "SWOT" (i.e. analyze) a particular industry (e.g. www.digitalswot.com).

Business schools

Business schools play an important role in the spread of management knowledge [START_REF] Sahlin-Andersson | The expansion of management knowledge: Carriers, flows and sources[END_REF]. Business schools have played a very important role in the SWOT fashion arena. Business schools have been active in several ways, from teaching students about SWOT, mentioning it in textbooks and educational materials, and by conducting research and reports using SWOT. To the first point, SWOT has been extensively taught in business schools around the world for several decades. Today, most courses in strategic management and marketing involve a discussion of SWOT in some way or another. SWOT is typically discussed in textbooks in strategic management and marketing (e.g. [START_REF] Hill | Strategic management: theory: an integrated approach: Cengage Learning[END_REF][START_REF] Mcdonald | Marketing plans: How to prepare them, how to use them[END_REF]. Pickton and Wright (1998, p. 103) noted that "there are many corporate planning and marketing texts which refer to SWOT". In addition, SWOT is one of the most common tools taught in MBA programs and shorter executive education programs, which bestows some academic legitimacy on the idea.

In addition, recent literature reviews have shown that there is much academic research utilizing the SWOT framework [START_REF] Abdi | SWOT methodology: a state-of-the-art review for the past, a framework for the future[END_REF][START_REF] Helms | Exploring SWOT analysis-where are we now? A review of academic research from the last decade[END_REF]. As Figure 1 and 2 clearly show, there has been a steady increase in the number of academic articles containing the keyword "SWOT" in the databases ProQuest and ScienceDirect. Figure 1 shows that there was an "explosion" in the number of articles around 2008/2009, and since then the number has remained relatively stable at a high level.

Summary

To sum up, the analysis of the SWOT fashion arena has shown that business schools and academic have been the most influential actor group. Other actors such as consulting firms and software vendors have struggled to commercialize SWOT, while management gurus, conference organizers and book publishers have had limited market opportunities since SWOT is a well-known management idea with a low level of newsworthiness. Overall, SWOT is not supported by supply-side actors in the same way seen in the context of other management ideas such as Balanced Scorecard [START_REF] Madsen | The Role of the Management Fashion Arena in the Cross-National Diffusion of Management Concepts: The Case of the Balanced Scorecard in the Scandinavian Countries[END_REF], Knowledge Management [START_REF] Klincewicz | Management fashions: Turning best-selling ideas into objects and institutions[END_REF] or Lean [START_REF] Larsson | Management accounting fashion setting-Studies on supply-side actors in Sweden[END_REF]. In all of these cases, supply-side actors such as consulting firms, software vendors and conference organizers have played relatively more important roles in the diffusion and popularization processes.

The relatively low involvement of the SWOT fashion arena could be explained by the difficulties in commercializing the SWOT idea. Similar difficulties have been noted in previous research on the management accounting idea Beyond Budgeting. [START_REF] Becker | The Evolution of a Management Accounting Idea: The Case of Beyond Budgeting[END_REF] found that the consultants have struggled to commercialize the Beyond Budgeting idea since it can be seen as a "management philosophy" rather than an easy-to-implement solution. However, in the case of SWOT the reason is different. Rather than being a "too abstract" and "high level" management philosophy, SWOT is perhaps too simple, since it basically consists of templates and lists [START_REF] Kay | The history of strategy and some thoughts about the future[END_REF][START_REF] Pickton | What's swot in strategic analysis?[END_REF]. These days, it is arguably hard to make a living selling this type of management knowledge. Information about SWOT is readily available free of charge online, e.g. on websites such as Wikipedia, or in a large number of textbooks and handbooks.

THE DEMAND-SIDE OF SWOT

The demand-side of SWOT consists of managers and organizations considering adopting and implementing the idea. This section looks at trends in the interest in SWOT, diffusion rates in different countries and regions, as well as applications and "translations" of SWOT at different levels of the social context.

Interest in SWOT

One way to measure and monitor the interest in SWOT is by looking at search engine data using a tool such as Google Trends [START_REF] Choi | Predicting the present with Google Trends[END_REF]. Google Trends contains data dating back to 2004. A search for term SWOT shows that the level of interest has remained relatively steady in the period 2004-2015 (Figure 3). It should be pointed out that there has been a slight decrease in the volume of searches, but the downward trend could be explained by the fact that the idea has become more well-known in practice. Google Trends also shows that there are regional differences in the interest in SWOT. Figure 4 shows that the interest is currently highest in developing countries in Africa and Asia. A possible explanation for why these countries search more for information about SWOT could be that the level of knowledge and awareness is lower in these regions than in the West. For example, the SWOT idea has circulated in the business community in the US for about half a century, which means that it is by now a relatively well-known management idea and practice.

Diffusion of SWOT in different countries/regions

Several studies carried out over the course of the last 10-15 years suggest that the use of SWOT is quite high in different countries and regions (Table 5). In Finland, it ranks among the most commonly used strategy tools among executives [START_REF] Stenfors | High-Level Decision Support in Companies: Where Is the Support for Creativity and Innovation?[END_REF][START_REF] Stenfors | Executive use of strategy tools: Building shared understanding through boundary objects[END_REF]). In the UK, SWOT is used by 70% of organizations and ranks first of all strategy tools [START_REF] Gunn | Strategic tools: an empirical investigation into strategy in practice in the UK[END_REF]. Furthermore, these authors note that SWOT "appears to be a perennial favourite amongst practitioners and academics" (Gunn & Williams, 2007, p. 210). In the Czech Republic SWOT is also the most widely used strategy tool with a usage rate of 93% [START_REF] Afonina | The current strategic management tools and techniques: The evidence from Czech Republic[END_REF]. Studies also show that SWOT analysis is widely used outside of Europe. For example, in the Australasian region SWOT "dominates" [START_REF] Frost | The use of strategic tools by small and medium-sized enterprises: an Australasian study[END_REF], while in China SWOT ranks second, only slightly behind PEST analysis [START_REF] He | Strategic tools in China/strategic tools: An investigation into strategy in practice in China[END_REF]. Although these diffusion studies can say something about the extent to which SWOT is used, they provide little insight into how SWOT is used. As noted in Section 2, SWOT's interpretive space means that the idea is understood and interpreted in different ways. Moreover, since SWOT is presented as an universal solution it travels easily between different settings. The next section follows up on this point and takes a closer look at application of SWOT at different levels of the social context.

Applications of SWOT at different levels of the social context

SWOT has been applied at different analytical levels, ranging from the individual/personal level to the international level (Table 6). At the individual level, authors have proposed a "Personal SWOT" [START_REF] Ilott | The research assessment exercise: a personal SWOT analysis[END_REF], "Self-SWOT" [START_REF] Addams | The first step in proactively managing students' careers: Teaching self-SWOT analysis[END_REF] or "SWOT analysis for individuals" [START_REF] Von Bergen | SWOT Analysis for Individuals[END_REF]. The latter is used by HR professionals and employment counselors by having workers identify their strengths and weaknesses. At the organizational level, where SWOT has the most obvious fit, SWOT is used in a multitude of ways; some examples include facilitating strategic conversations in SMEs [START_REF] Sluismans | The use of SWOT as a tool to stimulate strategic conversation in SMEs[END_REF] and the strategy development process at universities [START_REF] Dyson | Strategic development and SWOT analysis at the University of Warwick[END_REF].

At the national level, SWOT has been applied in a number of contexts, including social work [START_REF] Westhues | A SWOT analysis of social work education in Canada[END_REF], development of national HIV/AIDS strategies [START_REF] Holtgrave | A SWOT Analysis of the Updated National HIV/AIDS Strategy for the US, 2015-2020[END_REF] and hotel industry reform [START_REF] Yu | Hotel reform in China: a SWOT analysis[END_REF]. Finally, at the international level, SWOT has been used to analyze multiculturalism in different countries and regions [START_REF] Ng | A SWOT Analysis of Multiculturalism in Canada, Europe, Mauritius, and South Korea[END_REF] or to analyze the competitive advantages and disadvantages of countries [START_REF] Hindle | Guide to management ideas and gurus[END_REF].

DISCUSSION

This section discusses the implications of the findings from the analysis for research on SWOT, and more generally, management ideas and fashions. The discussion centers around three themes: (1) whether SWOT can be considered a management fashion, (2) the impact of SWOT across time and space, and (3) how SWOT has become a mainstream management idea with broad societal impact.

Is SWOT a management fashion?

An interesting question is whether SWOT is a fashionable management idea. The analysis in Section 3 showed that SWOT is a management idea exhibiting many of the characteristics of management ideas with a high fashion potential, or what [START_REF] Røvik | The secrets of the winners: Management ideas that flow[END_REF] calls the "secrets of the winners". The studies cited in this paper also show that SWOT is widely diffused in the business community. A hallmark of widely diffused management fashions is that they are supported by fashion-setters such as consultants. However, the analysis of the supply-side in Section 4 showed that the SWOT fashion-setting arena has been less active than what is typically seen in cases of other comparable management ideas. In other words, the popularity of SWOT can to a large degree be attributed to the characteristics of the idea. For example, the interpretive space of SWOT has made the idea travel easily between different settings, and has contributed to translations and adaptations of the idea at different levels of the social context (e.g. individual and inter-country level).

Using the term "management fashion" implies that SWOT is a relatively short-lived phenomenon. However, in the management fashion literature it is increasingly recognized that ideas such as SWOT, under certain conditions, may become institutionalized so that they "stick around" for a relatively long period of time. In the next section, the impact of SWOT across time and space will be discussed in more detail.

The impact of SWOT across time and space

The impact of fashionable management ideas varies across time and space (Madsen & Stenheim, 2014a). When it comes to the spatial impact, the studies cited in this paper have shown that SWOT is frequently used in organizations in different parts of the world. As a whole, SWOT appears to be widely diffused, and more so than most other management ideas. With respect to the time dimension, SWOT has had been around for several decades and the typical inverted U-shaped management fashion lifecycle curve has not materialized. Instead, SWOT seems to be an "enduring" management fashion (cf. [START_REF] Grant | Knowledge Management, An Enduring but Confusing Fashion[END_REF]. The SWOT fashion seems to have reached a degree of permanence (cf. [START_REF] Perkmann | How are Management Fashions Institutionalized? The Role of Institutional Work[END_REF], making it more than a transient management fashion.

What is interesting about the high levels of both diffusion and institutionalization is that SWOT analysis is not supported by a constellation of supporting actors, at least not to the same degree seen in the case of other management-idea-movements such as the Balanced Scorecard [START_REF] Madsen | The Role of the Management Fashion Arena in the Cross-National Diffusion of Management Concepts: The Case of the Balanced Scorecard in the Scandinavian Countries[END_REF]. As pointed out by [START_REF] Perkmann | How are Management Fashions Institutionalized? The Role of Institutional Work[END_REF] a diverse group of supporting actors is important in diffusing and institutionalizing ideas. However, in the case of SWOT, the idea has enjoyed very high levels of popularity and acceptance without consulting firms and software firms extensively promoting and selling solutions related to it. Therefore, we may speculate whether SWOT is a prime textbook example of a management idea which over time has become firmly entrenched in the business community. The different sources of evidence suggest that SWOT has become widely accepted and taken-for-granted. This means that SWOT's popularity is not as dependent on supply-side actors continually breathing new life into the idea in the form of books, conference presentations etc.

Mainstreaming and societal impact

Finally, another interesting aspect of the evolution pattern of SWOT is that the idea has considerable impact even outside of the traditional business/management domain. Over time, SWOT has morphed from being primarily a business-level tool to a framework which can be used at the individual/personal level to the international level. Also, SWOT is not only used in business contexts to make businessrelated decisions. Rather, it has "travelled" widely and become an organizing framework which is frequently used in academic studies in fields typically decoupled from a business context, such as health policy and behavioral sciences (e.g. [START_REF] Holtgrave | A SWOT Analysis of the Updated National HIV/AIDS Strategy for the US, 2015-2020[END_REF]. In this respect, SWOT shares some commonalities with the Corporate Social Responsibility idea which also has a broad societal impact and is widely used outside of the traditional business domain [START_REF] Jutterström | CSR as a management idea[END_REF]Madsen & Stenheim, 2014b).

Finally, another interesting development is that SWOT appears to have a broad mainstream appeal. An illustrative example of this is the fact that SWOT has made its way into popular culture via the HBO hit series Silicon Valley. In an episode which is widely referenced on social media, two of main characters are faced with a moral dilemma, when another "corporate type" character suggests "SWOT-ing" the decision [START_REF] Youtube | SWOT -Silicon Valley -S02E06[END_REF]. Such popular culture references indicate a widespread institutionalization and "mainstreaming" of the SWOT idea far beyond the business community.

CONCLUSION

The current paper set out to analyze the history and evolution of SWOT using the lens of management fashion theory as a sensitizing framework. The analysis has revealed that SWOT has an unclear genealogy. However, it is clear that the idea has been around for about half a century. Over time, SWOT has evolved in different ways and "travelled" into new contexts. The evolution of SWOT is an interesting case since it differs in several respects from other comparable management ideas. There have been relatively few opportunities for fashion-setting actors to commercialize SWOT into sellable proprietary solutions and the market potential and newsworthiness of the idea is relatively low. Nevertheless, the SWOT idea has had considerable "staying power" both in academic circles and in organizational practice, evidenced by high levels of usage, acceptance, as well as considerable impact even at a broader societal level. These interesting aspects of SWOT should be investigated in more detail in future research.

It should be pointed out that the current study has been preliminary and exploratory in nature. This means that the conclusions should be interpreted with some caution. However, the research reported in this paper could be extended in many different ways. For example, more empirical work on the use of SWOT in different contexts is needed. Although there are some studies of uptake of SWOT and other strategic tools, extant studies have typically been conducted at different times using different research methods, which makes comparison problematic. Furthermore, inter-country studies of SWOT usage would allow for comparisons of how the idea is used in different social and cultural settings. Another way forward would be to utilize qualitative approaches to study how SWOT is applied in organizational practice. For instance, researchers could study how consultants draw on fashionable management ideas such as SWOT in organizational change projects (cf. [START_REF] Heusinkveld | Consultants and organization concepts[END_REF]. Another possibility would be to study how managers are exposed to and "handle" the SWOT idea in the post-adoption phase [START_REF] Madsen | The Balanced Scorecard: Fashion or Virus?[END_REF][START_REF] Røvik | From Fashion to Virus: An Alternative Theory of Organizations' Handling of Management Ideas[END_REF]. Such investigations could provide insight into how processes related to implementation and use of SWOT unfold over time.

Figure 1 :

 1 Figure 1: Print-media discourse about SWOT (source: ProQuest database, 11/15/2015)Figure2also shows an overall increase in the discourse related to SWOT. However, the pattern is slightly different, as the increase has been more gradual and steady.

Figure 2 :

 2 Figure 2: Print-media discourse about SWOT (Source: ScienceDirect database, 11/15/2015)

Figure 3 :

 3 Figure 3: Data Source: Google Trends (www.google.com/trends), 11/15/2015

Figure 4 :

 4 Figure 4: Data Source: Google Trends (www.google.com/trends)

Table 1 : Views on the origins of SWOT Analysis Actors Time period Reference

 1

	Harvard	Business	School	1950s and 1960s
	professors during the 1950s

Table 2 : Key characteristics of management ideas applied to SWOT Characteristic Applied to SWOT

 2

	Label	 Acronym = Label
		 Used as a verb (e.g. SWOTing)
		 Multiple variations of the SWOT acronym (e.g. SOFT, USED,
		SORF)
	Performance
	enhancements

 Featured in textbooks, but not a clear seminal work or bestselling book  Seductive and appealing to managers because of its simplicity  Not closely associated with a particular consulting or software firm  Criticized by both academics and practitioners Interpretive space  Open and unstructured nature  Easily combined with other management ideas  Can be re-interpreted in different ways Universal applicability  Universal in nature  Generic solution  Can be applied across different analytical levels

Table 3 : Actors involved in the SWOT fashion arena Actor Activity level Examples

 3

	Software firms	Low	 Difficult to make advanced software solutions
				associated with SWOT
				 Some tools for making SWOT Analysis diagrams
				(Creately, Gliffy, Grapholite, SmartDraw, SWOT
				Analysis Generator and SWOT Map)
	Business media	Low	 Difficult to write (long) books about a relatively simple
				tool
				 Low newsworthiness (been around since the 50/60s)
				 Some shorter e-books and handbooks
	Management gurus Low-medium	 Thinkers/gurus played a role in the historical
				emergence of SWOT (1950s-1980s)
				 No single guru closely associated with SWOT
				 Difficult to make a living giving speeches about SWOT
				because of its simplicity
	Conference/seminar	Low-medium	 Relatively small market for conferences/seminars
	organizers			centered around a simple and well-known tool such as
				SWOT
				 "Crowd-pleaser" (easy to understand for participants)
	Business	schools	Medium-high	 Extensively taught in business schools
	and academia		 Discussed in most textbooks in strategic management
				and marketing
				 Part of courses in MBA programs
				 Much academic research utilizing the SWOT
				framework

Consultants Medium-low

 Difficult to commercialize and market as a "solution"  Part of a consultant's toolbox and repertoire

Table 4 : Examples of books about SWOT

 4

	Title

Table 5 : Examples of take-up of SWOT Analysis in different countries/regions

 5

	Country/Region	Take-up	Reference
	Finland	"the most frequently named tools are	Stenfors et al. (2004, p. 639)
		SWOT analysis, spreadsheet applications
		and Balanced Scorecard applications"
		"clearly the most common tool used by	Stenfors and Tanner (2006, p.
		executives to support the making of major	222-223)
		decisions"
	UK	70% (rank 1st)	Gunn and Williams (2007)
	Australasia region	"The tools that dominate in this present	Frost (2003, p. 59)
		study are SWOT, PEST and budgeting"
	Czech Republic	93% (rank 1st)	Afonina and Chalupský (2012)
	China	58.46% (rank 2nd)	He et al. (2012)

Table 6 : Applications of SWOT at different analytical levels

 6

	Level	Theme	References
	Individual	Personal SWOT	Ilott (1997)
		Self-SWOT	Addams and Allfred (2013)
		SWOT analysis for individuals	Von Bergen (2013)
	Organizational Strategic conversations in SMEs	Sluismans et al. (2010)
		Use and misuse among HRD professionals	Chermack and Kasshanna (2007)
		Strategy development process at a university Dyson (2004)
	National	National HIV/AIDS strategies	Holtgrave and Greenwald (2015)
		Social work	Westhues et al. (2001)
		Hotel industry reform	Yu and Huimin (2005)
	International	Multiculturalism	Ng and Bloemraad (2015)
		Competitive advantages and disadvantages	Hindle (2008)
		of countries

AUTHOR PROFILE:

Dag Øivind Madsen earned his Ph.D. at the Norwegian School of Economics (NHH) in 2011. He currently works at Buskerud and Vestfold University College in Norway.


Amelia Carolina Sparavigna
email: amelia.sparavigna@polito.it

Mauro Maria Baldi
email: mauro.baldi@polito.it

A Study of the Regular Pentagon with a Classic Geometric Approach

Keywords:

In this paper we will consider a regular pentagon and discuss three of its properties, which are linking side, radius, diagonal and apothem to the golden ratio. One of the properties, that regarding the ratio between the diagonal and the radius of the circumscribed circumference is strictly connected to the construction of the regular pentagon with compass and straightedge.

Introduction

In a previous paper [START_REF] Sparavigna | Symmetry and Golden Ratio in the Analysis of Regular Pentagon[END_REF], we have discussed some of the properties of a regular pentagon using an approach based on an analytic method. Here we will discuss three properties of the regular pentagon, determining them with the classic geometry. We will show that: 1) in a regular pentagon, the ratio between diagonal and side is the golden ratio φ, 2) in a regular pentagon, the ratio between apothem and the radius of its circumscribed circumference is half the golden ratio, and 3) in a regular pentagon, the ratio between diagonal and radius is 1 2 + ϕ , while the ratio between side and radius is Figure 1. Geometry for the geometric study of the regular pentagon. EA is the side of the pentagon having length l. EB is a diagonal, having length d. OE is the radius having length r and OH is the apothem with length a.

The classical method and the first property

We have that α = 360°/5 = 72°, and 2β = 180° ─ α = 108°, which implies β = 54°. From Figure 1 we also have that triangle CFD is rectangular because, due to the symmetry of the regular pentagon, is isometric to triangle BMC, which is clearly rectangular. Thus, β + γ + 90° = 180°, which implies γ = 36°. Since the pentagon is regular, we have

°= = = 180 2 ˆβ E D and γ = = A D E C D B
ˆ Therefore, δ = 2β ─ 2γ = 108° ─ 72° = 36° = γ. This equivalence, in addition to the consideration that triangles EAC and EAG are also sharing the same angle ε, implies that these triangles are similar. Hence:

(1) Since triangle EAC is clearly isosceles, so is triangle EAG, thus EA = EG. Moreover, by the symmetry due to the regularity of the pentagon, in a similar way we can prove that

Number 2 / ) 5 1 ( + = ϕ (4)
is the golden ratio. Therefore, from (4), we have the first fundamental property of a regular pentagon, which links the diagonal and the side: in a regular pentagon, the ratio between the diagonal and the side is the golden ratio φ:

(5)

The second fundamental property

The second fundamental relationship is the one that links the apothem a of the regular pentagon to the radius. From Figure 1, we apply Pythagoras' theorem both to triangles EHC and EHO, recognizing that |OH| = a, |OE| = |OC| = r and |CH| = r + a. These considerations, in addition to the first fundamental property, provide the following system of equations:

(6) If we use the third equation of (6) in the first one, we have:

(7)
After, using the second equation of (6), we get:

AG AE AE AC = l d l l d - = ( ) l d l ld d l l d d 2 5 1 0 2 2 2 ± = → = - - → = - ⋅ l d 2 5 1+ = ϕ = + = 2 5 1 l d l d r l a d l a r ϕ = = + = + + 2 2 2 2 2 2 4 4 ) ( 1 4 ) ( 4 4 1 ) ( 2 2 2 2 2 2 - + = →       - = + ϕ ϕ a r l l a r (8)
After some calculations, we have that:

(9)

A trick we use here consisting of replacing φ 2 with φ + 1. In fact, if we use 0

2 2 = - - l ld d
, assuming l = 1 so that d = φ, we have: The reason of this substitution will be clear after computing the discriminant ∆ of equation ( 11). We have: Thus, (12) Note that the substitution 1 2 + = ϕ ϕ allowed us to express the discriminant ∆ as a perfect square, with a significant simplification in calculation. We have:

(13)
We ignore the second solution because the apothem a must be have a positive length. Therefore, using again identity

1 2 + = ϕ ϕ , we have: (14)
This is the second fundamental property: in a regular pentagon, the ratio between apothem and radius of its circumscribed circumference is half the golden ratio.

The third property

The third property links side and diagonal to the radius. If we apply Pythagoras' theorem again to triangle EHO taking into account the second fundamental property, we have:

0 ) 1 2 ( 2 2 2 2 2 = - - + r ra a ϕ ϕ 0 ) 1 2 ( ) 1 ( 2 2 2 = + - + + r ra a ϕ ϕ 2 2 2 2 2 2 ) 3 4 ( ) 9 24 16 ( ) 1 2 )( 1 ( 8 r r r r + = + + = + + + = ∆ ϕ ϕ ϕ ϕ ϕ . ) 1 ( 4 ) 3 4 ( 1 ) 1 ( 4 r r a + + ± - = + ∆ ± - = ϕ ϕ ϕ . ) 1 ( 2 1 2 r a r a - = ∨ + + = ϕ ϕ r r r r r a 2 ) 1 ( 2 ) 1 ( ) 1 ( 2 ) 1 ( 2
1 ) 1 ( 2 1 2 2 ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ = + + = + + = + + + = + + = ) 1 4 ( ) ( ) 1 4 ( 2 2 2 2 2 - = + + - ϕ ϕ r a r a 0 1 2 = - -ϕ ϕ (15)
We can apply the first fundamental property, so that ) 4 ( 4

The third property in an analytic approach

The third property can also be computed through the analytic approach to the geometry of regular pentagon. In [START_REF] Sparavigna | Symmetry and Golden Ratio in the Analysis of Regular Pentagon[END_REF], we used this alternative approach to prove the first and the second property.

ϕ ϕ ϕ - = → - = →         - = - = r l r l r a r l 2 3 2 1 3 2 3 3 ) 3 )( 1 ( ) 1 4 )( 1 ( 2 2 + = + + - - = + + - = - + - = - + = - - + = ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ r r r r r r d 1 2 2 + = + = ϕ ϕ r r d 2 2 2 2 1 1 1 1 φ ϕ ϕ ϕ ϕ ϕ + = + = + = = r r r d l
Here, we briefly recall the main results of this methodology in order to prove the third property of the regular pentagon. Without loss of generality, we can restrict ourselves to the case where the radius is equal to one, i.e., 1 = r . If we choose five vertexes of the regular pentagon like in Figure 2 in terms of unknown coordinates α and β then, after a number of mathematical computations reported in [START_REF] Sparavigna | Symmetry and Golden Ratio in the Analysis of Regular Pentagon[END_REF], one can find the following values for α and β :

ϕ ϕ + = , ( 20
)
which can also be written as

2 1 1 1 ϕ ϕ - = . ( 21
)
Second, we recall that

( ) ( )( ) ( ) ( ) . 2 1 5 4 1 5 2 1 5 1 5 2 1 5 1 5 1 5 2 1 5 2 1 - = - = - - = - + - = + = ϕ (22)
From Figure 2 we have that:

2 5 5 2 2 - = = = α HA l . ( 23
)
Using ( 21) and ( 22) into (23) we have:

2 2 1 1 1 1 2 1 2 2 5 1 2 2 5 1 4 2 5 5 ϕ ϕ ϕ + =         - - = - = - + = - + = - = l , ( 24
)
which is (18) with 1 = r and this furtherly proves the third property of the regular pentagon.

The construction of the regular pentagon.

The reason why we wrote the ratio between side and radius like in (18) is because this particular form justifies the construction of the regular pentagon given the radius of the circumscribed circumference. Let us remember that, if we want to construct a pentagon using compass and straightedge, we have to start from a given segment, for instance AB, and bisect it, to find point O. Once we have O, we have the circumference in which we inscribe the pentagon. After, we put the point of the compass in A, with the same radius OA. We find points E and F. Let us note that we obtain a figure of the sacred geometry, the Vesica Piscis [START_REF] Sparavigna | A Mathematical Study of a Symbol: the Vesica Piscis of Sacred Geometry[END_REF]. From the Figure 4, we can see that: The final complete construction is reported in Figure 5 (the image was obtained using TikZ, [START_REF]TikZ and PGF examples[END_REF][START_REF]Tikz & PGF Manual for Version 2[END_REF]) and is the procedure to inscribe a regular pentagon within a given circumference using compass and straightedge only. We prove next that this popular procedure uses property (18). We have: The interesting thing of construction in Figure 5 is that it does not depend on the inclination of the initial segment AB, but it holds in general, as witnessed in Figure 6.

| AO | = | CO | = r, | GO | = | AO | /2 = r /2.

  This implies that also triangle CEG is isosceles, thus EG = GC. Let |AC| = d be the length of the diagonal and |AE| = l be the length of the side of the pentagon, then |EA| = |EG| = |GC| = l and |AG| = |AC| ─ |GC| = d ─ l. Plugging these values into (1), we have:(2) Since, by construction, l ≠ 0 and d ─ l ≠ 0, we can multiply both sides of (2) by l•(d ─ l) l > 0, we use just the positive root. So we have:

.

  With this substitution, (9) becomes:(11)

2 (

 2 the reason of this articulate choice will be clear soon, when we will provide a geometrical interpretation of the relationship between side and radius involving 2 ϕ rather than ϕ ): and (18) make up the third fundamental property of the regular pentagon: in a regular pentagon,

Figure 2 .

 2 Figure 2. Frame of reference for the analytic geometry.

Figure 3 .

 3 Figure 3. The starting point to construct with compass and straightedge a pentagon inscribed in a circumference is the Vesica Piscis, the figure made by the two arcs EOF and FAE.

Figure 4 .

 4 Figure 4. Once we have GC, using a compass we determine the position of H, with |GC| = |GH|. After, using again the compass, with its point in C, we determine one of the sides (in red) of the pentagon.

Figure 5 .

 5 Figure5. Construction of the regular pentagon given the radius of the circumscribed circumference (image obtained using TikZ[START_REF]TikZ and PGF examples[END_REF][START_REF]Tikz & PGF Manual for Version 2[END_REF]).

Figure 6 .

 6 Figure 6. Construction of the regular pentagon given the radius of the circumscribed circumference, when the initial segment is inclined.


Jad Oueis

Razvan Stanica

Fabrice Valois

Linking the Environment, the Battery, and the Application in Energy Harvesting Wireless Sensor Networks

In this paper, we study photovoltaic energy harvesting in wireless sensor networks. We build a harvesting analytical model for a single node, linking three components: the environment, the battery, and the application. Given information on two of the components, limits on the third one can be determined. To test this model, we adopt several use cases with various indoor and outdoor locations, battery types, and application requirements. Results show that, for pre-defined application parameters, we are able to determine the acceptable node duty cycle given a specific battery, and vice versa. Moreover, the suitability of the deployment environment (outdoor, well lighted indoor, poorly lighted indoor) for different application characteristics and battery types is discussed.

Introduction

Wireless sensor networks (WSNs) are formed of multiple small-sized, low-cost, low-power embedded devices with sensing, computation and wireless communication capabilities [START_REF] Yick | Wireless Sensor Network Survey[END_REF]. The nodes self-organizing abilities, and the collaboration among them allows a wide range of applications such as military operations [START_REF] Lee | Wireless Sensor Network Design for Tactical Military Applications: Remote Large-scale Environments[END_REF], disaster relief [START_REF] Chen | Natural Disaster Monitoring with Wireless Sensor Networks: A Case Study of Data-intensive Applications Upon Low-cost Scalable Systems[END_REF], and environmental monitoring [START_REF] Oliveira | Wireless Sensor Networks: A Survey On Environmental Monitoring[END_REF], to name a few. Energy efficiency gained particular attention in WSNs design, since networks are required to run for long durations. However, node lifetime is limited by the finite capacity battery powering it. Regularly charging or replacing depleted batteries in a WSN is a complex and costly procedure, especially in large-scale networks, or in hard-to-reach deployment locations [START_REF] Basagni | Wireless Sensor Networks with Energy Harvesting[END_REF]. As a solution to this problem, Energy Harvesting WSNs (EH-WSNs) emerged.

EH-WSN Background. Energy harvesting consists of collecting energy from the surrounding environment and converting it to electrical energy [START_REF] Sudevalayam | Energy Harvesting Sensor Nodes: Survey and Implications[END_REF]. By implementing energy harvesting, the sensor nodes become self-powered, using the renewable environmental energy as their own power source. Harvestable energy can be provided by several sources in the node ambient environment, hence the numerous energy harvesting techniques such as photovoltaic [START_REF] Raghunathan | Design Considerations for Solar Energy Harvesting Wireless Embedded Systems[END_REF], piezoelectric [START_REF] Vijayaraghavan | Active Control Based Energy Harvesting for Battery-less Wireless Traffic Sensors: Theory and Experiments[END_REF], and wind energy harvesting [START_REF] Cammarano | Energy-harvesting WSNs for structural Health Monitoring of Underground Train Tunnels[END_REF]. The node energy intake depends on the output of the harvestable power source which may vary as a function of time. Thus, adapting power usage to the harvestable power generation pattern has been largely studied, and many harvesting-aware communication protocols were proposed [START_REF] Basagni | Wireless Sensor Networks with Energy Harvesting[END_REF]. In EH-WSN, the main focus shifts from energy conservation schemes to energy management, in order to optimally use harvested energy to enhance network performance [START_REF] Sudevalayam | Energy Harvesting Sensor Nodes: Survey and Implications[END_REF].

Paper Contribution. In this work, we focus on photovoltaic (PV) energy harvesting. We build an analytical PV energy harvesting model for a single node in a WSN based on three components: the environment, the battery, and the application. By linking energy collection, energy management, energy consumption and the interactions between them, the operational limits of any of the three components can be specified, given information on the two other components. To test our model, we adopt several use cases covering a wide range of environments, batteries and applications. We study two application classes: outage intolerant applications, where once the node suffers from a power outage, it stops its activity permanently; outage tolerant applications, where if a power outage takes place, the node is allowed to cease its activity, recharge the battery, and then return to the network. Using our model, we are able to determine the suitability of a battery, given the node duty cycle, and vice versa. Moreover, the feasibility of an application in a particular environment can be studied. Results show that even a small power outage tolerance leads to significantly higher duty cycles.

This paper is organized as follows. Sec. 2 gives an overview on the energy harvesting model. We detail the characterization, the modeling and the adopted use cases for each of the three components: environment, battery and application in Sec. 3, Sec. 4, and Sec. 5, respectively. Results on outage intolerant applications are discussed in Sec. 6, while the outage tolerant applications are studied in Sec. 7 and Sec. 8, respectively. Finally, Sec. 9 concludes the paper, with a perspective on future work.

General Objective

Three major factors contribute to the node activity in a photovoltaic EH-WSN: the environment, the battery, and the application.

The environment, where the network is deployed, determines light intensity. Each location is distinguished by specific lighting conditions, directly affecting the energy collection process. The battery plays the part of an energy storage component and an energy provider. It impacts the node lifetime, and controls to a certain extent the energy management scheme of the node. The application sets the WSN objectives, defines requirements, such as the duty cycle, and determines the node energy consumption. Each of these components is characterized by its own set of parameters which have been largely studied in literature [START_REF] Basagni | Wireless Sensor Networks with Energy Harvesting[END_REF][START_REF] Gorlatova | Networking Low-Power Energy Harvesting Devices: Measurements and Algorithms[END_REF][START_REF] Taneja | Design, Modeling, and Capacity Planning for Micro-solar Power Sensor Networks[END_REF][START_REF] Prayati | A Modeling Approach on the TelosB WSN Platform Power Consumption[END_REF]. In this work, we emphasize the existing relation between these components in order to analyze the trade-offs to be considered when deploying EH-WSNs. By linking energy collection, energy management and energy consumption, that are respectively dictated by the environment, the battery and the application, we elaborate an energy harvesting analytical model for a single node in a WSN. Using our model, the operational limits of a component can be specified given information on the other two.

In the following, we detail each component, and the corresponding use cases adopted in the numerical analysis.

The Environment Characterization

Energy Collection Model

A PV panel absorbs natural or artificial light, and converts it into electrical energy that powers the node. Hence, it is the light intensity that determines the amount of energy that can be harvested by the node.

Without loss of generality, we consider in the rest of this study that time is slotted into timeslots of duration T hours each. We denote by T the set of all timeslots τ , for the whole observation period. The harvested energy during a timeslot τ , denoted by E h (τ ), serves as input to our model. E h (τ ) depends on several factors such as the environment-specific light conditions, and the PV panel characteristics. We denote by S P V the PV panel illuminated area in m 2 , and by η P V the PV cell efficiency. Light intensity is modeled by the global horizontal irradiance, I gh (τ ), measured in W/m 2 , representing the total amount of shortwave radiation received by the PV panel. The harvested energy by the node during timeslot τ is measured in Joules, and computed as follows:

E h (τ ) = I gh (τ ) • S P V • η P V • T (1)

Use Cases

In our analysis, we consider deployment periods of approximately one year, divided in hourly timeslots, i.e. T = 1 hour. For the PV panel characteristics, we suppose an illuminated area S P V = 10 cm 2 , having an efficiency η P V = 0.25 [START_REF] Green | Solar Cell Efficiency Tables (v. 45)[END_REF].

We consider in our analysis both outdoor and indoor deployment scenarios, covering a wide range of lighting conditions. We determine the harvested energy at each timeslot E h (τ ) by using real-world datasets providing measurements of the hourly I gh (τ ). For the outdoor scenario, we use measurements collected in Los Angeles during the year of 2014, provided by the U.S. Department of Energy [START_REF] Andreas | Solar Resource & Meteorological Assessment Project (SOLRMAP)', Rotating Shadowband Radiometer (RSR)[END_REF]. The average daily irradiation is month-dependent, and varies between 39.04 J/cm 2 /day in December, and 109.56 J/cm 2 /day in June. For the indoor scenario, we consider datasets provided by Gorlatova et al. [START_REF] Gorlatova | CRAWDAD Dataset Columbia/Enhants[END_REF] presenting measurements in office buildings in New York City. We select two particular indoor locations with significantly different lighting conditions. Location A is poorly lighted, with window shading used at all times, and an average daily irradiation of 1.3 J/cm 2 /day. Conversely, location B is very well lighted, it has large windows with unobstructed view, and an average daily irradiation of 63 J/cm 2 /day.

The Battery Characterization

Battery Model

In harvesting-based WSNs, nodes are usually equipped with a rechargeable battery capable of storing the harvested energy, as well as powering the node. Rechargeable batteries are mainly characterized by their capacity E max , and their charge/discharge efficiency η bat < 1 that causes energy loss when the battery is used. It should be noted that battery characteristics may vary under different operating temperatures and battery age [START_REF] Buchmann | Batteries in a Portable World: A Handbook on Rechargeable Batteries for Non-engineers[END_REF]. Without loss of generality, we consider a constant discharge efficiency representing the average of the charge losses a battery may suffer from under different conditions.

In our model, we assume the presence of a power manager responsible of delivering the necessary amount of energy to the node. A node is powered, through the power manager, from the harvested energy alone, from the energy stored in the battery, or from both. The power manager has an output regulator, with an output efficiency η out < 1. This means that, when energy is delivered to the node, a certain amount of this energy is lost. Consequently, if we denote by E c (τ ) the energy consumption of a node during a timeslot τ (later detailed in Sec. 5), the power manager must deliver E c (τ )/η out Joules to the node in order to supply its demand [START_REF] Taneja | Design, Modeling, and Capacity Planning for Micro-solar Power Sensor Networks[END_REF].

To model the battery level variation as a function of time, we adopt the energy management model presented by Taneja et al. [START_REF] Taneja | Design, Modeling, and Capacity Planning for Micro-solar Power Sensor Networks[END_REF]. We extend their model by adding the battery charge/discharge efficiency η bat . We denote by E r (τ ) the battery residual energy level at the beginning of timeslot τ . At each timeslot, the node power source is determined by the power manager by comparing the amount of harvested energy E h (τ ), and the energy to be delivered to the node E c (τ )/η out . Two cases unfold, determining the battery behavior at each timeslot:

-E h (τ ) ≥ E c (τ )/η out : in this case, the harvested energy is enough to solely supply the node. The remaining amount of energy, unused by the node, is stored in the battery, causing the battery to charge according to Eq. 2:

E r (τ + 1) = min E r (τ ) + η bat • E h (τ ) - E c (τ ) η out , E max (2)
-E h (τ ) < E c (τ )/η out : in this case, the harvested energy is not enough to solely supply the node. The missing amount of energy must be provided by the battery. Consequently, two possibilities open up:

1. The amount of harvested energy, combined with the amount of the battery residual energy is enough to supply the node energy demand. The node is powered, and the battery discharges according to Eq. 3:

E r (τ + 1) = E r (τ ) + 1 η bat • E h (τ ) - E c (τ ) η out , if E h (τ ) + η bat • E r (τ ) ≥ E c (τ ) η out (3)
2. The amount of available energy is not enough to power the node. In this case, the node is in power outage situation, and cannot be properly powered. The node must cease its activity, and we refer to it as non-operational. Let T no be the subset of timeslots τ during which the node is non-operational:

τ ∈ T no ⊆ T ⇐⇒ E h (τ ) + η bat • E r (τ ) < E c (τ ) η out (4)
If power outage is tolerated, the nodes remain non-operational for a limited duration only, since the battery can still be recharged by the harvested energy. Once the available energy is sufficient again, a non-operational node resumes its activity. We consider that the tolerance for temporarily non-operational nodes depends on the specific application requirements. In this work, we study two classes of applications: outage intolerant and outage tolerant, further defined in detail in Sec. 5.

Use Cases

We consider in our analysis a variety of rechargeable batteries, with different characteristics. The most common rechargeable technologies are Nickel Metal Hydride (NiMH) and Lithium Ion (Li-ion). NiMH batteries suffer from low charge/discharge efficiency; however, they have a simple charging method, lowering their cost. Li-based batteries have higher charge/discharge efficiency, but a more complex charging method [START_REF] Basagni | Wireless Sensor Networks with Energy Harvesting[END_REF]. The set of batteries we consider in our analysis covers a wide range of characteristics, summarized in Tab. 1. Regarding the output regulator, we consider an efficiency η out = 0.8 [START_REF] Taneja | Design, Modeling, and Capacity Planning for Micro-solar Power Sensor Networks[END_REF].

Model

Type Volume (cm

The Application Characterization

Energy Consumption Model

The power consumption differs from one application to another, depending on the sensing activity by the sensor, the computation performed by the CPU, and the communication scheme of the radio transceiver. In this study, we consider that the radio transceiver is the main energy consumption source [START_REF] Prayati | A Modeling Approach on the TelosB WSN Platform Power Consumption[END_REF], disregarding other consumption sources. However, including CPU or sensing consumption in the model is straightforward. We suppose that during each timeslot τ of duration T , a duty cycle DC(τ ) is forced on the radio transceiver. The latter will be awake, and consuming power, during each timeslot, for a time equal to DC(τ )•T .

For the remaining time, the node is asleep, with a negligible power consumption. When awake, the transceiver switches between three states: receive, transmit, and listen. The power consumed in these states is very similar, as proven by experimental studies [START_REF] Prayati | A Modeling Approach on the TelosB WSN Platform Power Consumption[END_REF], and transceiver datasheets [START_REF]Chipcon CC2420 Datasheet[END_REF]. We consider that the power consumed by the radio while active is equal to the average of the power consumption of these three states, denoted by P avg . Thus, during a time period T , the energy E c (τ ) consumed by the transceiver is dictated by the duty cycle DC(τ ), such as:

E c (τ ) = P avg • DC(τ ) • T (5)

Application Classes

The application determines the tolerance for having a temporarily non-operational node. In this study, we consider the following application classes:

Outage intolerant: For these applications, a node cannot enter the nonoperational state. The node is required to sustain its activity without suffering from a power outage, meaning that continuous operation is a requirement. We denote by T co the set of consecutive timeslots during which the node is operational up until the first power outage takes place. We formally define continuous operation (c.o.) as:

c.o. ⇐⇒ E h (τ ) + η bat • E r (τ ) > E c (τ ) η out , ∀τ ∈ T co ⊆ T (6)
The node lifetime in this case is equal to the duration during which the node is continuously operational, up until the first power outage takes place. We refer to it as the continuous operation lifetime. With timeslots of duration T , the continuous operation lifetime is equal to

|T co | • T .
Outage tolerant: For these applications, the node can be temporarily nonoperational. A node will remain non-operational as long as the amount of harvested energy combined with the battery residual energy are below the node energy requirement. Once the delivered energy is enough, the node resumes its activity. During a non-operational timeslot, the harvested energy is only used to recharge the battery:

E r (τ + 1) = min(E r (τ ) + η bat • E h (τ ), E max ) ( 7 )
In this work, we consider the duty cycle to be the percentage of time during which a node is active in the timeslots where the node is operational. In nonoperational timeslots, where the node is inactive, the duty cycle is null:

DC(τ ) =
DC, ∀τ ∈ T \ T no 0, ∀τ ∈ T no [START_REF] Vijayaraghavan | Active Control Based Energy Harvesting for Battery-less Wireless Traffic Sensors: Theory and Experiments[END_REF] We limit our study to static duty cycles, such as the duty cycle is set to a fixed value DC in the operational timeslots. Although dynamic duty cycles are out of the scope of this paper, expanding the framework to include adaptive duty cycles in each timeslot is straightforward.

In outage tolerant applications, it is possible that the node frequently switches between the non-operational and the operational state. We define n c as the consecutive number of timeslots during which the node is non-operational. Each time the node enters the non-operational state, a new instance n c (τ ) of the counter n c is created. We denote by n cmax the maximum number of consecutive non-operational timeslots:

n cmax = max τ ∈Tno n c (τ ) ( 9 )
Finally, we define r no as the percentage of time during which the node is non-operational out of the whole observation period T :

r no = 100 × |T no | |T | (10)

Use Cases

In our analysis, we do not limit the study to specific applications, but we study different application requirements, which can be matched to a target application afterwards. Our use cases are representative of several WSN applications. We study outage intolerant applications, where continuous operation is required. We also consider several cases of outage tolerant applications with different values of n cmax and r no . Regarding energy consumption, based on the CC2420 transceiver datasheet [START_REF]Chipcon CC2420 Datasheet[END_REF], we fix the energy consumption during a one hour timeslot to P avg • T = 180 J.

Outage Intolerant Applications

In this section, we consider outage intolerant applications, where continuous operation is required (Eq. 6). Using our model, we are able to determine the continuous operation lifetime, i.e. the time duration before the first power shortage takes place. With timeslots of duration one hour, the continuous operation lifetime is equal to |T co | hours. For comparison, we use the metric r co , which represents the percentage of the continuous operation out of the whole observation period, such as r co = 100 × |Tco| |T | .

Outdoor

Fig. 1. Percentage of the continuous operation out of the whole observation period -Outdoor.

Fig. 1 shows a comparison of r co for an outdoor, one year deployment. We compare the results for the deployment starting at different months of the year. The fixed duty cycle values are such that DC ∈ {20%, 33%, 50%}. The choice of such high duty cycles is not uncommon in harvesting-based WSNs, where energy constraints are alleviated [START_REF] Raghunathan | Design Considerations for Solar Energy Harvesting Wireless Embedded Systems[END_REF]. Having higher duty cycles is beneficial, since it allows lower communication delays, and higher throughput.

For DC = 20% (Fig. 1a), all the batteries are capable of guaranteeing continuous operation during the whole year, except for the smallest Li batteries. In fact, with the 10 mAh Ultrathin battery, the node is continuously active for 2 hours only. For DC = 33% (Fig. 1b), continuous operation is achieved for a whole year for all the Li batteries, except the smallest ones, no matter the deployment month. However, for the NiMH batteries, continuous operation is only achieved for the AA-sized battery having the largest capacity, and only if the deployment starts at January. For DC = 50% (Fig. 1c), none of the batteries are capable of achieving continuous operation for a whole year, no matter the month of deployment. These results suggest that Li-based batteries generally outperform NiMH batteries. This is due to the high charging efficiency of Li batteries, as opposed to the low efficiency of NiMH batteries causing them to charge less and discharge more aggressively. On the other hand, the smallest Li batteries (43 and 10 mAh) are limited by their relatively small capacity. This suggests that much lower duty cycles are recommended when using these batteries.

A pattern concerning the effect of the deployment month on the achieved lifetime emerges. This is due to the significant difference in the amount of harvestable energy from one month to another. It is generally around November and December that the aggressive discharge will take place considering the few recharge opportunities. Thus, it is more likely that a node will enter the nonoperational state during these months. Fig. 2 shows a comparison of r co for the indoor locations. Since harvestable energy indoor is far less available than outdoor, smaller duty-cycles are considered: DC ∈ {1%, 5%, 10%}. Unlike the outdoor scenario, we do not have the deployment month dependency. At the well lighted location B, Fig. 2b shows that, with DC = 1%, all the batteries, except the 10 mAh Ultrathin, are capable of achieving continuous operation for the whole observation period. This means that any of these batteries can be used with a duty cycle DC = 1% or lower. Fig. 2a shows that, at the poorly lighted location A, the longest time for which the node is capable of sustaining its continuous operation is equal to r co = 73% of the observation period, for DC = 1% and two AA-sized NiMH batteries. The results show that duty cycles on the order of DC = 5% are relatively high for indoor applications, since no battery is capable of guaranteeing continuous operation for longer than r co = 24% of the observation period. Another observation in Fig. 2a is that the Ultrathin 43 mAh and 10 mAh batteries are only suitable for applications requiring duty cycles even lower than DC = 1%.

Indoor

Non-operational Time in Outage Tolerant Applications

In this section, we consider outage tolerant applications, where continuous operation is not a requirement. The node may become non-operational for a certain duration before regaining enough energy to resume its activity. Some applications set regulations for the non-operational period, by bounding the outage tolerance parameters n cmax (Eq. 9) and/or r no (Eq. 10). Using our model, we compute n cmax and r no for a given fixed duty cycle DC. Fig. 3a and Fig. 3b show values of n cmax and r no , respectively, during a one year deployment in the outdoor location, for different battery models, and for different static duty cycle values: DC ∈ {20%, 33%, 50%}. Since continuous operation is no longer a target, the month of deployment does not affect the output. Tolerance for non-operational time and the required duty cycle, set by the application, are used to determine the suitable battery. For example, a node powered by a 43 mAh Ultrathin battery, with DC = 20%, is in power outage for two consecutive hours maximum, and remains operational for a total of 97% of the whole deployment period. For applications tolerating these conditions, a node can be equipped with this type of battery. In an outage intolerant application, such batteries were not even capable of surviving one month under the same conditions. the tolerance for non-operational time must be high. As the duty cycle increases and the battery capacity decreases, the total non-operational time increases significantly. The values of the total non-operational time reached in location A (Fig. 4b), are highly impractical in real-life deployments. It is useless to have the node non-operational for 80% of the time, for example, as required by most batteries. In location B, we can see in Fig. 4d that there is no power outage for DC = 1%, except with the Ultrathin 10 mAh battery. This is in accordance with the results shown in Fig. 2b. With the Ultrathin 10 mAh battery and DC = 1%, for an outage intolerant application, the node is active for only 30% of the observation period. However, for outage tolerant applications, results show that the node is active, with DC = 1%, for 96.6% of the time, while staying in the non-operational state for a maximum of 10 consecutive hours. For the higher duty cycles, total non-operational time increases significantly.

Outdoor

Indoor

Duty Cycle Dimensioning in Outage Tolerant Applications

We consider now the complementary problem of the previous section. Given predetermined boundaries on n cmax and r no , we compute the maximum achievable DC value. Fig. 5a and Fig. 5b show the maximum achievable duty cycle DC in the outdoor location, with the AA-sized NiMH batteries, and the Ultrathin 43 mAh battery, respectively. As anticipated, the more we tolerate outages, the more DC increases. Since r no is bounded, the maximum achievable value of DC is also bounded. With the NiMH batteries, Fig. 5a shows that the maximum achievable duty cycle with no tolerance for outages is DC = 34%, a relatively high value. As the tolerance for non-operational time increases, duty cycles as high as DC = 93% can be achieved, with the node being non-operational for a maximum of 15 consecutive hours, and for 33% of the observation period. However, conditions are more strict for the Ultrathin 43 mAh battery, as shown in Fig. 5b. The maximum achievable duty cycle with no tolerance for outages is DC = 18%.

Outdoor

Indoor

Fig. 6a and Fig. 6b show the maximum achievable DC in indoor locations, A and B, respectively, with AA-sized NiMH batteries. The difference is clear in terms of the achieved duty cycle between these two locations. In the poorly lighted location A, the duty cycle reaches a maximum of DC = 1.3% being non-operational for 43% of the time, with 200 maximum consecutive non-operational hours. In the well lighted location B, the achieved duty cycle for the same non-operational conditions is DC = 5%. Higher duty-cycles are achieved at the costly expense of having a large amount of time during which the node is non-operational. Some of the non-operational constraints may be impractical, meaning that applications requiring higher duty cycles as well as short outage time are difficult to accommodate to indoor environments.

Conclusion

In this paper, we present a PV energy harvesting model for a single node in a WSN. We build our model around three major components: the environment, the battery, and the application. Based on our model, given two of the three components, we can characterize the third one. We define several use cases using real-world datasets of light intensity, in both indoor and outdoor scenarios, a wide range of rechargeable batteries, and various application parameters. We show that, given particular application parameters, we are able to determine which batteries are suitable, given the node duty cycle, and vice versa. Furthermore, the feasibility of an application in a specific environment, or for a specific battery, can be studied. Results show that tolerating short power outage periods allows extending the node lifetime, with higher duty cycle values.

For future work, it is of utmost importance to further expand the model from a single wireless node to the whole network. Collaboration between the nodes, and relaying functionalities may influence the node behavior. Moreover, the outage tolerant applications raise new challenges on how to deal with the unexpected "disappearance" of a node when non-operational, followed by its "reappearance" in the network.

Fig. 2 .

 2 Fig. 2. Percentage of the continuous operation out of the whole observation period -Indoor.

Fig. 3 .

 3 Fig. 3. Outage tolerance parameters -Outdoor.

Fig. 4 Fig. 4 .

 44 Fig.4shows values of n cmax and r no , for indoor locations A and B, for different batteries, and for different static duty cycle values: DC ∈ {1%, 5%, 10%}. In location A, Fig.4aand Fig.4bshow that even with the relatively low DC = 1%,

Fig. 5 .

 5 Fig. 5. Maximum achievable duty cycle for pre-determined conditions -Outdoor.

Fig. 6 .

 6 Fig. 6. Maximum achievable duty cycle for pre-determined conditions with 2*AA-NiMH batteries -Indoor.

Table 1 .

 1 Comparison of rechargeable batteries characteristics[START_REF] Sudevalayam | Energy Harvesting Sensor Nodes: Survey and Implications[END_REF][START_REF]Ultrathin Rechargeable Lithium Polymer Batteries from Powerstream[END_REF].

	AA	NiMH	7.7	10800	2500	0.66 AA-Ni
	AAA	NiMH	3.8	5625	1250	0.66 AAA-Ni
	AA	Li	7.7	9857	740	0.99 AA-Li
	Ultrathin 200 Li	2.7	2664	200	0.99 U-Li-200
	Ultrathin 100 Li	1.3	1332	100	0.99 U-Li-100
	Ultrathin 43	Li	0.6	573	43	0.99 U-Li-43
	Ultrathin 10	Li	0.6	133	10	0.99 U-Li-10

3

) Emax (J) Capacity (mAh) η bat Notation