Mustafa Erdem Sakinc

Share Repurchases in Europe -A Value Extraction Analysis

Keywords: Shareholder value, corporate finance, corporate payouts, share repurchases, Europe JEL codes: D22, D30, G35, G38

Encompassed by maximization of shareholder value ideology, large US corporations raised corporate distributions to record high levels, particularly by share repurchases which provide short-term boosts to their stock prices. Since the early 1980s, the deregulation of the US economy and the financialization wave provided incentives for companies to direct financial resources towards shareholder value instead of innovation and job creation. This study examines the repercussions of these trends in the context of Europe. It shows that despite there is a lag in deregulation that helped European corporations to establish similar attitudes of shareholder value orientation, large European companies have been increasingly focused on corporate distributions to the cost of decreasing investment in productive resources and employment opportunities. Although share repurchases remained concentrated in a smaller number of companies and they are performed occasionally, together with dividends, European companies distribute corporate cash to shareholders as much as US companies. Increasing value extraction in Europe in the form of corporate payouts will only aggravate the vulnerability of the continent's economy in the long run.

Financialization and the European corporation

Extensively studied in the last two decades by scholars from a variety of disciplines, financialization became a convenient word to describe the rising importance of any financial tool, measure, motive or actor within the functioning of economic activity. There has also been a growing public interest in financialization and its negative impact on economic performance since the US-led global financial crisis of 2008.

The impact of financialization, which also includes ideological and discourse-based instruments, can be extended to any act aiming to reap the returns of any investment through different mechanisms. Depending on the extent of power that is to be exerted by a specific economic actor, the benefits and the perils of financialization are unequally distributed. The literature on financialization has investigated a variety of actors of economic activity including but not limited to institutions, households, nations and corporations as creators and users of financial resources. The choice of research questions on financialization centers around specific group of actors depending on the focus. Where to locate financialization in the operation of the economy, and how it affects economic performance [START_REF] Lazonick | Reforming the Financialized Business Corporation[END_REF] are the central questions of any research on financialization.

The value extraction that defines financialization depends on a previous period of value creation. The massive value creation generated by the US managerial revolution made the United States the twentieth-century leader of the world economy [START_REF] Chandler | Scale and Scope: The Dynamics of Industrial Capitalism[END_REF]. This successful model of capitalistic production stumbled, however, with internal problems of conglomeration from the 1960s and innovative competition coming from foreign economies, especially from Japan in major consumer and capital goods sectors from the 1970s [START_REF] Lazonick | Maximizing Shareholder Value: A New Ideology for Corporate Governance[END_REF]. Since the 1980s the actors in the economy who have been able to extract value have differed from those who create value [START_REF] Lazonick | The Risk-Reward Nexus in the Innovation-Inequality Relationship: Who Takes the Risks? Who Gets the Rewards?[END_REF]. A finance-led growth perspective emerged in response to these productivity and profitability questions [START_REF] Boyer | Is a Finance-led growth regime a viable alternative to Fordism? A preliminary analysis[END_REF] with important changes in the internal power structure of the firm [START_REF] Lazonick | Controlling the Market for Corporate Control: The Historical Significance of Managerial Capitalism[END_REF][START_REF] Stockhammer | Financialisation and the Slowdown of Accumulation[END_REF]. This paper is a part of a research project focused on the financialization at the corporate level with its roots in business activity and the structural changes in business organization, employment and productive activity since the early 1980s with varying consequences for different actors involved. The empirical analysis of the paper is based on the assertion that the roots of financialization can only be found within real economic or productive sectors where the value is created and extracted. The paper is primarily focused on value extraction through dividend payments and stock buybacks performed by public corporations. Excessive value extraction in these forms can undermine the longrun processes of creating value in business firms and in the economy. The damaging impacts on buybacks and dividends on innovation will only become apparent in the future [START_REF] Lazonick | Profits Without Prosperity[END_REF]Lazonick, 2015b).

The significant role of financialization in the US context in the last 40 years and its impact on different aspects of economic activity have been deeply researched by a large group of scholars, not only restricted to economics. However, in the case of Europe, the discussion has remained limited and restricted to national contexts that are not comparable at the continent level. Compared to the research on the US and to some extent on the UK, many aspects of financialization in Europe have not yet been investigated. Thus, the purpose of this paper is to approach to the issue of the financialization of the corporation from a European perspective.

One would expect financialization to be less severe in Europe given the influence of opposing institutional and political economic forces of the continent. Any analysis of the historical-institutional framework of Europe that also has an impact on transforming corporate strategies is beyond the scope of this paper. However, although it is the world's largest economy, the microfoundations of financialization have been scarcely studied at the European level. The analysis of European transformation towards shareholder value requires concept or action specific research on the roots and causes of these transformations in corporate finance and corporate governance. One can later identify the interrelations between these themes around a common research framework aiming to explore the dynamics of European integration, financialization and corporate transformation. Thus, this paper aims to identify the course of value extraction at the corporate level and the underlying regulatory changes at European level related to corporate payouts. It seeks to find evidence if the prominent aspects of value extraction in the US corporation are also valid in the context of Europe and it tries to identify the differentiating aspects of corporate financialization in Europe. Together with the research on executive compensation in large European companies [START_REF] Kotnik | Executive compensation in Europe: Realized gains from stock-based pay[END_REF], this is a first attempt to explore the micro dynamics of continent level transformations in corporate activity and their consequences.

The context of financialization in Europe

The roots of financialization of the US corporation have been identified by a broad range of studies in the last two decades [START_REF] Lazonick | Maximizing Shareholder Value: A New Ideology for Corporate Governance[END_REF][START_REF] Crotty | The Neoliberal Paradox: The Impact of Destructive Product Market Competition and Impatient Finance on Nonfinancial Corporations in the Neoliberal Era[END_REF][START_REF] Duménil | Capital Resurgent: Roots of the Neoliberal Revolution[END_REF][START_REF] Boyer | From Shareholder Value to CEO Power: The Paradox of the 1990s[END_REF][START_REF] Krippner | The financialization of the American economy[END_REF][START_REF] Fligstein | Shareholder Value and the Transformation of the U.S. Economy, 1984-2000[END_REF][START_REF] Orhangazi | Financialization and capital accumulation in the non-financial corporate sector: a theoretical and empirical investigation on the U.S. economy, 1973-2003[END_REF][START_REF] Lazonick | Financialization of the U.S. corporationwhat has been lost and how it can be regained[END_REF]2014). However, the research on the transformation of European finance during the same period has remained highly fragmented and the limited number of existing studies which are focused on specific elements or countries within Europe are not deep enough to give a clear picture of the impact of financialization on European economy. Indeed, the story of European capitalism in the last quarter of the twentieth century has not been extensively written from a political economic perspective which may help us to understand the depth and impact of financialization and shareholder value ideology in the following period. Little is known about whether financialization at microeconomic level is rooted deep in the 70s and 80s or is a more recent phenomenon that began only in the late 1990s. Some early research found limited evidence of the infiltration of shareholder value ideology in continental Europe and especially Germany [START_REF] Dupuy | Institutional Investors and the Car Industry Geographic Focalisation and Industrial Strategies[END_REF][START_REF] Jürgens | Shareholder value in an adverse environment: The German case[END_REF]Stadler et.al, 2006). The evidence of adoption of shareholder-value ideology indicates that it was a modified form of the US version incorporating incremental changes through stakeholder consensus resulting in a negotiated form of shareholder value orientation [START_REF] Vitols | Negotiated Shareholder Value: The German Variant of an Anglo-American Practice[END_REF] or a slow transition process [START_REF] Jackson | Corporate Governance and Employees in Germany: Changing Linkages, Complementarities, and Tensions[END_REF]. Although such views continued to be endorsed by others (Deeg, 2014), some more recent accounts on European financialization stress its impact on rising inequalities, degrading industrial relations practices and changing corporate governance mechanisms in favor of a 'shareholder' perspective [START_REF] Hein | Finance-dominated capitalism and re-distribution of income: a Kaleckian perspective[END_REF]2015;[START_REF] Peters | The Rise of Finance and the Decline of Organised Labour in the Advanced Capitalist Countries[END_REF][START_REF] Prosser | Financialization and the reform of European industrial relations systems[END_REF] highlight a fundamental break with the earlier period of capitalism, a very similar case to the US. In a similar vein, some other studies also link the full establishment of financialization in Europe to the integration of the European Union and the introduction of the single currency area, allowing free mobility of financial capital [START_REF] Eichacker | German Financialization, the Global Financial Crisis, and the Eurozone Crisis[END_REF][START_REF] Rossi | Financialisation and monetary union in Europe: the monetary-structural causes of the euro-area crisis[END_REF][START_REF] Nölke | Finanzialisierung als Kernproblem eines sozialen Europas[END_REF].

Nevertheless, some major issues related to financialization are much less analyzed for Europe. There is a research gap in firm-level issues like the role of European-level takeovers and M&As as 'engines of shareholder wealth maximization'; share-based remuneration of executives and employees in relation to shareholder value; and the trend of shareholder value distribution in European firms during the financialization era. Investigation of such highly interconnected issues is needed for a fullscale understanding of European corporate financialization. This study is an attempt to push forward that research agenda, focusing on value extraction through corporate payouts, and specifically share repurchases.

Regulatory background of share repurchases

Offered as a solution by economists known as agency theorists to the corporate management problems of the day, shareholder-value creation gradually turned into a discursive construct, independent of a firm's productive performance [START_REF] Froud | Financialization and Strategy Narrative and Numbers[END_REF]. Turning into a principle of corporate governance first among Anglo Saxon corporations, it also became part of discussion in Europe. In 1999, the OECD issued 'The OECD Principles of Corporate Governance' emphasizing that corporations should be run, first and foremost, in the interests of shareholders (OECD 1999, in Lazonick and[START_REF] Lazonick | Maximizing Shareholder Value: A New Ideology for Corporate Governance[END_REF] and its similar tone has continued in the 2014-2015 review of the principles (Lazonick, 2015a).

One major manifestation of shareholder value-oriented corporate governance is the practice of corporate payouts, and especially share repurchases.

The first European-level regulation on share repurchases was codified in the Second Council Directive 77/91/EEC of 13 December 1976 on 'coordination of safeguards' (EEC, 1977). Aiming to establish a common framework for the understanding of shareholder and creditor protection in European Economic Community countries, the directive also gave shape to some basic rules of share repurchasing in order to prevent any corporate abuse of shareholder and creditor rights. These rules included the sources to be utilized, authorization, duration, the interval of price to be paid and volume of shares to be repurchased in member countries even if its restrictions were not stringent. The directive only concerned the EEC countries where the laws permit a company to buy back its own shares. Until the late 1990s share repurchases were either prohibited or very difficult to implement due to legal restrictions in most of the Continental European countries. The only country which facilitated share repurchases through legislation before the 1990s was the UK. The amount of UK share buybacks made up the bulk of total European share repurchase programs [START_REF] Rau | Regulation, Taxes, and Share Repurchases in the United Kingdom[END_REF]. In France, Germany and other major European economies, share repurchase was made easy to implement or legal only after regulatory changes between 1998 and 2000 (see Annex for more details).

Subsequently, in December 2003 the European Commission initiated a new regulation on buy-back programs in order to separate them from insider dealing and market manipulation ('market abuse') activities which were prohibited by another directive earlier in the same year. In the new regulation, share repurchases are regarded as a useful tool in stabilizing markets and market abuse regulations should not be applied to buy-back programs (EC Directive 2003/6/EC and EC Regulation 2273/2003). The regulation defined necessary conditions and restrictions regarding buy-backs to provide a safe harbor for companies as long as they observe certain conditions. It was binding and directly applicable for member states without any further action on the part of the national authorities but the EU member states to establish monitoring mechanisms to provide transparency of disclosure in order to prevent abuses. Indeed, sanctions and administrative measures are valid only when the competent national authority defines an action as a market abuse.

In April 2014, the previous directives prohibiting insider trading and market abuse within the EU were repealed and replaced with an updated EU regulation which entered into force following its publication. The regulation was followed with a supplementing text published in early 2016 on buyback programs, updating the 2003 directive.

Whether EU level regulation defined the scope of repurchase activity in detail, country specific rules still represent a diversity although the EC regulation brought, in some cases, greater flexibility to firms having share repurchase activity. Despite existing differences between the US and European legislation of share repurchases, repurchase activity in Europe quickly surged upward in 2000s and followed a similar trend with the US before the global economic crisis.

The following part provides country level share repurchase information including repurchase regulation, tax and insider issues regarding repurchases. The fourth part discusses the limited and mostly empirical literature on European repurchases and their findings. In the fifth part, a descriptive analysis of the repurchase activity of major European countries is provided for a 16-year period starting with 2000. The annex provides detailed information on major EU economies and Switzerland about their share repurchase regulations.

Country specific regulatory information †

France

In France, share repurchases were not illegal before the modification of the law in 1998, but they were difficult to implement and the acquired shares could not be cancelled [START_REF] Ginglinger | Ownership Structure and Open Market Stock Repurchases in France[END_REF]. Since 1998, a French company can acquire up to 10% of its outstanding shares within a period of 18 months after the announcement of the repurchase program and it can cancel shares or reserve them. The regulation was slightly changed in October 2004 to comply with the EC regulation and the disclosure period is limited to seven days after the repurchase day, which was the beginning of the following month for the repurchases of a given month [START_REF] Ginglinger | Share repurchase regulations: Do firms play by the rules?[END_REF]. 1998 Regulation made shareholders' gain of repurchases subject to capital gains tax that companies are required to pay a fee of 0.15% of the total value of shares repurchased to the stock market's related directorate. According to [START_REF] Dereeper | Rachats d'actions versus dividendes: effet de substitution sur le marché boursier français?[END_REF], right after the regulatory change in 1998, the ratio of quoted companies that initiated a repurchase program increased from 8.9% in 1998 to 42.1% in 2001 and 324 companies out of 600 companies that have programs performed stock buybacks for a net amount of €37.2 billion between 1998 and 2001. During the same period the same group of companies distributed €47.8 billion in the form of dividends.

UK

In the UK, share repurchases were legalized by the Companies Act in 1981 with various restrictions, a year before the safe harbor promulgation of Rule 10b-18 in the US. A UK company can only repurchase its shares during an authorization only valid between two consecutive annual general meetings which is usually 12 months and companies must publish their repurchase activity on the regulatory news services on the next business day with every detail [START_REF] Crawford | Is the market underreacting or overreacting to open market share repurchases? A UK perspective[END_REF]. A repurchase during an authorization period cannot exceed 15% of total outstanding shares and the price to be paid should not be more than 5% above the average price for the five business days before the repurchase day (Kim et al., 2003). Moreover, the company has to cancel all the shares repurchased.

A major difference with the US, UK companies are prohibited to repurchase their shares during the same period when their executives are not allowed to trade in their own shares of the companies. Practically, share repurchases are not allowed two months before the publication of annual and semiannual earnings and one month before the publication of quarterly results [START_REF] Rau | Regulation, Taxes, and Share Repurchases in the United Kingdom[END_REF].

Germany

In Germany, repurchasing shares was prohibited until 1998 when the regulation was changed and share repurchases were allowed. German companies are allowed to repurchase up to 10% of nominal share capital only with the funds that could have otherwise been paid out to shareholders in the form of dividends. Repurchases programs have to be authorized by the annual general meeting of shareholders for a maximum period of 18 months and announced to the public (Hackethal and Zdantchouk, 2005). Maximum number of shares to be repurchased, minimum and maximum repurchase prices, and the method of repurchasing must be declared in the announcement similar to the EC regulation.

Switzerland

Share repurchases in Switzerland started after the revision of the Swiss Corporate Law in 1992 even though there was no open ban of repurchases before the revision [START_REF] Mueller | Share Repurchases and Repayments of Nominal Value: The Swiss Alternative to Dividends[END_REF]. Swiss companies are eligible to purchase up to 10% of outstanding shares without shareholder approval or any definite period of time and price limits. The only restriction concerning a repurchase program is that the acquisition of shares must be financed by retained earnings and/or freely distributable reserves [START_REF] Pfenninger | Buyback of equity and debt securities in Switzerland[END_REF]. A company can repurchase its shares only ten days prior to the earnings announcement and daily repurchases cannot exceed 25% of the average daily volume on the first trading line over the previous month. A company must declare the number of shares acquired and the price paid per share at the latest on the fifth trading day following repurchase of its own shares.

Sweden

Sweden was the last major country in the EU to allow share repurchases. Companies quoted on the Swedish stock exchange were allowed to repurchase their own shares beginning with March 2000 with the usual claims of more flexible capital structures, better use of excess cash or protection against hostile take-overs [START_REF] Peterson | Common Stock Repurchases A First Year Swedish Sample and Comparative Reactions on the US and Finnish Markets[END_REF].

Although Sweden implemented the EC's 2003 directive in 2005, the Stockholm Stock Exchange has stricter rules on the implementation of repurchase programs and their disclosure. The board of directors must announce when they have decided to initiate a share repurchase program and the initiation announcements by the Swedish companies are always followed by actual repurchases. And according to Swedish law, companies may not engage in trading in their own shares during the 30 days prior to the publishing of interim reports and companies are required to disclose their repurchase transactions on a daily basis [START_REF] Råsbrant | The price impact of open market share repurchases[END_REF].

Spain

Spanish public companies can repurchase up to 10% of their shares and hold them as treasury shares. Companies are free to reissue these treasury shares in the market or to cancel them through a capital reduction (Gonzales and Gonzales, 2004). When the number of shares repurchased is over the limit of 10%, the companies are obliged to choose between one of these two options Otherwise the acquired shares must be disposed or redeemed within three years after acquisition. The companies must create a reserve for the same amount as the repurchase of the securities. Thus, the company's equity is not reduced below the aggregate of the share capital and the non-distributable reserves after any repurchase [START_REF] Hoedl | Spain Treasury Shares Guide[END_REF].

Italy

The legislation on share repurchases in Italy was also put in order in the late 1990s with the changes in Italian Civil Code. With minor changes, it was streamlined with the EU directory in 2004. The law allows companies to launch repurchase programs only if they purchase fully paid shares and they have sources (profits and/or reserves) available as stated by the last approved balance sheet. They cannot get loans or give guarantees for the purchase of their own shares except for dedicated authorization provided by the extraordinary shareholders' meeting [START_REF] Sorge | Italy Treasury Shares Guide[END_REF]. The companies can sell the shares that were previously bought back as long as the selling of treasury shares has been authorized by shareholders. Therefore, Italian companies have the possibility to purchase and sell back their shares in the open market without any other formal procedure [START_REF] Cesari | Stock repurchases and treasury share sales: Do they stabilize price and enhance liquidity?[END_REF].

The analysis on the regulatory background shows that there is a variety between European countries in the implementation of repurchase programs adopted with shareholder approval even though many EU countries implemented EC recommendations and directives into their corporate law throughout the 2000s. In many countries, the distribution of cash through share repurchase is restricted to the available resources in the form of 'distributable profits' which establish a direct link between profits and corporate distributions in the form of share repurchases that may or may not provide incentives for companies to distribute cash to shareholders depending on the company, industry or country level dynamics of economic and financial relations among different stakeholders.

Mainstream literature on share repurchases in Europe

The literature on share repurchases in Europe is highly limited and most of the studies are reapplications of the work on share repurchases in the US which is mostly done by mainstream financial economists. Research questions of these empirical studies mainly focus on the determinants of share repurchases and their results in terms of stock-market valuation. Most of this literature has adopted the perspective and tools of agency theory, and they mainly analyze the patterns of sharerepurchase activity across Europe or in specific European countries. Several hypotheses tested before for the US companies are reapplied with continent or country-level data and they find evidence to support the hypotheses of liquidity (De Cesari, et.al, 2011) or the cash-flow hypothesis that companies use repurchases mainly to distribute cash flows in order to reduce agency conflicts [START_REF] Lee | Cash holdings and share repurchases: International evidence[END_REF][START_REF] Benhamouda | A research note on the determinants of UK corporate share repurchase decisions[END_REF]Bessler, et.al, 2014). Another group of studies also analyzes the stock market reactions to share repurchases in specific countries [START_REF] Andriosopoulos | The market valuation of share repurchases in Europe[END_REF]Bessler et.al, 2014;[START_REF] Crawford | Is the market underreacting or overreacting to open market share repurchases? A UK perspective[END_REF][START_REF] Råsbrant | The price impact of open market share repurchases[END_REF].

Apart from these papers, only a very small number of studies discuss other aspects of share repurchases in Europe. [START_REF] Dereeper | Rachats d'actions versus dividendes: effet de substitution sur le marché boursier français?[END_REF] discuss the relation between dividends and share repurchases, and they find evidence that these two are complementary in the case of France with a sample of 600 companies quoted on the Paris stock market between 1998 and 2001, contrary to the common belief of substitution effect between dividends and stock buybacks. [START_REF] Von Eije | Dividends and share repurchases in the European Union[END_REF] study the same relation at the EU level for a longer period between 1989 and 2005 and find a similarity with the US that the number of companies paying dividends is decreasing while their total dividend payments are increasing that complements the surge in share repurchases, especially after 2000. They also examine the impact of privatization on payout policies of divested companies, and find that these companies account one quarter of the EU dividends and share repurchases while they represent less than 2% of the number of quoted companies.

Finally, [START_REF] Ginglinger | Share repurchase regulations: Do firms play by the rules?[END_REF] examine the compliance of French companies with share repurchase regulations and document illegal repurchases before earning announcements, with very few companies fully complying with regulations. In the most well-known case, right after the September 11 attacks, Vivendi bought back its shares worth around $1.2 billion illegally. Later, its CEO and some other executives were found guilty, and were given fines and suspended sentences.

Data analysis

This part discusses the empirical data of corporate financial behavior among largest European companies. We analyze the companies of the S&P Europe 350 index in order to directly compare them with S&P 500 US companies, another index of the same provider. The index covers around 70% of Europe's market capitalization, and the companies constituting the index are among the largest European companies. As of 2015, these companies employ more than 22 million people around the world. The dataset is comprised of selected financial data of these 350 companies between 2000 and 2015, depending on their IPO years. Table 1 provides the information on the number of companies in the analysis from the represented countries in the Index. Source: Capital IQ and company web sites

The historical data of 298 companies since 2000 allow us to see the trend in major sources and uses of funds across these companies during the period. The first figure below show the total amounts of selected financials of 298 companies during the period in eurozone inflation adjusted values. The second figure provides the growth of these financials as well as total debt, total revenue and employment when 2000 is taken as the base year. In the second figure, the negative growth of net income and capital expenditures is especially visible. Very moderate growth of total revenues and employment is far outstripped by the increase in cash levels, total debt and total dividends of the same companies. Big fluctuations of share repurchases before and after the global recession were stabilized with a moderate growth at the end of the period compared to 2000. Figure 4 shows the average levels of corporate payouts and their ratios for the same group of European companies. From 2000 through 2015 these 298 companies expended €945 billion on stock repurchases, an average of €3.17 billion per company, and distributed a total of €2.88 trillion in cash dividends, an average of €9.66 billion per company. Combined, all the 348 companies in the S&P 350-Europe Index in January 2016 repurchased €64 billion of their own stock and distributed €284 billion in dividends in 2015, representing 110% percent of their net income. The table below shows year-to-year changes in net income, repurchases and dividends of these 298 companies for the same period to show whether the changes in the payout ratios are driven by changes in dividends and share repurchases (numerator) or by the changes in net income (denominator). The percentage changes indicate that the net income and payouts are equally important to determine the sign of year-to-year change in payout ratios. The underlined percentage changes in the net income, share repurchases and dividends show a decisive impact on the change in the total payout ratio in that year compared to the previous year. More than two thirds of the period, net income had either a positive or negative impact on the payout ratio providing its opposite sign of change. In around half of the period, it is the increase or decrease in payouts that define the sign of change of the payout ratio. Beside stock price appreciation to increase capital gains, two main forms of maximizing shareholder value are the distributions in the form of dividends and share repurchases. In the last 20 years, especially in the United States, share repurchases became 'systemic and massive' [START_REF] Lazonick | Profits Without Prosperity[END_REF] and together with dividends they reached more than 90% of net income among large US corporations between 2000 and 2015. In Europe, they were also intensified after regulatory changes in late 1990s and early 2000s facilitating the share repurchase activity of large European corporations. Nevertheless, Figure 5.1 shows that the extent of stock buybacks in Europe is still limited compared to the US. Repurchase activity in Europe didn't recover after the peak years of global recession as it has happened in the US. The main form of shareholder value distribution in Europe is common and preferred dividend payments as it is shown in Figure 5.2. Shown in Figure 5.3, large European companies distribute as much as US companies on average when share repurchases and dividends are added together. The widening gap since 2014 can be explained by record high share repurchases by large US companies in the last two years of the period and the depreciation of the Euro against US dollar during the same period.

The last figure (5.4) shows the comparison of total payout as a proportion of net income between the US and Europe. For the first time during the period, in 2015 annual total payout exceeded net income in a non-recession year on both sides of the Atlantic. This shows the insistence to the shareholder value maximization of US and European corporations despite all the criticism they have faced since the beginning of the global recession. In his research, Lazonick ( 2014) documented an increase in share repurchases of S&P500 companies when the S&P500 index is also on the rise during the last two decades. Although the US corporate executives claim that they do share repurchases only when the stock prices of their companies are undervalued, the data show the opposite. The European data is not different. Figure 6 The following table shows the country distribution of corporate payouts of the dataset during the same period. The averages per company and per year for each company show that each company spent on average around €200 million on stock repurchases and €600 million on dividends each year since 2000. In total, these companies on average spent around 77% of their net income on share repurchases and dividends during the period. The distributions of companies from Switzerland, UK, France, Finland and Italy exceeded the Europe average. In Italy, the ratio was greater than 100% and in the UK, it became very close to the total net income of the companies during the period. While the distribution through share repurchases accounts for only around one fourth of the total payouts on average, in countries like Switzerland, Netherlands, Denmark and Luxembourg, share repurchases have higher proportions compared to dividends. These are the "repurchase-intensive" countries with above average share repurchase to dividend ratios.

In countries like Germany, Netherlands, Finland and Spain, there is a very strong concentration of share repurchases that are performed by a very small number of companies. In Germany, Deutsche Bank, Siemens and E.ON, the top three repurchasers, constitute around 50 percent of the total share repurchases performed by 33 companies of the country in the dataset. In the Netherlands, the share of top three (Royal Dutch Shell, Philips and KPN) in total repurchases of the country's 16 companies in the dataset is 53 percent. This ratio for Finland and Spain is 94 and 76 percent respectively. Share repurchases are concentrated in a smaller group of largest European companies.

Source: CapitalIQ and company annual reports

The next table shows the distribution of payouts across different industry groups. In a handful of industries, the total payout ratios are very close to or exceed 100 percent. Despite heavy losses they incur in crisis years, companies in sectors like utilities, telecommunication, technology equipment and media kept spending large amounts in share repurchases and dividends resulted in very high payout ratios for the whole period. And despite very high amounts of average share repurchases and dividends, in sectors like pharmaceuticals, energy and foods & beverages, total payout ratios are around the total average due to very high profitability in these sectors.

Source: CapitalIQ and company annual reports

The last table shows the top 30 repurchaser companies in Europe during the period. Similar to the US, oil, ICT, pharmaceutical and financial companies are major repurchasers. A large number of these companies have very high total payout ratios.

Even though BP stopped repurchasing its own shares and reduced dividend amounts for a period after 2009, it was the biggest repurchaser in Europe during the 16-year period. In 2010, BP caused the largest marine oil spill in history, and the company agreed to pay $20 billion to cover environmental damage and other claims by the Mexican Gulf states and local governments. The expected court decision of a $20 billion penalty didn't stop the company from relaunching share repurchases in 2013 and increasing its dividend payments even though it stopped repurchases in 2015 due to a massive loss because of decreasing oil prices and negative net income.

BP is followed by a group of mostly British and Swiss companies in these four major repurchasing industries. Another interesting case is Nokia. The company couldn't compete in mobile devices segments and divested its mobile devices business in 2014 after heavy losses in the previous years.

During the period between 2003 and 2008, when many other companies were getting prepared for the technological breakthroughs in mobile devices, the company spent €18.5 billion on share repurchases and distributed €9.5 billion as dividends. In the last two years of the period until its merger with Alcatel, the company restarted distributing payouts in the form share repurchases and dividends and spent €0.6 and €1.9 billion on buybacks and dividends respectively. And in the period after the merger, the company didn't stop its payout activity and spent another €1.1 billion on these two forms of payouts in 2016 despite its -€766 million negative income for that year.

Pharmaceutical companies are among the top repurchasers. Although there are only 13 pharmaceutical and biotechnology companies, representing only 4.4 percent of the S&P350 sample, in the top 30, there are five pharmaceutical companies with very high share repurchase and dividend figures and three of them are among the top 10. These companies devote between 84 and 96 percent of their net incomes in payouts while they continuously argue individually or through their industry associations like PhRMA that they need high prices to fund their R&D expenditures.

Conclusion

This study is a preliminary effort to understand the change in the dynamics of value distribution at corporate level in Europe. Preliminary results of the descriptive analysis of value extraction among largest European companies show that the trend of increasing payouts, decreasing investment and mediocre growth of employment despite the continuing consolidation of industries through merger and acquisition, which continue to shape the European landscape of large corporations.

The economic crisis that continues to put strain on European communities, pressure on working conditions and increase insecurity across the continent, has had very little impact on the value extraction orientation of big corporations that is largely shaped by the maximization of shareholder value ideology. Despite stagnant growth or European economies, corporations continued to choose to increase payouts and reduce investments throughout the period analyzed.

Given the ongoing rise in inequality and the loss of employment opportunities across the continent, the dead end of increasing value extraction in Europe will only aggravate the vulnerability of the continent's economy and will result in a structural impotency to solve ever the growing economic and social problems of communities.

Further research on the shift in corporate governance practices including the changes in ownership structures, executives' understanding of the purpose of business enterprise and their disconnection from the idea of a social and equitable European economy will help to unveil the root causes of rising shareholder value distribution and put the findings of this study in its place. The issuer's purchases on that day do not exceed 25% of the average daily trading volume of its shares, except for a purchase of a "block" of shares Repurchase Timing The issuer does not affect any purchase of its shares during the final 30 minutes (10 minutes for 2 actively-traded shares) before the close of the session in the principal market for the issuer's common stock and in the market where the purchase is effected Repurchase Price

The issuer does not bid for or purchase its shares at a price that is higher than the highest independent bid or last independent transaction price, whichever is higher, quoted on the consolidated system Disclosure Period

Quarterly disclosure of all issuer repurchases of shares or other units of any class of the issuer's equity securities that are registered by the issuer Disclosure Content Issuers are required to report the total number of shares (or units) purchased (reported on a monthly basis), the average price paid per share, the total number of shares (or units) purchased as part of a publicly announced repurchase plan or program and the maximum number (or approximate dollar value) of shares (or units) that may yet be purchased under the plans or programs Disclosure Authority Securities and Exchange Commission (SEC)

France

Repurchase Period No later than 15 days before results announcements or if in possession of nonpublic information Repurchase Volume 25% of the average daily volume traded in the month preceding the month of public disclosure of that program and fixed on that basis for the authorized period of the program Repurchase Timing No purchase may constitute the opening or closing transaction of the current trading day Repurchase Price

The purchase price is lower than the higher of the price of the last independent trade and the highest current independent bid on the trading venues where the purchase is carried out Disclosure Period Within 7 days after the repurchase day and disclose monthly to the public Disclosure Content -Disclosure Authority Commission des opérations de bourse (COB) Germany Repurchase Period -Repurchase Volume -Repurchase Timing -Repurchase Price -Disclosure Period Monthly Disclosure Content The management board is required to inform the shareholders during the next shareholders' meeting of the purpose of the acquisition, the number of shares acquired, the amount of the share capital that they represent, the proportion of the share capital that they represent, and the purchase price of the shares Disclosure Authority Bundesaufsichtsamt für den Wertpapierhandel (BAW)

Sweden

Repurchase Period Firms may not engage in trading in their own shares during the 30 days prior to the publishing of interim reports Repurchase Volume The company may not purchase more than 25% of the average daily volume traded in the month preceding the month of the public disclosure of the repurchase program Repurchase Timing No repurchase can take place in the last 30 minutes of the trading day Repurchase Price

The company may not purchase shares at a price higher than the higher of the price of the last independent trade and the highest current independent bid on the trading venues where the purchase is carried out Disclosure Period

All trades, with information on the number of shares repurchased and average price paid, must be reported to the SSE Disclosure Content -Disclosure Authority Stockholm Stock Exchange (SSE) Switzerland Repurchase Period 10 days before earnings announcements or the release of any price-sensitive information. Repurchase Volume Issuer must not, on the regular trading line, repurchase more than 25% of the shares' average daily trading volume (based on the daily volumes of the last 30 trading days on that trading line) Repurchase Timing The issuer must not place repurchase orders during the opening and closing auctions, nor during the auction performed after a "stop trading" Repurchase Price

The premium paid on a second trading line should not exceed 5% of the price prevailing in the stock market at the same time Disclosure Period

On the first trading day after the end of the offer period, the issuer must report the total number of shares repurchased in each category and disclose them every 10 trading days Disclosure Content -Disclosure Authority The Swiss Takeover Board (TOB)

Spain

Repurchase Period -Repurchase Volume In an amount, up to 25% of the average daily trading volume in its stocks Repurchase Timing -Repurchase Price Price not higher (lower, in case of sales) than the highest (lowest, in case of sales) independent published bid or last independent transaction price Disclosure Period

Companies have to notify the Stock Exchange of all repurchases that represent at least 1% of the firm common stock before seven days following the repurchase Disclosure Content -Disclosure Authority Madrid Stock Exchange United Kingdom Repurchase Period Companies are not allowed to buy back shares during periods when officers and directors are not allowed to trade in their company's shares. In practice, this means that share repurchases are not allowed in the 2-month period preceding the publication of annual earnings or semiannual earnings and in the 1 month before the publication of quarterly results. Repurchase Volume -Repurchase Timing -Repurchase Price Not more than 5% above the average of the market value of those shares for the 10 business days before the repurchase is made Disclosure Period

According to UK Listing Rules, once repurchases are made, these too must be reported to the UKLA as soon as possible or no later than 7:30 AM on the following business day. Disclosure Content The report must include the date of purchase, the number of equity shares purchased, and the highest and lowest purchase prices in a day. Disclosure Authority Financial Services Authority

Italy

Repurchase Period -Repurchase Volume The daily volumes do not exceed 25% of the average daily trading volume registered on the six months preceding each relevant trad Repurchase Timing -Repurchase Price

The purchase price should not be higher than the last price of the day before Disclosure Period Monthly Disclosure Content -Disclosure Authority Commissione Nazionale per le Società e la Borsa (Consob)

Figure 1 :Figure 2 :

 12 Figure 1: Selected financials of 298 S&P Europe 350 companies, 2000-2015, Eurozone inflation adjusted euro values (2015 = 100)

Figure 3 :

 3 Figure 3: Proportional values of selected uses of funds of 298 S&P Europe 350 companies, 2000-2015, Eurozone inflation adjusted euro values (2015 = 100)

Figure 4 :

 4 Figure 4: Payout ratios and average values of dividend payments and stock repurchases of 298 S&P Europe 350 companies, 2000-2015, in MM€

Figure 5 . 1 :Figure 5 . 2 :Figure 5 . 3 :Figure 5 . 4 :

 51525354 Figure 5.1: Average share repurchases of 419 US S&P500 and 298 S&P Europe 350 companies, 2000-2015, in MM$

  below shows the average dividend and share repurchase expenditures for the 298 companies in the S&P Europe 350 index in relation to the movement of the index. Both dividends and share repurchases follow the same trend with the index and their averages have been increasing during periods of high stock prices.

Figure 6 :

 6 Figure 6: S&P Europe 350 annual average index value and average distributions per company, 2000-2015, in MM€

Table 1 :

 1 S&P Europe 350 constituents as of January 2016

		Number of firms in	Number of
	Country	the S&P Europe 350	firms with IPOs
		as of January 2016	before 2000
	Netherlands	19	16
	Switzerland	28	26
	Spain	20	12
	United Kingdom	99	88
	France	48	41
	Germany	38	33
	Finland	9	9
	Denmark	11	9
	Belgium	10	9
	Luxembourg	4	2
	Norway	6	4
	Sweden	24	23
	Italy	19	16
	Austria	3	3
	Ireland	8	6
	Portugal	2	1
	Total	348	298

Table 2 :

 2 Year-to-year changes in net income and corporate payouts in percentages

		Net Income	Share	Dividends	(TD+RP)/NI
			Repurchases
	2001	-58,9	43,2	18,2	203,1
	2002	-58,4	-17,0	-7,8	114,9
	2003	300,9	-28,5	-6,0	-78,1
	2004	46,0	89,0	16,4	-9,1
	2005	34,2	35,4	25,3	-4,2
	2006	21,5	14,2	27,2	1,1
	2007	4,5	48,5	2,4	11,8
	2008	-51,9	-40,5	8,1	84,4
	2009	13,2	-79,7	-26,2	-47,5
	2010	60,7	125,7	7,7	-26,3
	2011	-11,3	68,0	15,4	40,4
	2012	-12,5	-41,7	-1,2	2,1
	2013	0,7	26,3	12,5	13,8
	2014	8,9	20,8	1,6	-3,7
	2015	-17,1	6,7	9,8	31,7

Table 3 :

 3 Per country average share repurchases and dividends and total share repurchases and dividends as a proportion of net income of 298 S&PEurope 350 companies, 2000Europe 350 companies, -2015

	Country	# of	Average	Average	RP/NI TD/NI (TD+RP)	RP/TD
		firms	repurchase per	dividend per			/NI	(repurchase
			company	company				intensity)
			2000-2015 total	2000-2015 total
			€MM	€MM
	Switzerland	26	6630	10632	0,31	0,50	0,81	0,62
	Netherlands	16	6487	13647	0,22	0,46	0,68	0,48
	Spain	12	3396	13518	0,13	0,50	0,63	0,25
	United Kingdom	88	3279	9680	0,24	0,71	0,95	0,34
	France	41	3242	10682	0,18	0,61	0,79	0,30
	Germany	33	2694	10507	0,12	0,46	0,58	0,26
	Denmark	9	2569	4539	0,25	0,44	0,68	0,57
	Finland	9	2559	6913	0,24	0,64	0,88	0,37
	Belgium	9	1673	7836	0,12	0,58	0,70	0,21
	Luxembourg	2	1548	3068	0,25	0,50	0,76	0,50
	Norway	4	1247	6306	0,09	0,46	0,55	0,20
	Sweden	23	1129	6148	0,10	0,52	0,62	0,18
	Italy	16	1003	13051	0,07	0,94	1,01	0,08
	Austria	3	770	3327	0,10	0,42	0,52	0,23
	Ireland	6	666	2065	0,12	0,36	0,48	0,32
	Portugal	1	159	7638	0,01	0,57	0,58	0,02
	Total	298	3171	9660	0.19	0.58	0.77	0.33

Table 4 :

 4 Per industry average share repurchases and dividends and total share repurchases and dividends as a proportion of net income of 298 S&PEurope 350 companies, 2000Europe 350 companies, -2015

			Average	Average	Average	Average
			repurchase	repurchase	dividend	dividend
	GICS Industry Group	# of firms	per company	per company	per company	per company	RP/NI TD/NI	(TD+RP) /NI
			2000-2015	per year	2000-2015	per year
			€MM	€MM	€MM	€MM
	Automobiles & Components	12	1403	88	6688	418	0,06 0,28	0,34
	Consumer Durables & Apparel	11	995	62	4312	269	0,09 0,39	0,48
	Consumer Services	6	1707	107	5472	342	0,21 0,69	0,90
	Media	12	2162	135	4718	295	0,80 1,74	2,54
	Retailing	4	2845	178	7450	466	0,24 0,62	0,85
	Food & Staples Retailing	9	2062	129	5325	333	0,22 0,57	0,80
	Food, Beverage & Tobacco	15	5524	345	12785	799	0,23 0,53	0,76
	Household & Personal Products	6	4003	250	11824	739	0,16 0,49	0,65
	Energy	13	9336	584	26881	1680	0,17 0,49	0,66
	Banks	27	2457	154	15712	982	0,09 0,57	0,65
	Diversified Financials	12	5972	373	6135	383	0,43 0,44	0,86
	Insurance	16	2494	156	11597	725	0,11 0,52	0,63
	Real Estate	6	416	26	3903	244	0,06 0,53	0,58
	Health Care Equipment & Services	5	627	39	2457	154	0,10 0,40	0,51
	Pharmaceuticals, Biotech & Life Sciences	13	9755	610	19264	1204	0,27 0,53	0,80
	Capital Goods	38	2087	130	4638	290	0,23 0,51	0,74
	Commercial & Professional Services	12	1031	64	2445	153	0,27 0,64	0,91
	Transportation	12	968	60	4006	250	0,11 0,44	0,54
	Semiconductors & Semicon. Equipment	4	1329	83	1395	87	0,37 0,39	0,75
	Software & Services	4	1532	96	3440	215	0,15 0,33	0,48
	Technology Hardware & Equipment	4	4868	304	8392	525	0,60 1,03	1,63
	Materials	28	1970	123	5205	325	0,19 0,50	0,69
	Telecommunication Services	13	5994	375	24398	1525	0,57 2,30	2,87
	Utilities	16	2827	177	14543	909	0,16 0,81	0,97
	TOTAL	298	3171	198	9660	604	0.19 0.58	0.77

Table 5 :

 5 Top 30 share repurchasing companies in Europe, 2000-2015

					Total Share	Total
	Rank Company	Country	GICS Industry Group	Repurchases 2000-2015	Dividends 2000-2015	RP/NI TD/NI	(TD+RP) /NI
					€MM	€MM
	1 BP	UK	Energy	47046	80416	0,29	0,49	0,78
	2 Nestle	Switzerland	Food, Beverage and Tobacco	40779	52663	0,37	0,48	0,85
	3 Novartis	Switzerland	Pharmaceuticals, Biotech. & Life Sci.	32684	45721	0,35	0,49	0,84
	4 GlaxoSmithKline	UK	Pharmaceuticals, Biotech. & Life Sci.	32322	62426	0,33	0,63	0,96
	5 Royal Dutch Shell Netherlands Energy	29875	108302	0,13	0,47	0,60
	6 UBS	Switzerland	Diversified Financials	29812	18727	0,89	0,56	1,45
	7 Total	France	Energy	28484	64851	0,20	0,45	0,65
	8 Vodafone Group	UK	Telecommunication Services	27624	86726	n/a	n/a	n/a*
	9 AstraZeneca	UK	Pharmaceuticals, Biotech. & Life Sci.	22740	31644	0,38	0,53	0,91
	10 Deutsche Bank	Germany	Diversified Financials	19455	15263	0,53	0,41	0,94
	11 Nokia	Finland	Technology Hardware & Equip.	19370	20642	0,53	0,57	1,10
	12 Telefonica	Spain	Telecommunication Services	15328	47450	0,24	0,74	0,98
	13 Credit Suisse Group Switzerland	Diversified Financials	15316	14749	0,56	0,54	1,10
	14 BNP Paribas	France	Banks	15135	29040	0,19	0,37	0,56
	15 Koninklijke Philips Netherlands Capital Goods	14948	6904	0,80	0,37	1,17
	16 Novo Nordisk	Denmark	Pharmaceuticals, Biotech. & Life Sci.	14268	9397	0,53	0,35	0,87
	17 Siemens	Germany	Capital Goods	13639	25376	0,21	0,40	0,61
	18 Sanofi	France	Pharmaceuticals, Biotech. & Life Sci.	12813	32913	0,25	0,63	0,88
	19 Diageo	UK	Food, Beverage & Tobacco	12200	19855	0,34	0,56	0,90
	20 Barclays	UK	Banks	11743	32982	0,23	0,64	0,86
	21 E.ON	Germany	Utilities	11547	30190	0,30	0,78	1,08
	22 L'Oréal	France	Household & Personal Products	11306	13541	0,32	0,38	0,70
	23	British American Tobacco	UK	Food, Beverage & Tobacco	11049	32126	0,24	0,69	0,92
	24 Rio Tinto	UK	Materials	10903	24479	0,22	0,50	0,72
	25 Koninklijke KPN	Netherlands	Telecommunication Services	10211	9854	3,09	2,98	6,07
	26 Iberdrola	Spain	Utilities	10047	10337	0,31	0,32	0,64
	27 BASF	Germany	Materials	9768	24572	0,20	0,50	0,69
	28 Ing Groep	Netherlands Banks	9673	20832	0,14	0,30	0,45
	29 Koninklijke Ahold Netherlands	Food & Staples Retailing	8685	3391	0,97	0,38	1,35
	30 Daimler	Germany	Automobiles & Components	8237	27693	0,14	0,48	0,63
	*Vodafone's payout ratios are not calculated due to negative total net income value for the period.
	Source: CapitalIQ and company annual reports

Table A . 3 :

 A3 Repurchase activity restrictions and disclosure rules

	US	Repurchase Period Anytime during the program
		Repurchase Volume

† For a detailed discussion of the history of share repurchases in the US, see[START_REF] Lazonick | Financialization of the U.S. corporationwhat has been lost and how it can be regained[END_REF]Lazonick, , 2015c

This project has been part of the work done for the European Union Horizon 2020 Research and Innovation action under grant agreement N° 649186 (ISIGrowth: Innovation-Fuelled Sustainable and Inclusive Growth) * The Academic-Industry Research Network

Annex

Share Repurchase Regulation in the US and Major European Economies


Ricardo Pérez-Marco

Cyril Grunspan

Ricardo P Érez-Marco

Proof of Reputation

Keywords: 2010 Mathematics Subject Classification. 68M01, 91-00 Bitcoin, blockchain, proof-of-work, selfish mining. 1

We present the new mining protocol Proof-of-Reputation (PoR) for decentralized Proof-of-Work (PoW) blockchains, in particular for Bitcoin. PoR combines the classical PoW with the new ingredient of cryptographic reputation. The same level of security compared to pure PoW can be achieved with a significant energy consumption reduction (of the order of 30%) for the same security level. The proper implementation of a decentralized reputation protocol is suitable with an extra layer of mining security: Certified Mining.

Introduction and background

1.1. Proof-of-Work and decentralization. The aim of the present article is to enhance the classical Proof-of-Work (PoW) at the base of the decentralized consensus algorithm which runs Bitcoin protocol invented by Satoshi Nakamoto [START_REF] Nakamoto | Bitcoin: a peer-to-peer electronic cash system[END_REF]. Although we have in mind the Bitcoin protocol, our analysis is not restricted to it and applies to blockchains based on PoW.

One of the major criticism of Bitcoin is its important energy use. The security of the protocol relies on this energy consumption. Some fundamental reasons, based on the Second Law of Thermodynamics, indicate that there is no viable satisfactory shortcut without energy consumption in order to achieve the same level of security and full decentralization. Other propositions as Proof-of-Stake (PoS) lack of the main security features as Bitcoin, for example an attacker can rebuild the full blockchain, therefore monitorization by a central entity is constantly necessary. So far, no blockchain with PoS does function without supervision as Bitcoin does.

A criterion for a blockchain to be fully decentralized is that no entity or individual is able to stop it. Observe that this entails a level of cybersecurity unseen elsewhere, for example, no hacking can stop it. Also this implies that the network is permisionless and no entity is able to censor transactions. For a PoW based blockchain this is true as long as no one is in control of more than 50% of the available computing power running the PoW algorithm, which, assuming homogeneous hardware efficiency is equivalent to more than 50% of the energy in use.

Decentralization and reputation. The energy consumption defends against

Sybil attacks of the network, that is, it prevents the network being flooded by dishonest validators (miners). In an open protocol, decentralization requires that anyone is free to join the network. Censorship is incompatible with decentralization. This is the reason that the so-called "private blockchains", where participation is approved by a higher entity, cannot be decentralized blockchains. The simplest solution in order to avoid a Sybil attack would be to weight the voting rights of any participant (node) by some system of reputation. Unfortunately, so far, no decentralized reputation system has been invented. Reputation is a subtle notion difficult to implement algorithmically. In Nakamoto's PoW proposal, the voting weight of each participant is directly proportional to the work provided. This is possible thanks to the pseudo-random properties of the hash function used in Bitcoin's PoW algorithm. It has the advantage that we don't need any "memory" or knowledge of past behavior of the participant. It has the drawback that no reputation of past well behavior is incorporated. This presents also a security weakness since anyone without any prior credentials that can achieve more than 50% of the energy dedicated to mining, and can take control of the whole network. In some sense, Nakamoto's PoW replaces reputation by actual verifiable work being done in the present.

As was observed in bitcointalk forum, it is interesting to point out that in the early Bitcoin code, Satoshi was trying to implement a reputation system ( [START_REF] Bitcointalk Forum | Weird note by Satoshi on unreleased Bitcoin 2008 version[END_REF]) based on mining as his comment suggests "Add atoms to user reviews for coins created". More recently, in the context of Proof of Stake, there have been propositions of reputation system as RepuCoin ( [START_REF] Yu | Repucoin: Your reputation is your power[END_REF]).

Thinking along these lines, we explore how to go one step further. We want to encode reputation mathematically with a secure cryptographic procedure. The essential nature of reputation is based on proper past behavior. The most common way of acquiring reputation is by past verifiable work. Other ways to acquire reputation is also by endorsement by reputed individuals, but this "second level reputation" is easier to manipulate and we will discard it for now.

The classical PoW is modulated by a parameter, the difficulty, which is adjusted so that the validated blocks flow at a constant rate. The difficulty is the same for all miners. If we are able to assign some type reputation to miners, it is natural to require for those that are reputed a lower difficulty. This is how we can implement a reputation bonus. This type of reasoning is a standard procedure in everyday dealings. For example, we trust more a dealer that we already know and that has a verifiable past track. The security requirements for engaging in trading with him is lower that with an unknown dealer that may well be a scammer.

The novel idea at the root of the reputation system presented is to have a variable difficulty parameter for miners. In this way we can improve the protocol with a reputation ingredient: We assign a reputation bonus to miners that mined blocks in the past, that is, to anyone that has in the past contributed to the security of the network by providing energy and work. Because of his verifiable past track, we allow this miner, to validate blocks with a lower difficulty, hence with a lower use of energy.

The nature of reputation makes that this reputation bonus should decay with time. Common sense indicates a higher trust in a dealer with recent successful deals that someone else with the same successful deals but from many years ago. In the next section we propose a mathematical implementation of these natural ideas.

2. Proof-of-Reputation.

2.1. Reputation bonus sequence. We consider a positive sequence (λ n ) n≥0 with 0 < λ n < 1, (λ n ) decreasing, and summable with total sum Λ with [START_REF] Nakamoto | Bitcoin: a peer-to-peer electronic cash system[END_REF] 0

< Λ = n≥0 λ n < 1
The quantity Λ is the total reputation bonus of the network and can be adjusted from 0 to 1 interpolating between a pure PoW and a pure PoR protocols. The quantity λ n is the reputation bonus earned by validating the block at depth H -n where H is the current blockchain height.

More precisely, for a miner x, we define

λ n (x) = λ n if x mined block H -n 0 otherwise
The total bonus reputation of miner x is then

(2) Λ(x) = n≥0 λ n (x) .
Observe that the total reputation bonus of the network is

(3) Λ = x Λ(x)
We use the coinbase public payment address as the miner digital identity. In this way the bonus reputation of a miner can be computed from the data in the blockchain. If a miner wants to accumulate bonus reputation he should use always the same payment address. We can easily add the possibility of multiple payment addresses by requesting a proof of ownership of these other addresses by signing simultaneously with the other addresses for which the miner wants to earn reputation bonus. This opens the possibility of selling reputation bonus that we may not want. Also a simpler way of having a reputation market would be to issue a reputation token with each payment in the coinbase transaction, but this is not in the spirit of the proposal presented in this article because we want to prevent anyone with large ressources to launch an immediate 51% attack.

2.2. Taylored difficulty. The output of the Proof-of-Work is in the range of SHA256 which is a 256 binary number. The target value 0 ≤ D ≤ 2 256 -1 is the threshold under which the output is successful. The empiral pseudo-randomness property of SHA256, shows that the average number of iterations before finding a solution is d = 2 256 /D that we define as the difficulty. Thus, for a given hardware, the average energy needed for a validation is proportional to the difficulty d = 2 256 /D.

If miner x has a reputation bonus Λ(x) his new taylored difficulty will be

d(x) = d(1 -Λ(x))
and target value

D(x) = D 1 -Λ(x)
Thus, with a reputation bonus Λ(x) the miner saves a percentage Λ(x) of energy to ensure the same security. Assuming that all miners use their reputation bonus, we can achieve the same level of security saving a percentage Λ of the total energy. We can also argue that for the same energy consumption, we increase the security (measured in energy) by a factor (1 -Λ) -1 .

2.3.

Structure of the reputation bonus sequence. As explained before, it is natural to request that the reputation bonus decays over time, this is why we want the sequence (λ n ) to be decreasing. It is also natural to request decay uniform over time. This leads to the natural choice of

λ n = λ 0 e -χn
where χ > 0 is the decay constant. We can request that the reputation bonus is halved every year. For example, in the case of Bitcoin protocol this leads to a value χ = log 2 52560 ≈ 1.31877.10 -5

which leads to a decay of 0.19% per day of the bonus reputation.

Then we have

Λ = λ 0 1 -e -χ
If we set a target energy savings of 30%, that is Λ = 0.3, then for the previous example with Bitcoin we get λ 0 ≈ 3.956.10 -6

It also makes sense to implement a reputation bonus sequence (λ n ) that does not decay exponentially initially, but only after some period of time (like a year for example). Several other reasonable choices are possible.

3. Security analysis.

3.1. 51% attack. We consider a miner x owning a fraction 0 < q < 1 of the hashrate. In the long run he can expect to earn a reputation bonus of Λ = qΛ since he mines on average a proportion q of the blocks. If everybody else uses his reputation bonus, the apparent hashrate will still be q. Then the 51% can still only be performed when q > 1/2. But, in the most unfavorable situation where no one else uses its reputation bonus, his apparent hashrate is higher. We have Proposition 3.1. Assuming the previous conditions, the apparent hashrate of the only miner using his reputation bonus is h 1-Λ = h 1-qΛ where h is his hashrate.

Proof. Let T , resp. T, be the random variable of the time that it takes to miner using his reputation bonus, resp. the rest of the miners, to mine a block. Then we have

E[T ] = d(1 -Λ ) h = d h /(1 -qΛ) E[T] = d h
where h is the hashrate of the rest of the miners in the network. Now we prove: Proposition 3.2. Assuming the previous conditions, the miner only miner using his reputation bonus succeeds in a 51% attack when

q > q 0 = 1 2 - √ 4 + Λ 2 -2 2Λ
Proof. The condition to succeed a 51% attack exactly means that it is more likely that the attacker miner mines a block earlier than the rest of the network, i.e.

P[T < T] > 1/2

The random variables T and T follow exponential distributions (see for example [START_REF] Grunspan | Double spend races[END_REF]) with parameters α , resp α, α = 1

E[T ] = h d(1 -qΛ) α = 1 E[T] = h d
We have

P[T < T] = α α + α = h d(1-qΛ) h d + h d(1-qΛ) = h (1 -qΛ)h + h = h h+h 1 -qΛ h h+h = q 1 -qΛ(1 -q) Therefore, the condition P[T < T] > 1/2 becomes q > 1 2 (1 -Λq(1 -q))
which is equivalent to Λq 2 -(Λ + 2)q + 1 < 0 The discriminant is ∆ = 1 + Λ 2 and the quadratic polynomial has one root > 1 and another root 0 < q 0 < 1 given by the formula in the statement.

For a value of Λ = 0.3 this means that q > q 0 = 0.4627 . . .. This is not significantly lower than 50 %. The attacker must prepare the attack with time ahead in order to gain the 4% reputation bonus. We clearly achieve the same or betterlevel of security. From the view pont of the security of the network, in some sense, we trade pure hashrate for time and work previously performed.

Reputation attack.

In the Proof-of-Reputation protocol, we will have some miners that have acquired along their PoW history some reputation. The new miners are free to gain this reputation bonus through their work. As we know, most miners pool together in "pools" in order to mitigate the volatility of their income because a block validation is a rare event for a low hashrate. Thinking about the pool system in place, we can see a dangerous scenario in the PoR protocol: The pool with higher reputation will be more profitable and will attract all the miners. Therefore will quickly reach more than 50% hashrate. This can compromise the security of the network.

As we can see, what is really happening is that miners joining the pool take advantage of the reputation bonus previously earned by the pool in order to lower their mining difficulty. We need another key idea for a proper functioning of a reputation system: We should be able to certify that whoever benefits from any reputation bonus is the same virtual identity that has done the past work that provided the reputation bonus. In the present situation, there is a cryptographic solution to this problem: Certified Mining.

3.3. Certified mining. We describe Certified Mining for a PoW algorithm based on a hash function as the one for Bitcoin. We remind that Bitcoin's Pow consists in formatting a block, and hash (more precisely, double SHA256) its header which contains critical information about the block and the transactions, in particular it contains the Merkle root of the transactions in the body of the block. A variation of the nounce, the extra nounce, or the format of the body of the block, provides new output hashes and the goal is to get one hash below the difficulty threshold. In their regular operations, a mining pool formats the blocks and provide the headers to hash to the miners. They do format the block with a payment address of the coinbase transaction that they do control (this is where the block reward is paid). The solution to avoid the reputation usurpation is simple: Once the block is formatted as it is done classically, we require the header of the block to be signed with the secret key of the payment coinbase address. This signature is appended at the end to the block header. Each time the nonce is changed, a new signature is required. The bulk of the PoW is then the signatures more than the hashes, and this work can only be provided by the entity in control of the payment address. In some sense, the payment public address of the coinbase transaction is the id of the miner (he can also have several addresses that can be used to cumulate reputation bonuses and provide a proof of ownership).

Obviously, for security reasons, the pool cannot share the secret key of the payment address, and in general, only the owner of the payment address can perform the signature. Observe that the signature includes the nonce, extra nonce, etc and the main computational task is to sign the header (the double hash is much faster to do). Hence this modification of the PoW does not allow to subcontract the PoW taking advantage of a reputation bonus earned by someone else. This procedure seems to make impossible a pooling system, but this is not so. A pooling system is viable where each one contributes and gets a share weighted by its verifiable reputation.

3.4. Transition to a PoR system. It is natural to imagine how will be a transition to PoR. Obviously this requires a hardfork of the protocol that changes the mining algorithm to allow a taylored difficulty for different miners. The authors do not advocate for any hardfork of the Bitcoin protocol whose ideal state is converging to ossification as a payment protocol. If such a hardfork is implemented, it needs to be performed with extraordinary caution. The transition to PoR can indeed be realized gradually. For example, the value of Λ could be increased gradually during a large period of time (for example, 10 years) from 0 to its limit value (0.3 in our numerical example). For these conservative values, there is little risk for Bitcoin security.


Wacothon Coulibaly

Affi Sopi

James Titah

Mamadou Guy-Richard Koné

Affoué Estelle

Brigitte Yao

Camille Déliko Dago

Jean-Pierre Bazureau

Josh Daniel Mcloud

Benié Anoubilé

Karime

Christelle N'ta Ambeu

Nahossé Ziao

Anti-proliferative Activity Study on 5-Arylidene Rhodanine Derivatives Using Density Functional Theory (DFT

Keywords: 5-Arylidene Rhodanine, Anti-proliferative Activity, Quantitative Structure Activity Relationship, Density Functional Theory Method, Molecular Descriptors Coulibaly Wacothon Karime et al.: Anti-proliferative Activity Study on 5-Arylidene Rhodanine Derivatives

come   L'archive ouverte pluridisciplinaire

Introduction

Tumor refers to an increase in volume or size of a tissue in humans. It is can also been seen as the formation of massive body tissues caused by the disruption of cell growth; benign or malignant. A malignant tumor is called cancer. The treatment of benign tumor is by surgical removal of the tumor mass while the treatment of malignant tumor (cancer) is through chemotherapy. It is within this framework that medicinal, pharmaceutical or therapeutic chemistry, which is a scientific discipline at the interface of chemistry and pharmacy, are involved in the design and development of new drugs.

The biological activities of 2-thiazolidin-4-one derivatives, traditionally referred to as rhodanine have been studied for over 100 years; a lot of research is still ongoing on these compounds because of their numerous or interesting biological activities [START_REF] Lesyk | 1-4-thiazolidones: history, centenary, current situation and perspectives of modern organic and medicinal chemistry[END_REF][START_REF] Jain | Recent developments and biological activities of thiazolidinone derivatives[END_REF]. Rhodanine and its derivatives have been used as anti-convulsant, anti-bacterial, anti-viral, anti-diabetic, anti-tuberculosis, pesticides, fungicides, anti-inflammatory, anti-thyroid, anti-tumor drugs for many years [START_REF] Manjal | Synthetic and medicinal perspective of thiazolidinones: A review[END_REF][START_REF] Bulic | Rhodanine-based tau aggregation inhibitors in cell models of tauopathy[END_REF][START_REF] Alegaon | Synthesis, characterization and antimicrobial activity of azole-pyrazolidin-3-one derivatives[END_REF][6][START_REF] Benson | Additivity rules for the estimation of molecular properties. Thermodynamic properties[END_REF][START_REF] Kumar | A simple and effective mechanochemical route for the synthesis of 2-aryl benzothiazoles and substituted benzimidazoles M[END_REF][9][START_REF] Rao | Synthesis and biological evaluation of new epalrestat analogues as aldose reductase (ARI) inhibitors[END_REF][START_REF] Szafran | WO 0076988 A1[END_REF][START_REF] Bozdag-Dundar | [END_REF][13]. Numerous derivatives of rhodanine have been synthesized, characterized and tested for their biological activities or properties; these include 5-arylidene-2-thioxo-1,3-thiazolidinin-4-ones or 5-arylidene rhodanines. These molecules have been observed to inhibit protein kinases [14]. To improve the anti-tumor activity of 5-arylidene rhodanines first requires a mastery of its physicochemical properties and structure activity relationship so that new compounds may be synthesized or designed. In this study, we would use the Quantitative Structure Activity Relationship (QSAR), which is one of the best and most widely used methods for the design and development of new therapeutic agents to design 5-arylidene rhodanine and derivatives [START_REF] Chhabria | QSAR Study of a Series of Acyl Coenzyme A (CoA): Cholesterol Acyltransferase Inhibitors Using Genetic Function Approximation[END_REF][START_REF] Buha | Biological Evaluation and QSAR Study of a Series of Substituted Quinazolines as Antimicrobial Agents[END_REF][START_REF] Tropsha | Best Practices for QSAR Model Development, Validation, and Exploitation[END_REF]. Computational or density functional theory (DFT) methods are increasingly being used to design new drugs in medicinal and therapeutic chemistry as they reduce the excessive number of experiments, sometimes long and expensive [START_REF] Oprea | Chemoinformatics in Drug Discovery[END_REF][START_REF] Rekka | Chemistry and Molecular Aspects of Drug Design and Action[END_REF]. The main objective of this study is to conduct a descriptive and predictive study of the anti-tumor activity on thirteen (13) derivatives of 5-arylidene rhodanine.

Details of the 5-arylidene derivatives in this study may be observed in Table 1.

Methodology

Calculation Methodology

The thirteen 5-arylidene rhodanine molecules studied were divided into two groups for convenience in comparison; nine molecules were used for the test set and four molecules were used to validation the test set. The compounds were tested for their anti-proliferative activity to determine their IC 50 values (molecular concentration required to achieve 50% inhibition of the enzymatic activity). A molecule is considered inhibitory when it exceeds 50% inhibition compared to the control. The ability to inhibit the growth of cell lines in this work was evaluated from two [START_REF] Jain | Recent developments and biological activities of thiazolidinone derivatives[END_REF] We used the logarithm to base 10 to compare the activity (-log10 (IC 50 )) in order to obtain higher mathematical values for the effective interpretation of the results [START_REF] Diudea | QSPR/QSAR Studies for Molecular Descriptors[END_REF][START_REF] Esposito | [END_REF][START_REF] N'guessan | Quantitative Structure Anti-Cancer Activity Relationship (QSAR) of a Series of Ruthenium Complex Azopyridine by the Density Functional Theory (DFT) Method[END_REF][START_REF] Kablan | QSAR Studies of the Antifungal Activities of α -Diaminophosphonates Derived from Dapsone by DFT Method[END_REF]. Using IC 50 in µM, the anti-proliferative potential can be defined by the equation 1 below:

p CI50 = -log(p IC50 x 10 -6 ) = - * 10 (1)

DFT Level of Calculation

The geometries of the molecules were optimized at the DFT calculation level with the B3LYP functional [START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF][START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF][START_REF] Traoré | Qsar Approach to Estimating the Analgesic Activity of a Series of Tri-Substituted Pyrimidine Derivatives[END_REF][START_REF] N'dri | Combining of DFT and QSAR Results to Predict the Antibacterial Activity of a Series of derived from Dapsone as Inhibitors of Bacillus Subtilis and Pseudomonas Aeruginosa[END_REF] in the 6-31 G (d) base using the Gaussian 09 software [28]. This Hybrid functional gives better energies that agree with the ab initio methods of higher levels [START_REF] Kapp | H 2 XO and (CH 3 ) 2 XO Compounds (X= C, Si, Ge, Sn, Pb): Double bonds vs carbene-like structures can the metal compounds exist at all[END_REF][START_REF] Johnson | The performance of a family of density functional methods[END_REF]. The split-valence and double-dzeta base (6-31G (d)), were sufficiently extended and to account for the polarization functions. This is important for explaining the free doublets of the heteroatoms. The modeling was done using the multilinear regression method implemented in Excel spreadsheet [31] and XLSTAT [START_REF]XLSTAT Version[END_REF].

Molecular Descriptors Used

The success of any quantitative structure activity relationship (QSAR) model relies on the choice of molecular descriptors used. In this study, we used the descriptors from quantum chemistry to predict the anti-proliferative activity as well as the cytotoxic inhibition properties of 5-arylidene rhodanines. Out of the thirteen descriptors selected for 5-arylidene rhodanines, there of them were in good correlation with the anti-proliferative activity of the molecule to be used for model development. These descriptors were the lowest unoccupied molecular orbital energy (E Lumo ), the C-N distance d (C-N) and the C=O vibration frequency ѵ (C=O) .

The lowest unoccupied molecular orbital energy (E LUMO ) describes the ability of a molecule with an empty molecular orbital to accept electrons. Its value was obtained by a quantum chemistry calculation using the Gaussian 09 software [28].

The C-N distance d (C-N) was determined by the length of the bond between the carbon atom (C) and the nitrogen heteroatom (N) contained in the core of the rhodanine derivatives. This descriptor was obtained from the DFT-optimized geometries of rhodanine derivatives and was expressed in angstrom (A) (Figure 2).

The C=O vibration frequency ѵ (C=O) . This descriptor is obtained after the DFT-optimized structure of rhodanine derivatives (Figure 1).

Figure 1. Geometric descriptors of 5-arylidene rhodanines d(C-N) and v(C=O).

The interdependence of the descriptors was evaluated by bivariant linear correlation coefficients a ij between the pairs of the descriptor set. Here, two descriptors were said to be independent when a ij < 0.70 [START_REF] Vessereau | Méthodes statistiques en biologie et en agronomie[END_REF].

Development of Models and Their Validations

The different models were constructed using the multiple linear regression method (Multiple Linear Regression, MLR) implemented in the Excel 2013 spreadsheet [31]. The Regression tool in this spreadsheet performs a linear regression analysis using the least squares method to find a line from the observed values. The MLR method is a statistical technique that allows us to linearly connect a series of independent explanatory variables (descriptors) to the dependent variable , in order explicitly to explain the anti-proliferative activity, 50. This method was the most used for the development of predictive models. The goal was to get an equation of the form in equation 2 below:

= + + + + ⋯ (2)
Where the are the coefficients of the regression.

Correlation and prediction tests would be performed on our compounds for comparison once the model has been established and trusted. In order to validate the correlation method on the test data set, the statistical indicators; R 2 are the coefficients of determination, the standard deviation; S, the correlation coefficients of the cross-validation; Q 2 CV and Fischer; F were considered. The Excel software was used to calculate the statistic tests [31]. The statistical indicators (R 2 , S and F) relate to the adjustment of the calculated and experimental values. These values were used to describe the predictive ability within the limits of the model. This allows us to estimate the accuracy of the values calculated on the learning set [START_REF] Snedecor | Statistical Methods[END_REF][START_REF] Diudea | QSPR/QSAR Studies for Molecular Descriptors[END_REF]. The coefficient of determination R² gives an evaluation of the dispersion of the theoretical values around the experimental values (precision in measurement). The quality of the modeling was better when the points are close to the right of adjustment [START_REF] Esposito | [END_REF][START_REF] Ouattara | Contribution to The Molecular Lipophilicity Scale By Qspr Models Of Lipophilicity Prediction[END_REF][START_REF] Kpidi | Monitoring and Modeling of Chlorophyll-a Dynamics in a Eutrophic Lake: M'koa Lake (Jacqueville, Ivory Coast)[END_REF][START_REF] N'dri | Quantitative Structure antifungal Activity Relationship (QSAR) study of a series of Schiff bases derivatives from4-aminobenzenesulphonamide by DFT method[END_REF]. The adjustment of points to this line can be evaluated by the correlation coefficient equation below:

= 1 - ∑ !,#$% & !,'(#) * + ∑ !,#$% , !,#$% * + (3)
Where:

,-./ : The experimental value of the anti-proliferative activity & ,01-2 : The theoretical value of the activity and , ,-./ : The average value of the experimental values of the anti-proliferative activity The closer the value of R² to unity, the more the theoretical and experimental values are correlated

In addition, the variance; 3 is determined by the relation in equation 4:

3 = 4 = ∑ !,#$% !,'(#) * + 5 6 (4)
Where: k is the number of independent variables (descriptors) n is the number of molecules in the test or learning set, n-k-1 is the degree of freedom. The standard deviation; S (equation 5) is another statistical indicator used. This evaluated the reliability and accuracy of the model: The Fisher test; F was used to measure the level of the statistical significance of the model, that means, the quality of the choice of descriptors constituting the model.

4 = 7 ∑ !,#$% !,'(#) * +
F = ∑ !,'(#) !,#$% * + ∑ !,#$% !,'(#) * + * 5 6 6 (6)
The coefficient of determination of the cross validation; Q 2 CV , was used to evaluate the accuracy of the prediction on the test set and is calculated using equation 7.

9 :; = ∑ !,'(#) , !,#$% * + ∑ !,'(#) !,#$% * + ∑ !,'(#) , !,#$% * + (7)
To estimate the predictive power of the models, the method of external validation was used on the set of the four remaining molecules of the database. In this framework, the established QSAR models were used to determine the predicted inhibition potentials (pIC 50 ) of the four molecules. Validation of the models was performed by considering the cross-correlation coefficient of the test set Q 2 CV and the ratio between the predicted and experimental inhibit potentials noted; <.

< =

/=> ?@ %A#B!' /=> ?@ #$%éA!D#E'FG [START_REF] Kumar | A simple and effective mechanochemical route for the synthesis of 2-aryl benzothiazoles and substituted benzimidazoles M[END_REF] The predictive power of a model was considered good if 9 :; or < T approaches unity. According to the value of this statistical indicator, Eriksson and al. [START_REF] Eriksson | Methods for Reliability and Uncertainty Assessment and for Applicability Evaluations of Classification-and Regression-Based QSARs[END_REF], define the performance of a mathematical model. A model whose value of 9 :; > 0,5 was said to be satisfactory while the one whose value 9 :; > 0,9 was described as excellent. According to Eriksson et al., for a given test name a model will be efficient if the acceptance criterion -9 :; < 0,3.

Results and Discussion

Interdependence of Descriptors and Experimental Inhibitory Potentials

The values of the anti-proliferative potentials (MDA-MB231 and NCI-H727) and those of the various descriptors of the test set and the validation set are presented in Table 2.

Table 2. Quantum descriptor values and experimental potentials of lineages MDA-MB231 and NCI-H727.

ELumo (eV) ѵ(C=O) (cm -1 ) d(C-N) (Å) MDA-M B231

NCI-H72 It should be noted that the external validation of the models MDA-MB231 and NCI-H727 were performed respectively on rhodanine derivatives (AR-1, AR-6, AR-12, AR-13), and (AR-2, AR-6, AR-7, AR-12). In order to highlight the interdependence of the selected descriptors, the values of the bivariant linear correlation coefficients; a ij between the pairs of descriptors (E Lumo , ѵ (C=O) ), (E Lumo , d (C-N) ), (ѵ (C=O) ) and d (C-N) ), are less than 0.70 (a ij < 0.70) (Table 3). In addition, two descriptors are said to be interdependent when a ij < 0.70. This demonstrates the independence of the descriptors used to develop the models. From table 3, it can be seen that the linear correlation coefficients; a ij calculated from majority of the descriptors used were less than 0.7 (a ij < 0.7). This reflects the non-dependence of the descriptors used in developing the models.

Modeling of Anti-proliferative Activities

For the different anti-proliferative sources, the equations relating the different tumor lines with the descriptors are given in Table 4. The equations of the different models were obtained by using the descriptors ( N OPQR , d (C-N) , ѵ (C=O) ) determined from the DFT-optimized molecules or structures. A negative sign in a descriptor will mean that when the value of the descriptor is high, the biological activity will decrease and vice versa. On the other hand, a positive sign on the descriptor will indicate that when the value of the descriptor is high, the biological activity will increase and vice versa. For the tumor lines MDA-MB231 and NCI-H727 models, the signs of the different coefficients of In these models, 92.60 and 95.40% of the molecular descriptors (N OPQR , d (C-N) , ѵ (C=O) ) are taken into account with the root of the mean squared error of prediction ranging from 0.093 to 0.147. The significance of these models was determined by a coefficient of Fischer test; F ranging from 88.221 to 145.448. The adjusted coefficient of determination R 2 ajust of these models ranges from 0.882 to 0.927. In addition, the correlation coefficient of cross-validation; Q UV is between 0.926 and 0.954. These values are in complete agreement with literature values for excellent models [28]. In addition, the models are acceptable because they agree with the acceptance criteria of these authors:

Table 4. The most significant QSAR models for modeling anti-proliferative activities on the MDA-MB231 and NCI-H727 lines.

Tumor line Regression Equations

MDA-MB231

-Q UV = 0.000 < 0.3. Furthermore, the performance of these models is also reflected in the values of pIC 50 pred/pIC 50 exp report from literaure. The different equations permit us to obtain the theoretical activities of the molecules according to the tumor lines presented in Table 6.

From table 6 it can be seen that all the calculated ratios (pIC 50 pred/pIC 50 exp) tend to approach unity, indicating a good correlation between the experimental and predicted potentials of the molecules. Therefore, the different models are can be used to conveniently predict of the anti-proliferative activity of the rhodanine derivatives studied. From table 6 one can observe that all the calculated ratios (pIC 50 pred/pIC 50 exp) tend to approach unity, indicating a good correlation between the experimental and predicted potentials of the molecules. Therefore, the different models can be used to conveniently predict of the anti-proliferative activity of the rhodanine derivatives studied.

The different regression lines between the experimental and theoretical anti-proliferative activities of the test set (blue dots) and the validation set (red dots) for each tumor line are illustrated in Figures 2 and3 On the graphs obtained, we note a proximity or closeness of the points on the regression curve. This means that, there is a strong linear correlation between the predicted and experimental values of the anti-proliferative activity of the 13 different molecules of 5-arylidene rhodanines. These observations can also be confirmed by the different values of the coefficient of determination R 2 . On the other hand, the low values of the standard deviation; S ranging from 0.093 and 0.147 for the two models attest to the good similarity between the predicted and experimental values (Figure 4). These curves in figure 4 show a similar evolution of the data of these models for the prediction of the anti-proliferative activity of the 13 compounds of 5-arylidene rhodanines with minimal or insignificant discrepancies. However, it is important to determine the contribution of each in the prediction of the anti-proliferative activity using the two models as a function of three descriptors. Indeed, the knowledge of this contribution makes it possible to establish the order of priority of the various descriptors and to define the choice of parameters to use for optimize in order to obtain a good prediction and understanding of the anti-proliferative activity of the 13 compounds of 5-arylidene rhodanines.

Analysis of the Contribution of the Descriptors in the Models

The study of the relative contribution of the descriptors for the prediction of the anti-proliferative activity of 5-arylidene rhodanines were carried out on the different tumor lines from the XLSTAT version 2014 software [START_REF] N'guessan | Quantitative Structure Anti-Cancer Activity Relationship (QSAR) of a Series of Ruthenium Complex Azopyridine by the Density Functional Theory (DFT) Method[END_REF]. The different contributions are illustrated in Figure 5. According to the contribution of these descriptions, the C-N distance; d (C-N) has a larger contribution to the two tumor lines; MDA-MB231 and NCI-H727 compared to N OPQR and ѵ (C=O) . Therefore, the C-N distance; d (C-N) and N OPQR are the priority descriptors in the prediction of the anti-proliferative activity of the 5-arylidene rhodanines studied. It is important to note that our claim is in complete agreement with that proposed by Hansch, which states that one can establish models relating the biological activity with the hydrophobic, electronic and steric properties of the molecules [START_REF] Hansch | Fujita ρ -σ -π, analysis: method for correlation of biological activity and chemical structure[END_REF].

Conclusion

In this study, two QSAR models were developed on thirteen molecules derived from 5-arylidene rhodanines in order to understand their anti-proliferative activities on two representative tumor cell lines (NCI-H727; lung carcinoma, and MDA-MB 231; breast carcinoma) using DFT-quantum descriptors E Lumo , d (CN) , and ѵ (C=O) . This study can be extended to predict new molecules in order to determine their anti-proliferative activities. In addition, multiple linear regression (MLR) was used to quantify the relationships between molecular descriptors and anti-proliferative activity of 5-arylidene rhodanine and derivatives. Strong correlations between the predicted and experimental values of these two tumor cell lines indicate that the descriptors; E Lumo , d (CN) , and ѵ (C=O) are closely related to the anti-proliferative activity of 5-arylidene rhodanines with both models statistically supported. For the NCI-H727 model, we have R 2 = 0.926, R 2 ajust = 0.882, S = 0.147, F = 88.221, 9 >S = 0.926 and for the model MDA-MB231, we have R 2 = 0.954, R 2 ajust = 0.927, S = 0.093, F = 145.448, 9 >S = 0.954. The two models used in this study show that the C-N distance; d (C-N) and the energy of lowest unoccupied molecular orbital; N OPQR are the greatest descriptors in the prediction of the anti-proliferative activity of the 5-arylidene rhodanines derivatives studied. The different models obtained were validated using a validation set comprised of four molecules. The similarity in the curve in figure 4 perfectly illustrate this by the alignment of the points. For future work, this work could be extended to new molecules related to rhodanines and derivatives with the objectives of determining their anti-proliferative activities.

  = Ο) Density Functional Theory (DFT) and Quantitative Structure Activity Relationship (QSAR)

  the descriptors ( N OPQR , d (C-N) , ѵ (C=O) ) indicate that the anti-proliferative activity ( /LéM ) evolves in the same direction. The study of the significance of these different models was conducted by evaluating the statistical indicators and the relationship between the theoretical and experimental activities of the validation set. The values of the statistical indicators determined for each model are shown in

  .

Figure 2 .

 2 Figure 2. Model MDA-MB231 regression line.

Figure 3 .

 3 Figure 3. Model regression line NCI-H727.

Figure 4 .

 4 Figure 4. Similarity curve of the experimental and predicted values of these two models.

Figure 5 .

 5 Figure 5. Contribution of the different constituents in these two models.The order of priority of the different quantum descriptors with their respective normalized coefficients was classified

  cell lines of the ImPACcell platform.

	NCI-H727 (REF ECACC: 94060303): human lung tumor
	line.
	MDA-MB 231 (REF ECACC: 92020424): human breast
	carcinoma line.

Table 3 .

 3 Values of the bivariant linear correlation coefficients of the descriptors.

	Variables	ELumo	ѵ(C=O)	d(C-N)
	ELumo	1	-0.0817	-0.2569
	ѵ(C=O)	-0.0817	1	-0.6306
	d(C-N)	-0.2569	-0.6306	1

Table 5

 5

. The values of the statistical indicators listed in this table reflect a good correlation of the activity with the different descriptors.

Table 5 .

 5 Statistical indicators of multilinear regression.

	Statistical indicators of multilinear		MDA-MB2	NCI-H72
	regression		31	7
	Number of compounds N		13	13
	Coefficient of determination R 2		0.954	0.926
	Adjusted coefficient of determination R 2	ajust	0.927	0.882
	Standard deviation S		0.093	0.147
	Fisher's test F Correlation coefficient of cross validation 9 >S 0.954 145.448 R 2 -9 >S 0.000 Field of activity -./ (µM) 13-114	88.221 0.926 0.000 9-110
	Confidence level α		> 95%

Table 6 .

 6 Values of the relationship between the predicted and experimental anti-proliferative activities of the validation set.

		pIC50exp	pIC50pred	pIC50 pred / pIC50exp
	MDA-MB231
	AR-1	3.943	3.946	1.001
	AR-6	4.886	4.887	1.000
	AR-12	4.377	4.381	1.001
	AR-13	4.260	4.253	0.998
	NCI-H727
	AR-2	4.066	4.071	1.001
	AR-6	4.027	4.054	1.007
	AR-7	4.131	4.095	0.991
	DR-12	4.481	4.485	1.001