Christophe Bezes
email: cbezes@clickmbrick.net

E-COMMERCE WEBSITE EVALUATION: A CRITICAL REVIEW EVALUATION DES SITES INTERNET COMMERCIAUX : UN ETAT DE L'ART

Keywords: website, information system, communication channel, retailing Résumé site Internet, système d'information, canal de communication, canal de distribution, flow, richesse des medias

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In the history of management science, no topic has been the object of more academic research over such a short time than the Internet. This technology has provided a new interface linking businesses as well as individuals, and spanning many fields, from information systems to marketing, worldwide.

With the proliferation of websites (one hundred fold growth in ten years), academic and empirical research has sought to evaluate the features of ecommerce websites most likely to maximize Internet technology adoption, to attract Internet users, turn them into cyber buyers, encourage customer loyalty, improve service and ultimately increase profits. However, there has been great diversity in the research, with different skills involved (information technology, marketing, communication, etc.), as well as a wide range of websites being analyzed. The Internet is a field of research that is still evolving, with businesses and customers learning together, and little is known about how to develop commercial websites to maximize profit. [START_REF] Huizingh | The content and design of web sites: an empirical study[END_REF]. This is the reason why this article aims at identifying the different evaluation approaches, highlighting the main contributions of each, in order to recognize the concepts which could develop synergies between all or some of the different approaches. The literature reviewed includes some hundred research articles, as well as previous synthetic work, some of it [START_REF] Galan | Evaluation du site Web: une approche par l'expérience de service, 17ème[END_REF][START_REF] Bressolles | Vers une typologie des sites web destinés aux consommateurs[END_REF] organizing website evaluations according to the metrics used (behavioral or attitudinal); while some [START_REF] Bellaaj | Evaluation de l'impact de l'utilisation d'un site web commercial: une revue critique de la littérature[END_REF] focus their research on the concept being measured (website quality, success, buyer behavior, electronic system quality, impact of the site on the balance sheet).

Yet website evaluation depends largely on the approach used. It seems desirable therefore, following [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF], to propose a third approach to complement the two mentioned above. This approach stems from the definition of an e-commerce website. From the first generation of the Internet (EDI: Electronic Data Interchange) to today's Internet opening out onto a worldwide network, with virtually no barriers to entry and connecting suppliers and customers [START_REF] Huizingh | Why do consumers like websites?[END_REF], the aims and contents of websites have greatly evolved. Communication is no longer uni-or bi-directional, and an increasing number of websites today offer online payment and support [START_REF] Azzone | Corporate websites: the drivers of their different configurations[END_REF]. "Doing on line" tends therefore to replace "being on line" [START_REF] Griffith | The role of interface in electronic commerce: consumer involvement with print versus on-line catalogs[END_REF], although this is happening at varying speeds depending on the country of origin of the business, its sector, the complexity of products, and the buoyancy of the market [START_REF] Huizingh | The content and design of web sites: an empirical study[END_REF][START_REF] Zhang | Information Quality of commercial Web site home pages: an explorative analysis[END_REF].

Described as a "mediated interaction tool designed to implement a marketing strategy, used by an intelligent and motivated player in the buying process" [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF], an e-commerce website can therefore be considered concurrently or in turn as "a marketing channel", a retailing channel, "a servuction system element", or a medium [START_REF] Helme-Guizon | Le comportement du consommateur sur un site marchand est-il fondamentalement différent de son comportement en magasin? Proposition d'un cadre d'appréhension de ses spécificités[END_REF]. [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF] first identified an initial traditional and commonly used approach evaluating websites within the framework of information systems, focusing on the quality of the interface, then a second approach focusing on customer satisfaction and "considering the website as a type of store". Having reviewed the literature, a third approach seems appropriate: the website as a communication channel. As for the website as a servuction element, although it is the subject of an increasing amount of research, it can still fit into the "type of store" category.

Evaluations which approach websites as information systems will be studied first, followed by the other two evaluation approaches, respectively as communication channels and retailing channels, attempting to highlight the conceptual and methodological assets and liabilities of each. An overall synthetic picture will link the main concepts found in the literature before concluding with a few cross-concepts linking each of these evaluations in order to produce common indicators.

II. EVALUATION IN TERMS OF INFORMATION SYSTEMS

Before being considered as a communication or a retailing channel, each website was examined for its primary function: "to facilitate knowledge acquisition" [START_REF] Fang | An empirical study of web site navigation structures' impacts on web site usability[END_REF]. With this initial approach, the website is analyzed as a "system of inter-related components working together to identify, capture, organize and transfer knowledge between recipients and providers" [START_REF] Fang | An empirical study of web site navigation structures' impacts on web site usability[END_REF]. In this case, the aim is mostly to analyze the navigation conditions which optimize the rapid adoption of the new technological interface.

The original approach can be subdivided into two different paths, one strictly technical and the other more ergonomic.

II.1. PURELY TECHNICAL EVALUATIONS

Purely technical evaluations focus on Internet technology acceptance conditions for adoption by a maximum number of businesses and end users. To achieve this, evaluations use two constructs emanating from the business world, perceived usefulness of the information received -"the extent to which a person believes that using a particular system would enhance their work performance" [START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF] -and ease of use -"the extent to which a person believes that using a particular system would be effortless" [START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF] -the latter constituting an antecedent of perceived usefulness. Both constructs stem from the Technology Acceptance Model [START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF][START_REF] Davis | User acceptance of computer technology: a comparison of two theoretical models[END_REF] which states that perceived usefulness (enhanced productivity) and, to a lesser extent perceived ease of use (little effort), determine individual behavior in the use of the technology; increasing ease of use can never compensate for a lesser usefulness of the system [START_REF] Davis | User acceptance of computer technology: a comparison of two theoretical models[END_REF][START_REF] Koufaris | Applying the Technology Acceptance Model and flow theory to online consumer behavior[END_REF]. "Whether technology immediately produces the desired result … or contributes to it in part" [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF], the Technology Acceptance Model is underpinned by intrinsic motives such as enjoyment and satisfaction linked to the activity, as well as search effectiveness [START_REF] Venkatesh | Creation of favourable user perceptions: exploring the role of intrinsic motivation[END_REF] or social influence [START_REF] Venkatesh | A theoretical extension of the technology acceptance model: four longitudinal field studies[END_REF]Gefen and Straub, 2003).

The main limitation to this approach lies in its strong technological determinism, in spite of its definite ability to account for the adoption of the Internet. Technological determinism has at least two consequences. The first concerns data collection methods: researchers observe that by using factual rather than perceptual data as often as possible, they are better able to evaluate the quantity of information -number of visits, page hits -than its quality [START_REF] Alpar | Measuring the efficiency of web site traffic generation[END_REF].

The second consequence is more conceptual and lies in the incapacity of technical features to account on their own for the overall success of websites.

Although the combination of the two constructs has a direct influence on the intentions to return to the site (Hallegatte and Nantel, 2001) as well as on the intention to purchase, [START_REF] Van Der Heijden | Online store image: conceptual foundations and empirical measurement[END_REF] think it acts as a necessary but not sufficient condition since it has a negative rather than positive influence on the attitude toward online purchasing. Hence the frequent association of the Technology Acceptance Model and other constructs or models such as: SERVQUAL and transaction costs (Devaraj et al., 2003); enjoyment construct [START_REF] Igbaria | A motivational model of microcomputer usage[END_REF], which [START_REF] Childers | Hedonic and utilitarian motivations for online retail shopping behavior[END_REF] even consider as a predictive element in the attitude to online shopping; website trust as a direct influence on intention to use the website (Gefen et al., 2003) and intention to purchase [START_REF] Pavlou | Consumer acceptance of electronic commerce: integrating trust and risk with the technology acceptance[END_REF][START_REF] Van Der Heijden | Understanding online purchase intentions: contribution from technology and trust perspectives[END_REF]. Trust indirectly acts as antecedent of the two TAM constructs: perceived information usefulness and ease of use [START_REF] Pavlou | Consumer acceptance of electronic commerce: integrating trust and risk with the technology acceptance[END_REF][START_REF] Hallegatte | The intertwined effect of perceived usefulness, perceived ease of use and trust in a website on the intention to return[END_REF].

However, technology acceptance better explains the adoption of the Internet than its uses: [START_REF] Soopramanien | Adoption and usage of online shopping: An empirical analysis of the characteristics of "browsers" and "non-internet shoppers[END_REF] have shown that it can be used to distinguish online buyers from non-buyers, but not browsers. Thus, because of its low cost, [START_REF] Mathieson | Predicting user intentions: comparing the Technology Acceptance Model with the Theory of Planned Behavior[END_REF] recommends using TAM to evaluate the overall performance of the system, and Theory of Planned Behavior for the more specific and contextualized aspects.

While this initial approach puts the emphasis on ease of navigation, a significant variable in the lowering of price sensitivity [START_REF] Lynch | Wine online: search costs affect competition on price, quality, and distribution[END_REF], a more functionalistic and ergonomic evaluation method will better take into account the website as a whole, putting more emphasis on content and readability.

II.2. PREDOMINANTLY ERGONOMIC AND FUNCTIONALISTIC EVALUATIONS

Against the purely technical evaluations, the specificity of the second approach lies essentially in its taking into account of subjective perception, both in terms of website content and in terms of design. This perception varies with the expertise, the cognitive skills and the end goal of each Internet user. It enables us to study navigational comfort conditions: readability and page hierarchy so that the user feels like continuing his purchase, and maximizing the extraction of rational or emotional content; page design -easy identification of links, "dividing the page into meaningful units" and frame limitation [START_REF] Ladwein | Le web design et l'ergonomie des sites de e-commerce: vers l'élaboration d'un modèle, actes du colloque[END_REF] -which with high speed connections now appears as a greater handicap than connection speed; site structure (with an internal search engine or requiring the user to browse, specific and broader search).

Research in this area can be split into two categories. The first concerns the object analyzed and distinguishes content from design. For example, for [START_REF] Huizingh | The content and design of web sites: an empirical study[END_REF], content includes:

information content, since the primary objective of the website is to deliver commercial information both on the company and on the product, as well as non-commercial information on sponsored events, location, etc.

transactional content including ordering and requests for proposals, the size of which is directly related to the size of the website entertainment (jokes, cartoons, pictures, games and video clips). As for website design, it includes:

navigation tree -hypertext links -free or imposed in order to influence navigation; it can take the form of hierarchical network structures, the best one of these, according to [START_REF] Huizingh | The content and design of web sites: an empirical study[END_REF] being "somewhere between a tree and a full network"

search function, correlated to the size of the site protected information, though usually only found in the financial sector.

The second category of research is centered more on an "intermediate construct likely to regroup several factors relevant to the success of the website" [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF]. Reix distinguishes research centered on the quality of information and that centered on usability, the latter being defined by the International Organization for Standardization (ISO) as the "effectiveness, efficiency and satisfaction with which a specified set of users can achieve a specified set of tasks in a particular environment". Table 1 gives a synthetic description of research using this approach. Having examined research which evaluates websites as information systems, we note that the two approaches that make up this body of research use the paradigm of man/machine interaction [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF] as a common denominator. By focusing on the ability of the technological instrument to meet the expectations of Internet users, these approaches present the immense advantage of being applicable to all websites (e-commerce, non-commercial and blogs) and they highlight two major features of the online experience: navigation ease and content quality [START_REF] Flores | Potentiel relationnel et impact du site de marque sur la performance marketing[END_REF]).

Yet, while complementary, these approaches share the same limitations: a strong technological determinism along with a primary role being given to cognitive, usefulness and ergonomic factors [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF], and even to normative factors (Agarwal and Venkatesh's use of the Microsoft Usability Guidelines tool). By focusing on the cognitive costs through objectively measurable features, they tend to overvalue flow or expert opinion statistics. It is the case, for instance, in evaluations obtained from professional webmasters, who in the end say more about their beliefs than about real facts [START_REF] Liu | Design quality of websites for electronic commerce: fortune 1000 webmasters' evaluations[END_REF]. Using several data collection methods can sometimes lead to a robustness of measurements, as is the case with the constructs of [START_REF] Palmer | Web site usability, design and performance metrics[END_REF]. Moreover, information acquisition is not the sole reason for using the Internet; [START_REF] Korgaonkar | A Multivariate Analysis of Web Usage[END_REF] have described "social escapism" motivations, socialization and interactive control, as well as economic motivations, transaction-based security and privacy concerns.

The second research approach consisting in evaluating websites as communication channels will enable us to integrate new affective -as opposed to cognitive -dimensions, as well as attitudinal -as opposed to behavioraldimensions by using existing models for the evaluation of advertising by the traditional media. Although, as [START_REF] Huizingh | Why do consumers like websites?[END_REF] state: "it is tempting to consider all Internet related features as new -as in the new economy for example, we will understand this new phenomenon better by carrying out more systematic studies of the fundamental similarities and differences between the Internet and standard advertising supports".

III. EVALUATION IN TERMS OF COMMUNICATION CHANNELS

The web can be considered and evaluated as a new medium, though closely linked to traditional media. [START_REF] Eighmey | Profiling user responses to commercial web sites[END_REF] states that, just as traditional TV viewers do, Internet users enjoy being entertained (or stimulated) and informed (quantity, freshness, access to information). Websites may thus be compared to written or televised advertising to the extent that their common aim is to influence consumers [START_REF] Huizingh | Why do consumers like websites?[END_REF].

There are, however, some major differences. On the web, the customer is active and decides the terms of his exposure to the message in terms of time and intensity. Thus, web customer value creation might not be measured solely in terms of product or service, but also in how best to engage in and prolong the dialogue, whether informative or entertaining, and this implies packaging an informative or entertaining experience [START_REF] Huizingh | Why do consumers like websites?[END_REF]. The entertainment and information aspects, correlated to irritation by [START_REF] Ducoffe | Advertising value and advertising on the web[END_REF], may have an effect on attitudes to web advertising via advertising value.

Secondly, there may be differences in the hierarchy of the effects of web advertising compared to that of traditional media [START_REF] Huizingh | Why do consumers like websites?[END_REF]. In the case of web media, "product knowledge" and "need for cognition" omitted, cognition would come before attention, followed by affectionstrongly correlated to "need for cognition", then conation -consistent with reluctance to buy online and correlated with intensity of use.

In this approach of evaluation in terms of communication channels, two themes emerge: the first and major one is based on the concept of Attitude toward the site; the second and more recent one analyses the website in terms of personality.

III.1. EVALUATIONS IN TERMS OF ATTITUDE TOWARD THE SITE

Chen et al. ( 2002) adapt the concept of Attitude toward the site from the older concept of Attitude toward the ad (Aad), an advertising efficiency measurement defined by Mc Kenzie and Lutz (1989) as "a predisposition to respond in a favorable or unfavorable manner to a particular advertising stimulus during a particular exposure occasion". Aad has an impact on Attitude toward the brand (Ab) and on Purchasing Intentions (PI). In the same manner, [START_REF] Chen | Attitude toward the site[END_REF] propose that Attitude toward the website (Aws or Ast) be an indicator for website value.

Until now, research has essentially examined the factors influencing Attitude toward the site. Among the numerous perceptual dimensions found in the literature which contribute positively or negatively to customer website evaluation, Chen and Wells (1999) identified three main factors: "entertainment (fun, exciting, imaginative, entertaining, flashy), informativeness (informative, intelligent, knowledgeable, useful, resourceful, helpful), and organization (messy, cluttered, confusing, irritating)". The weighting of each factor relevant in the Attitude toward the website varies according to the website's purpose [START_REF] Chen | Attitude toward the site[END_REF], but also according to the profile [START_REF] Chen | Attitude toward the site II: new information[END_REF] and experience of the evaluator [START_REF] Bruner | Web commercials and advertising hierarchy-of-effects[END_REF]. Nevertheless, although the site need not measure up to all these criteria in order to obtain a good Aws score, it must imperatively be "useful, user-friendly and informative rather than clumsy, messy or confusing" [START_REF] Chen | Attitude toward the site II: new information[END_REF]. Hence the need for web designers to be wary of effects aiming at impressing visitors -or clients -lest they create a negative Aws right from the home page [START_REF] Singh | A communication view of web page perception[END_REF]. On this matter we must remember the "pivotal role" of the home page in fascinating or repulsing Internet users, Attitude toward the web page (Awp) being as important as Aws according to [START_REF] Singh | A communication view of web page perception[END_REF].

For their part, [START_REF] Chandon | Qualité du site web, attitude envers le site et attitude envers la marque: rôle modérateur de la familiarité avec la marque, Actes du colloque des 12èmes[END_REF] have explained that 75% of the attitude of a website visitor is accounted for by entertainment, informative content, ease of use and interactivity dimensions. With the advent of web 2.0, the last is particularly useful when comparing the persuasive effect of websites in relation to traditional media or to printed communication material [START_REF] Belvaux | Les effets persuasifs de la recherche d'information pré-achat par Internet, 22ème[END_REF]. Today, this type of research seems to centre more on Aws effects on online purchase intention [START_REF] Flores | Potentiel relationnel et impact du site de marque sur la performance marketing[END_REF][START_REF] Richard | Modeling the impact of internet atmospherics on surfer behavior[END_REF] or on Attitude toward the brand -a positive influence according to [START_REF] Chandon | Qualité du site web, attitude envers le site et attitude envers la marque: rôle modérateur de la familiarité avec la marque, Actes du colloque des 12èmes[END_REF].

One cannot fail to note that the research mentioned here tends to focus more on Internet advertising (banners, links, etc.) as a new medium shared among several advertisers rather than on the whole web site as a genuine advertising channel entirely controlled by the advertiser. Indeed, these evaluations are often limited to the home page or in an even restrictive manner, to the ads appearing on it. This is all the more regrettable as the advertisers now own one or several brand websites which significantly influence purchase intentions [START_REF] Flores | Potentiel relationnel et impact du site de marque sur la performance marketing[END_REF]. Hence, as a communication channel entirely controlled by the advertiser, these sites do not seem to have been studied so far except via the concept of personality of the site.

III.2. EVALUATIONS IN TERMS OF PERSONALITY OF THE SITE

Chen and Rodgers (2006) are two of the few researchers to have studied website personality, which they define as "the set of traits encompassing human characteristics and information technology features associated with a website." Although this definition uses the standard terminology of brand personality, the authors nevertheless insist on three points.

First, website personality differs from brand personality by the way in which it is built, notably through the site interface and design. Secondly, they integrate rational elements into it -perceived use and perceived ease of use -as proposed by [START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF]. Finally, they underline the advantages of modeling website personality on human personality, hence the attempts at designing the site to meet the needs of Internet users or their motivations, whether utilitarian or hedonic. Mediated interaction can sometimes be deemed to be more satisfying than direct human interaction, using the same evaluation criteria (fun, exciting, sociable). But although [START_REF] Childers | Hedonic and utilitarian motivations for online retail shopping behavior[END_REF] suggest increasing pleasure in the goal-directed profiles by using videos demonstrating products, [START_REF] Koufaris | Consumer behavior in web-based commerce: an empirical study[END_REF] warn against some excesses in sites that try too hard to adapt their interface to the behavior of each et all of their visitors as this technique seems to improve user performance but not overall satisfaction [START_REF] Koufaris | Consumer behavior in web-based commerce: an empirical study[END_REF].

Using a specific evaluation tool for web personality, the Website Personality Scale (WPS), [START_REF] Chen | Development of an instrument to measure web site personality[END_REF] have demonstrated that alongside the "Intelligent" criteria identified by [START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF], the "Fun" criteria -prevalent in research on advertising -plays a determining role compared to traditional functional and rational criteria. Nevertheless the Fun criteria is comparable to the Enjoyment construct already proposed by [START_REF] Igbaria | A motivational model of microcomputer usage[END_REF] to amend Davis's TAM model; it can also be compared to the Entertainment construct used by [START_REF] Müller | The impact of a World Wide Web site visit on brand image in the motor vehicule and mobile telephone industries[END_REF] for the Attitude toward the site. Applied to website personality, the "Sophisticated" criterion must be understood differently than when applied to brand personality, since in the latter it conveys concepts of upper-class, aesthetics and refinement while when applied to the former, it is more centered on how knowledgeable, comprehensive and mature the website is.

Therefore, although "a good website is a website that sells well -either directly or by the advertising it does" - [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF], we should note that the contribution from approaches considering websites as media or communication channels deal with information and advertising, but not with direct selling. Thus the first two approaches discussed (in terms of information systems and in terms of communication channels) analyze websites as "an avenue through which information flows travel" [START_REF] Palmer | Information intensity: a paradigm for understanding web site design[END_REF] and the interactivity makes this medium richer than "the text and graphics of a printed sales brochure or catalog" [START_REF] Palmer | Information intensity: a paradigm for understanding web site design[END_REF]. Information comes before the product, and communication before retailing. This role of websites is dealt with by a third approach.

IV. EVALUATION IN TERMS OF RETAILING CHANNELS

Today, several motives drive the proliferation of research on websites as retailing channels in their own right. First, in terms of strategy, the success of e-vendors who survived the Internet bubble is making researchers and practitioners look at this autonomous retailing channel in terms of logistics and relational marketing. Furthermore, adding an Internet channel is highly likely to enhance existing organizations (net-enhanced organizations by Straub et al., 2002b). Secondly, apart from "chore shopping" and "social shopping", all other attitudes which apply to shopping in a store ("leisure shopping", "utilitarian shopping", "salespeople relation shopping") are all present in the Internet mental imagery of people [START_REF] Bergadaa | L'attitude à l'égard d'Internet, du shopping et le comportement des internautes[END_REF].

Finally, the new technical potential of websites could enable them "to replace a physical sales environment" (Galan et al., 2001), with a well-designed interface able to make up for the gap between the experience of shopping in a store and virtual shopping [START_REF] Mahfouz | Web site interface design: external and internal factors[END_REF].

In that case, "web sites must be considered both a marketing communications vehicle as well as a transaction generator" [START_REF] Wolfinbarger | Shopping online for freedom, dominance and fun[END_REF]. Evaluations in terms of retailing channels are mostly concerned with "webmosphere" and consumer satisfaction.

IV.1. EVALUATIONS IN TERMS OF "WEBMOSPHERE"

Extending Kottler's 1973 concept of store atmosphere, [START_REF] Childers | Hedonic and utilitarian motivations for online retail shopping behavior[END_REF] coined the term "webmosphere". [START_REF] Dailey | Navigational web atmospherics: explaining the influence of restrictive navigation cues[END_REF] defined the concept as "as the conscious designing of web environments to create positive effects (e.g., positive affect, positive cognitions, etc.) in users in order to increase favorable consumer responses (e.g. site revisiting, browsing, etc.)." According to [START_REF] Childers | Hedonic and utilitarian motivations for online retail shopping behavior[END_REF], "webmosphere" includes structural attributes (frames, hyper-text links, pop ups, etc.), media dimensions (graphics, texts, audio, video, etc.) and site layout (organization and grouping of products). For this research approach, "the design of e-stores plays the same role as the layout of stores" [START_REF] Liang | Effect of store design on consumer purchases: an empirical study of on-line bookstores[END_REF]: "it seems reasonable to speculate that the design of e-stores (e.g. appearance and layout of home pages) may affect eshoppers' perceived psychic costs significantly and thus their propensity to shop at those stores" [START_REF] Baker | The influence of multiple store environment cues on perceived merchandise value and patronage intentions[END_REF].

However, the actual influence of "webmosphere" on consumers remains a source of debate. For some researchers, the screen is a compulsory passage which reinforces the dominance of "webmosphere" over atmosphere, as is its capacity to show texts, graphics (images, animations, videos) and sound satisfactorily, in order to create genuine "online atmospherics" (Galan and Gonzales, 2001). Thus, three emotional variables (pleasure, arousal, dominance) may equally describe on line and offline behavior [START_REF] Koufaris | Consumer behavior in web-based commerce: an empirical study[END_REF]. For example it may be that:

perceived dominance influences intention to return in repeat customers being involved in the product brings more pleasure to repeat visitors than the novelty of the site (as for Hoffman and Novak)

the enjoyment of the experience and perceived dominance (to create customer loyalty) are both important for new customers online shopping enjoyment increases with customer product involvement, stimulating challenges, and use of value added search mechanisms -online shopping enjoyment possibly has little influence on impulse buying for the category of products tested (video rental).

On the other hand, some researchers are much more cautious in their analysis. They observe that several atmospheric factors, such as temperature, smell, and touch, are not yet present on the Internet [START_REF] Eroglu | Atmospheric qualities of online retailing: a conceptual model and implications[END_REF], and they wonder whether using such tools as videos increases enjoyment or frustration due to download times (Chiders et al., 2001). They do however recognize that ecommerce presents distinctive features -if not advantages -over traditional commerce such as flexibility of time and space, as well as the reduction of the selling environment to the size of the screen.

IV.2. EVALUATIONS IN TERMS OF CUSTOMER E-SATISFACTION

The aim here is to "propose a construct gathering all the elements which contribute to customer satisfaction in order to confront it with the characteristics of the site" [START_REF] Madrid | Vers un outil d'évaluation de l'intégration du site Internet marchand dans la stratégie et l'organisation de l'entreprise[END_REF]. However, as far as satisfaction on the Internet is concerned, customers have multiple objectives. [START_REF] Keeney | The value of internet commerce to the customer[END_REF] has listed nine fundamental ones: "maximizing product quality, minimizing cost, minimizing delivery time, maximizing ease of transaction, minimizing time spent, maximizing confidentiality, maximizing shopping enjoyment, maximizing security, minimizing environmental impact" [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF] According to [START_REF] Keeney | The value of internet commerce to the customer[END_REF], means objectives are minimizing fraud, assuring system security, maximizing access to information, assuring reliable delivery, minimizing misuse of personal information, providing comparison shopping, maximizing product variety and availability, minimizing personal travel, and maximizing ease of use. These objectives underlie the constructs which influence attitudes and behavior of online consumers, whether for the purchase of goods or services. In fact, these satisfaction factors are the positive side of the irritation factors described by Helme-Guizon ( 2002): updating -broken links, impossible download, obsolete information; ease of navigation -structure, readability of menus, cluttered pages; aesthetics; information content; language; products offered; advertising; transfer time; security; forced selling -preformatted answers; competitive value of the website in relation to other forms of selling. We note that Wan, cited by [START_REF] Liang | Effect of store design on consumer purchases: an empirical study of on-line bookstores[END_REF], distinguishes the process (promotion, pricing, transaction, services) from values (information, friendship, responsibility, security).

Most of the evaluations in terms of e-satisfaction (table 2) show that the quality of websites is measured by end users following essentially functional criteria rather than hedonic or social criteria, although these are mentioned in some of the literature [START_REF] Rolland | La qualité des sites web marchands en distribution: proposition d'une échelle de mesure e-qual[END_REF]. Indeed, in the case of online services, [START_REF] Shankar | Customer satisfaction and loyalty in online and offline environments[END_REF] note that satisfaction is more influenced by content than by interactivity, although the latter is considered by many as being evidence of better dominance, enjoyment and ease of use. Aside from factors such as convenience or security, the structure of the site also seems to play a major role [START_REF] Song | A theoretical approach to web design in e-commerce: a belief reinforcement model[END_REF], and these features of websites appear to be compatible with Palmer's constructs (2002).

Furthermore, ease of access to information may contribute more to satisfaction and loyalty online than offline, hence the need for managers to identify the adequate quantity of information and to build a site enabling access to a specific type of information -rather than to all the information available -in the format chosen by the Internet user, with no graphics for example [START_REF] Shankar | Customer satisfaction and loyalty in online and offline environments[END_REF]. The graphic quality of sites may not be a factor which is directly taken into account by customers, but indirectly through other items [START_REF] Rice | What makes users revisit a Web site?[END_REF]. All this could corroborate the theory according to which the website may develop a way of dealing with information that is much more analytical than intuitive, with hedonic aspects coming as extras. According to [START_REF] Novak | Measuring the customer experience in online environments: a structural modeling approach[END_REF], customer help services are the key criterion to build a "smooth online shopping experience" coming before variety and quality of information, ease of ordering, contact, cancelling, payment, return, as well as delivery speed. This concords with [START_REF] Szymanski | E-satisfaction: an initial examination[END_REF], for whom the correlation between e-satisfaction and other elements of merchandising such as range of goods is not necessarily obvious except that the criteria taken into account as well as the weight they carry vary according to the type of product and risk levels [START_REF] Lowengart | Differential effects of product category on shoppers' selection of web-based stores: a probabilistic modeling approach[END_REF][START_REF] Venkatesh | Turning visitors into customers: a usability-centric perspective on purchase behavior in electronic channels[END_REF].

Table 2 -Synthetic view of e-satisfaction evaluation criteria

Szymanski and Hise (2000)

-Convenience -Merchandising (product offerings, product information) -Site design (ambience, organization, ease of navigation, speed of page posting…) -Financial security [START_REF] Liang | Effect of store design on consumer purchases: an empirical study of on-line bookstores[END_REF] -Hygiene factors: security, product tracking, service phone, allowing for product returns, consistent style -Motivators: search engine, easy to sign up, shopping carts, order on line, home delivery, multiple payment methods, credit card payment -Media richness factors: product organization, navigational hyperlinks, price comparison, customized information, valueadded information, special effects, on-line sales person, auctions [START_REF] Shim | Retailer web site influence on customer shopping: an exploratory study on key factors of customer satisfaction[END_REF] -Ready access to customer service and policy: policy, service phone -Amount of customer effort required to access product/service: number of clicks, scroll right

-Five factors relative to the quality of the information (relevance, timeliness, reliability, scope, perceived usefulness) -Four factors relative to the quality of the system (access, usability, navigation, interactivity).

Song and Zahedi (2005)

-Product promotion: price comparison, discounting, product recommendation, gift certificates, new products… -Service information: warranty, sales assistance, security, customer privacy, tracking order… -External interpersonal: product rating, expert and customer comments, forum, sales rank… -Ease of use and navigation: product cancellation, customization, audio and visual content, price information in product listing, uniformity of design formats, no crowded page, not too many clicks from home page to order page… -Purchase facilitation: picture and detailed product description, FAQ, links to other sites, possibility of adaptation of the product, payment and shipping options However, although the approach considering the website as a retailing channel in its own right enables the integration of a lot of the previous research, in particular in information systems, one should underline how little work there is on website image, when there is so much on that of physical stores. Such scarcity in the research on e-commerce sites is all the more regrettable as the "location" dimension in all likelihood having a lesser effect on behavior in the virtual world, channel image should therefore play more of a role in websites. But to influence beliefs then buying behavior of Internet users, these characteristics must not only exist but also be perceived [START_REF] Mckinney | The measurement of Web-customer satisfaction: an expectation and disconfirmation approach[END_REF][START_REF] Song | A theoretical approach to web design in e-commerce: a belief reinforcement model[END_REF].

From a more methodological stand point, although websites can be analyzed in the same way as a store [START_REF] Volle | Du marketing des points de vente à celui des sites marchands: spécificités, opportunités and questions de recherche[END_REF][START_REF] Helme-Guizon | Le comportement du consommateur sur un site marchand est-il fondamentalement différent de son comportement en magasin? Proposition d'un cadre d'appréhension de ses spécificités[END_REF], publications use composite criteria, mixing traditional retail outlet image dimensions with dimensions describing e-satisfaction for instance [START_REF] Lohse | Electronic Shopping[END_REF][START_REF] Van Der Heijden | Online store image: conceptual foundations and empirical measurement[END_REF], mostly in order to classify the sites. Further, even studies that are faithful to dimensions identified for store image (Katerrattanakul and Siau, 2003), and which attempted to measure the impact of website image on intention to purchase [START_REF] Chen | The impact of web site image and consumer personality on consumer behavior[END_REF] do not include "location" and "salespeople" dimensions. Yet, on the Internet, the former could be taken into account by Google's page rank, or by its presence on price comparison sites, and the latter by the possibility of contact by phone, or the performance of an search tool, FAQ or videos giving professional advice. One could also evaluate the effects of website characteristics not through attitudinal data, but using factual data: "cost savings, expanded markets, incremental additional sales, reduced search costs, time savings" (DeLone and Mclean, 2003).

V. POTENTIAL LINKS BETWEEN THESE EVALUATIONS

As we have just shown, at present there is no single method to evaluate websites. All depends on the role assigned to the site -information flow, advertising channel, retailing channel -and on the company's strategic choices, for example in terms of channels. The results will then depend on collection mode, whether factual or perceptual, the sites analyzed, real or experimental, the size of the business and how long it has been in the market, the features of the merchandise, as well as its cultural background, profile, degree of experience, utilitarian or hedonic orientation of the customers. Each method will therefore call on different concepts to describe the phenomena and measure their impact. Even within a single approach, it is difficult therefore to compare the relevance of the evaluations or to evaluate the general influence the whole of these constructs might have on intentions to purchase.

On the basis of the links previous literature has established between the main concepts described above, figure 1 contributes to a convergence of concepts and measurements; it shows the successive layers enabling evaluation of a website in all its technical and commercial dimensions. Because of their cross-relevance, the theory of media richness as well as those of virtual affordances and of flow could also contribute to bringing together all or some of the different research approaches, thus improving their implementation. We propose to give a brief sketch of the links which have already been established between these concepts and Internet site evaluation.

V.1. MEDIA RICHNESS

Whether it is video mail, video catalogues, or Web TV, rich media appears today as the easiest and quickest way to make a website stand out and it will soon be a prerequisite.

Although it is always tricky to transpose a theory from one realm -that of organizations and managers -to another -that of markets and customers -and even more so to a new technology which is by nature still unstable in its uses [START_REF] Reix | Evaluation des sites Web: nouvelles pratiques, anciennes théories, 8ème colloque de l[END_REF][START_REF] Kalika | La théorie du millefeuille: de la non-substitution entre communications électroniques et face à face[END_REF], nevertheless, the theory of media richness [START_REF] Daft | Organizational information requirements, media richness and structural design[END_REF][START_REF] Steuer | Defining virtual reality: dimensions determining telepresence[END_REF] deserves to be used more often:

first because the Internet, as a new medium, has already been the subject of a body of research in an organizational context [START_REF] Dennis | Testing media richness theory in the new media: the effects of cues, feedback and task equivocality[END_REF])

Perceived usefulness of information

Ease of use

Attitude toward the brand

The website as an information system

The website as a medium

The website as a retailing channel

secondly because, ever since [START_REF] Doody | Next revolution in retailing[END_REF] published their ground breaking article on e-commerce, the quantity and quality of information available seem to be the main source of differentiation between one website or another and traditional commerce. This added value of the Internet which, by acting on several dimensions [START_REF] Li | The role of virtual experience in consumer learning[END_REF], consists in improving decision by "complex, non-linear and nonoriented questions" [START_REF] Koufaris | Consumer behavior in web-based commerce: an empirical study[END_REF], could provide an incentive for Internet users to visit and revisit a site [START_REF] Rice | What makes users revisit a Web site?[END_REF] finally, because the distinction between high task-relevant / low taskrelevant information has already permitted to link up intrinsic and extrinsic motivations of Internet users [START_REF] Eroglu | Atmospheric qualities of online retailing: a conceptual model and implications[END_REF] and model the impact of "webmosphere" on the behavior of cyber-buyers [START_REF] Richard | Modeling the impact of internet atmospherics on surfer behavior[END_REF].

V.2. VIRTUAL AFFORDANCES

The concept of virtual affordances, defined by [START_REF] Li | The role of virtual experience in consumer learning[END_REF] as "what a 3D product can offer for the inspection of the consumer" appears equally promising at the dawn of Second Life, to develop new typologies of products adapted to e-commerce, but also to compare the advantages of the Internet medium over those of televised advertising, as much in terms of attitude toward the brand as of purchase intentions, for geometric or mechanical objects, but not for tactile products [START_REF] Li | The role of virtual experience in consumer learning[END_REF].

In an Internet environment, visual imagery takes precedence over other types of imagery -mental, aural, tactile, olfactory, taste, and motor-sensorial [START_REF] Gavard-Perret | L'imagerie mentale: un concept à (re)découvrir pour ses apports en marketing[END_REF][START_REF] Bergadaa | L'attitude à l'égard d'Internet, du shopping et le comportement des internautes[END_REF]. The capacity to generate these types of affordances in 3D could "compensate for the lack of physical contact" [START_REF] Mckinney | The measurement of Web-customer satisfaction: an expectation and disconfirmation approach[END_REF] and frustration which is all the stronger as the Internet combines great ease of use with great perceived risk [START_REF] Koufaris | Consumer behavior in web-based commerce: an empirical study[END_REF]. However, although image seems to beat text as an incentive to buy familiar products, it is less the case for less familiar products (Chau and Au Kar Yan Tam, 2000). By combining "interactivity, life and mental imagery", the virtual affordances generated by 3D visualizations could even overtake perceived affordances by increasing the "sense of presence" [START_REF] Li | The role of virtual experience in consumer learning[END_REF].

V.3. FLOW

The third concept which would enable us better to integrate the different research approaches studied above is flow. This extremely intense quasihypnotic state, characterized by the individual being totally absorbed in a task deliberately undertaken along with a loss of consciousness of the surroundings (Csiksentmihalyi, 1997), was adapted to hypermedia navigation environment by [START_REF] Hoffman | Marketing in hypermedia computer-mediated environments: conceptual foundations[END_REF]. Aside from better retention of what the Internet user experiences and sees on the screen (see Attitude toward the website), flow may increase the appeal of the website, reduce sensitivity to price and influence purchasing behavior [START_REF] Mathwick | Pay, flow and the online search experience[END_REF].

This concept has given rise to such diverse conceptualizations that it makes definition difficult [START_REF] Koufaris | Applying the Technology Acceptance Model and flow theory to online consumer behavior[END_REF]: [START_REF] Ilsever | Extending models of flow and e-loyalty[END_REF] for example, suggested a model in which users' cognitive characteristics (concentration, satisfaction) along with website characteristics (Internet system quality, structure and visibility of content) are antecedents of flow and customer loyalty. But, so far, the concept of flow has hardly been tested empirically except for [START_REF] Hausman | The effect of web interface features on consumer online purchase intentions[END_REF], who have shown its positive impact on intention to purchase and intention to return, and by [START_REF] Agarwal | Time flies when you're having fun: cognitive absorption and beliefs about information technology usage[END_REF] who integrated flow into the broader concept of cognitive absorption. Although the two tests lead to the same results in terms of final behavior, they are in opposition in the role of flow in attitudes: flow is considered by most writers (including [START_REF] Hausman | The effect of web interface features on consumer online purchase intentions[END_REF] as a consequence of perceived utility and ease of use, while [START_REF] Agarwal | Time flies when you're having fun: cognitive absorption and beliefs about information technology usage[END_REF] rather see in it an antecedent of the two constructs, when it accompanies the enjoyment construct. Furthermore, the role of flow on impulse purchases has yet to be validated [START_REF] Koufaris | Applying the Technology Acceptance Model and flow theory to online consumer behavior[END_REF].

This calls for further experimentation. Yet we can but regret the fact that the concept of flow should today essentially, and sometimes abusively, be used in experiential evaluations in terms of webmosphere. [START_REF] Novak | The influence of goal directed and experiential activities on online flow experience[END_REF] have retracted their 2000 claim, and suggest that the state of flow is not strictly restricted to autotelic behavior. Two things stem from the above. On a practical level, web designers should not only try to stimulate experiential behavior in Internet users with spellbinding presentations, they should also seek to create a state of flow in goal-oriented Internet users by respecting their demands for ease of use and navigation [START_REF] Novak | Measuring the customer experience in online environments: a structural modeling approach[END_REF][START_REF] Huizingh | Why do consumers like websites?[END_REF]. Thus, in matters of e-satisfaction, [START_REF] Koufaris | Consumer behavior in web-based commerce: an empirical study[END_REF] insist on the capacity of the website to implement functionalities reinforcing as much feelings of perceived dominance (goal-centered behavior) as feelings of pleasure (experiential enjoyment) in order to increase the rate of revisits. On a theoretical level, the research, which tends to relativize or even reject the role of experiential criteria in the context of online purchasing (e.g. [START_REF] Zeithaml | Service quality delivery through web sites: a critical review of extant knowledge[END_REF], cannot reject the role of flow at the same time, on the pretext that it may only be experiential. In this regard, taking into account the two cognitive and affective psychological paths [START_REF] Filser | Commerce en magasin et e-commerce: les apports des modèles de choix du point de vente, 4ème Colloque Etienne Thil[END_REF], which guide online visits and purchases, would enable us better to adjust the determining characteristics of websites. According to [START_REF] Huffman | Goal-oriented experiences and the development of knowledge[END_REF], goal-centered individuals seem more "capable of concentrating and learning efficiently than those who have no goal, or have several".

VI. CONCLUSION, CONTRIBUTIONS AND LIMITATIONS

Our attempt at establishing a critical review cannot claim to be exhaustive, and its main objective is to accelerate, or at least to facilitate sedimentation of research on e-commerce website evaluation. Hence the purpose of the suggested classification is not purely academic in that it does not aim at compartmentalizing new research into an existing trend; on the contrary, it is meant to encourage cross-fertilization between these different evaluation approaches.

We have seen that e-commerce websites were first analyzed as information systems. With the emphasis mainly on the conditions of adoption of the technology and on the ergonomics of the site, this approach dipped in heavily objectively measurable behavioral data as well as expert opinions, running the risk of giving too prominent a place to normative and cognitive aspects.

Often neglected or diluted by literature reviews, a second approach evaluated websites as a distribution and advertising channel, introducing new affective dimensions and adapting the measurements of attitude toward advertising to this new medium; the significant growth of brand websites should, in all logic, take this research well beyond a simple evaluation of website personality. Finally, a third and last approach, which is becoming increasingly prevalent as more businesses join online selling, evaluates e-commerce websites as retailing channels, measuring e-satisfaction and "webmosphere" while website image and online experience evaluations are still rare.

VI.1. CONTRIBUTIONS AND AREAS FOR FUTURE RESEARCH

With this panorama which we hope was representative of the research carried out in the last ten years, our contribution is essentially theoretical. As the Internet matures, our work seeks to encourage research to set up build between the different approaches we have identified. This can be done by testing the relationship between existing concepts, as we started to sketch in Figure 1, but also by defining some common indicators to the different approaches in order to construct, then test, a global model. Increasing use of pluridisciplinary concepts such as media richness, flow and virtual affordances could greatly contribute to achieving this. From a managerial point of view, this synthesis shows businesses with ecommerce websites or brand websites that they would do well to integrate the specific dimensions of their activity into their evaluations. Too many ecommerce websites are still evaluated by means of conventional technical criteria of ergonomics and usability (graphic identity, visual paths, ease of navigation…), and this leads to ignoring or even erasing competitive differences.

VI.2. LIMITATIONS

As a critical review, our research has three main limitations. The first one resides in the number of articles studied, the second in the proposed classification, and the third one stems from our initial challenge, which consisted in summarizing the main website evaluations as well as their conceptual links already tested in the literature, without proposing a global conceptual model to be tested.

-

  Fundamental objectives: convenience, ecology, vendor-customer relation, product value -Means objectives: online payment, product choice, vendor trust, shopping travel Gefen (2002) -Tangible dimensions: website layout -Combined dimension : responsiveness, reliability and assurance -Empathy: customized content, individualized e-mail… Mc Kinney et al.

Figure 1 -

 1 Figure 1 -Synthetic view of main website evaluations with conceptual links

Table 1 -

 1 Synthetic view of predominantly ergonomic evaluations

	Information	Katerrattanakul and Siau	Zhang et al. (2000)	Chae et al.(2002)
	quality	(1999)	-Presentation	-Connection Quality
		-Intrinsic Quality:	graphics, colors, layout	responsiveness,
		accuracy of the contents;	-Navigation	stability,
		accurate workable and	quantity and relevance	-Content Quality
		relevant hyperlinks	of the links	objectivity,
		-Contextual Quality:	-Quality	believability, amount
		provision of author's	accuracy of	-Interaction quality
		information	information, ability to	structure, navigation,
		-Representational Quality:	attract visitors	presentation
		visual settings or		-Contextual quality
		typographical features,		timeliness,
		consistency, vividness and		promptness
		attractiveness
		-Accessibility:
		navigational tools
		provided to locate the right
		information
	Usability	Palmer (2002)	Agarwal and Venkatesh	Kim et al. (2002)
		-Download Delay	(2002)	-Firmness
		-Navigation/Organization	-Content (relevance,	internal stability,
		-Interactivity	media use,	external stability
		-Responsiveness	depth/breadth, current	-Convenience
		-Information/ Content	information)	information
			-Ease of Use (goals,	gathering, order
			structure, feedback)	processing
			-Promotion	-Delight
			-Made-for-the-	system interface,
			medium connmunity,	communication
			personalization,	interface
			refinement
			-Emotion


Frédérique Badaud

Search for new physics in top decays at DØ

Keywords: Top quark, DØ, W, fourth generation t quark, FCNC PACS: 14.65.Ha Top quarks -14.65.Jk Other quarks (e.g., 4th generations) -14.70.Pw Other gauge bosons

The results of search for new processes, performed with top quark events at DØ are summarized in this paper. It presents three updated DØ results : search for heavy W resonances, search for fourth generation t quark and search for flavor changing neutral current. Neither of these measurements reveal any deviation with respect to the standard model predictions.

INTRODUCTION

The Tevatron p p collider at Fermilab operates with a center-of-mass energy of 1.96 TeV. This review is focused on the search for new physics performed with top quark events in DØ, one of the two multipurpose detectors located on the Tevatron. It presents three updated or new DØ results.

SEARCH FOR W → tb RESONANCES WITH LEFT-AND RIGHT-HANDED COUPLINGS TO FERMIONS

Many models of physics beyond the standard model (SM) predict the existence of additionnal charged bosons, generally called W , that are more massive than the W boson of the SM. Independent of specific models, the most general, lowest-dimension lagrangian for the interaction of a W boson with fermion fields f is given by [1]

L = V ij g w 2 √ 2 fi \ µ (a R ij (1 + \ 5 )+a L ij (1 -\ 5 ))W µ f j +h.c., (1)
where a L/R ij are the left/right-handed couplings of the W boson to the fermion doublet f i and f j and g w is the weak coupling constant of the SM. If the fermions are quarks, the V ij are the element of a 3x3 identity matrix.

A search for a W boson that decays to a top quark and an anti-bottom quark (or charge conjugates) has been performed by the DØ collaboration using 2.3 fb -1 [2]. The top quark decays to Wband the W boson is required to decay to eƒ or µƒ. Thus the final state contains an electron or muon, missing transverse momentum ( / E T ) from the undetected neutrino, and two jets from the fragmentation of the two b-quarks. The selection is analogous to the single top selection [3]. The dominant backgrounds arise from W + jets production and from t t pairs.To improve discrimination multivariate discriminants based on boosted decision trees are trained. No significant deviation from SM predictions is found and limits are set on the production cross-section times branching fraction for such W bosons. For the first time they are translated into limits for arbitrary combination on left-and right-handed gauge couplings. Each of the combinations of a L , a R and M(W ) is considered as a model. Values for any two of the three parameters a L , a R and M(W ) are assumed and the cross section limit is interpolated in the third parameter value.

SEARCH FOR A FOURTH GENERATION t QUARK

A search for pair production of a fourth generation t quark and its antiparticle, followed by their decays to a W boson and a jet, based on an integrated luminosity of 5.3 fb -1 has been performed by the DØ collaboration [4]. Events with one isolated muon or electron, with high transverse momentum, a large imbalance in transverse momentum and at least four jets corresponding to events in which one of the W bosons decays to quarks are selected. The two main SM processes that produce such events are t t and W + jets production. The third most important source of events arises from mismeasured multijet events in which a jet is misidentified as an electron or a muon from heavy flavor decay appears isolated. Two-dimensional histograms of H T , the scalar sum of / p T and of the transverse momenta of all jets and the charged lepton, versus m fit , the mass of the t quark reconstructed with a kinematical fit to the t t → ƒbq q b, are used to test for the presence of signal in data and to compute 95 % C.L. upper limits on the t t production Observed and expected upper limits and predicted values for the t t production cross section as a function of the mass of the t' quark. The shaded regions around the expected limit represent the ± 1 and ± 2 standard deviation bands. cross section as a function of mass. Figure 2 shows the resulting cross section limits compared to the limits expected in the absence of t t production and to the predicted NLO t' pair production cross section as a function of the t mass. t t production for t quark mass values below 285 GeV are excluded at 95 % C.L.

SEARCH FOR FLAVOR CHANGING NEUTRAL CURRENTS IN DECAYS OF TOP QUARKS

A search for flavor changing neutral currents (FCNC) in decays of top quarks based on an integrated luminosity of 4.1 fb -1 been performed by the DØ collaboration [5]. FCNC allow for transitions between quarks of different flavors but same electric charge. As they are highly suppressed in the SM, FCNC are sensitive indicators of physics beyond the SM. The search has been performed in top pair production, where either one or both of the top quarks decay via t → Zq or their charge conjugate. We assume that the t → Zq decay is generated by an anomalous FNCN term added to the SM lagrangian:

L FCNC = e 2 sin ¡ W cos ¡ W t\ µ (v tqZ -a tqZ \ 5 )qZ µ + h.c., (2)
where q, t, and Z are the quantum fields for up or charm quarks, top quarks, and for the Z boson respectively, e is the electric charge, ¡ W the Weinberg angle, and v tqZ and a tqZ are dimension-4 vector and axial-vector couplings as defined in [6]. For the first time, the search is performed in channels where W and Z bosons decay leptonically, giving rise to a final state with three charged leptons (e or µ), / E T and zero, one or two jets. It provides a distinct signature with low background albeit at the cost of statistical power. Pair of electrons or muons with opposite electric charges are used to identify the Z boson decay. The main backgrounds arise from SM WZ production, ZZ and t t. In events with more than one jet, the invariant mass m reco t is reconstructed from the 4-momenta of the jet and the identified Z boson. As no deviation to SM is observed, limits on the branching ratio B(t → Zq) are obtained and converted to limits at the 95 % C.L. on the FCNC vector v tqZ and axial-vector a tqZ couplings as defined in Eq. ( 2) using the relation given in [6]. This can be done for any point in the (v tqZ , a tqZ ) parameter space and for different quark flavor. Assuming only one non-vanishing v tqZ coupling (a tqZ = 0) we derived an observed (expected) limit of v tqZ < 0, 19(< 0.21) for m top = 172.5 GeV. Figure 3 shows current limits from experiments at the LEP, HERA, and Tevatron colliders as a function of the FCNC coupling £ tu\ (defined in Ref. [6]) and v tqZ for m top = 175 GeV.

FIGURE 1 .

 1 FIGURE 1. (a) Contour plots of 95 % C.L. lower limits on m(W ) in the (a L , a R ) plane, and (b) 95 % C.L. upper limits on the coupling a L in the (a R , M(W )) plane.

Figure 1 (

 1 a) shows contours of lower limits for the W mass in the (a L , a R ) plane, while Fig. 1(b) shows contours of upper limits for the coupling a L in the (a R , M(W )) plane. In the case of M(W ) > m(ƒ R ), M(W ) < 863(885) GeV are excluded at 95 % C.L. for purely left(right)-handed couplings, and M(W ) < 916 GeV if both left-and righthanded couplings are present. The limit for right-handed coupling improves to 890 GeV if M(W ) < m(ƒ R ).

FIGURE 2 .

 2 FIGURE 2.Observed and expected upper limits and predicted values for the t t production cross section as a function of the mass of the t' quark. The shaded regions around the expected limit represent the ± 1 and ± 2 standard deviation bands.

1 FIGURE 3 .

 13 FIGURE 3. Upper limits at the 95% C.L. on the anomalous £ tu\ and v tqZ couplings assuming m top = 175 GeV. Limits obtained at LEP by the L3 experiment, at HERA by the ZEUS experiment , and at the Tevatron by CDF are also shown. The region above or to the right of the respective lines is excluded.

SUMMARY

This contribution reports the most recent results on searches for new physics in top decays at DØ. No significant data excess has been observed and the results have been interpreted as 95 % C. L. exclusion limits.


Aurélia Fraysse
email: fraysse@lss.supelec.fr

Thomas Rodet
email: rodet@lss.supelec.fr

A GRADIENT-LIKE VARIATIONAL BAYESIAN ALGORITHM

Keywords: Variational Bayesian, infinite dimensional optimization, sparse reconstruction

In this paper we provide a new algorithm allowing to solve a variational Bayesian issue which can be seen as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. Another important part is the application of our algorithm to a class of linear inverse problems where estimated quantities are assumed to be sparse. Finally, we compare performances of our method with classical ones on a tomographic problem. Preliminary results on a small dimensional example show that our new algorithm is faster than the classical approaches for the same quality of reconstruction.

INTRODUCTION

The recent advances of information technologies have widely increased the size of data involved in reconstruction problems. Simultaneously, signal processing techniques have allowed to overcome instrumentation limitations, creating hence new theoretical challenges. In particular, the size of datasets collected nowadays can be very large. There is therefore a need for reconstruction methods for large dimensional inverse problems.

A classical approach when dealing with these ill posed problems is to introduce additional information. The Bayesian methodology involved in this paper consists in a modelisation of sources as probability density functions, see for instance [START_REF] Demoment | Image reconstruction and restoration: Overview of common estimation structure and problems[END_REF] for details. This approach allows the development of unsupervised methods, where the so called hyperparameters, i.e. parameters of the model, are adjusted automatically to tune the weight between the a priori information and the information coming from the data. We call these methods "fully Bayesian" as they consist in a construction of a posterior distribution of parameters of interest and of hyperparameters. In practice, most of "fully Bayesian" approaches use Markov Chain Monte Carlo (MCMC) [START_REF] Robert | Monte-Carlo Statistical Methods[END_REF] algorithms to estimate the posterior mean. For instance, in the case of deconvolution problems, where the covariance matrix is easily invertible, efficient samplers can be developed and this method can easily be handled. So there are many MCMC approaches that developed fully Bayesian [START_REF] Giovannelli | Unsupervised bayesian convex deconvolution based on a field with an explicit partition function[END_REF]. However, in general, the use of MCMC is limited by the lack of an effective sample of correlated vectors.

Therefore D. MacKay proposed in 1995 an alternative methodology, the so called variational Bayesian method [START_REF] Mackay | Ensemble learning and evidence maximization[END_REF]. The main idea of this method is to approximate the posterior distribution by a separable density. Even if it gives approximate solutions, this method could be more efficient that MCMC in large dimensional cases, especially when the covariance matrix is no longer invertible. Indeed, as the calculations are analytical, the rate of convergence is much better than for the MCMC approaches. This methodology is applied in lot of areas: sources separations using ICA [START_REF] Choudrey | Variational Methods for Bayesian Independent Component Analysis[END_REF], deconvolution [START_REF] Chantas | Variational Bayesian image restoration based on a product of t-distributions image prior[END_REF], recursive methods [START_REF] Smidl | Variational bayesian filtering[END_REF]. However, as we will see later, variational Bayesian method leads to an implicit solution. Hence iterative methods are used to approximate this solution. And classical iterative methods used in this context are often too heavy to be efficient for large dimensional dataset.

The main contribution of this paper is to define an iterative algorithm able to provide, in few iterations, a close approximation of the solution of the variational Bayesian problem. The original idea is to adapt a classical finite-dimensional optimization algorithm, the gradient descent method [START_REF] Nocedal | Numerical Optimization. Series in Operations Research[END_REF], to the space of probability distributions. Another contribution of this paper is the application of our method to a class of linear inversion problems involving sparse prior information. As an example, we apply this new algorithm to a classical problem of tomography.

In section 2 we recall the classical variational Bayesian approach whereas in section 3 we introduce our algorithm. Section 4 gives an application of this method on a linear problem with sparse information illustrated in section 5. Finally, Section 6 concludes the paper.

BAYESIAN VARIATIONAL METHODS

We first introduce the key principle of the variational Bayesian method presented in [START_REF] Choudrey | Variational Methods for Bayesian Independent Component Analysis[END_REF]. This Bayesian method is mainly used for ill-posed inverse problems where the posterior distribution takes intricate forms. The main idea is to approximate the true posterior by separable distributions, close to this posterior in the sense of the Kullback-Leibler divergence. This approximation step turns the estimation problem as an optimization paradigm which enlarges the range of validity of Bayesian methods in terms of complexity of the inverse problem.

In the following we denote by Y ∈ R M the M dimensional vector containing the data information whereas W ∈ R N represents the vector of hidden variables to be determined. We assume that W is random with a known distribution p(W), the a priori distribution. The main challenge is to determine the corresponding posterior distribution p(W|Y). Note that even for a simple a priori distribution, the posterior distribution can have an intricate form. We thus have to approximate it by a separable probability density q.

To determine this approximating law, we first consider the loglikelihood of data which can be written, see [START_REF] Choudrey | Variational Methods for Bayesian Independent Component Analysis[END_REF], as:

log p(Y) = F (q(W)) + KL[q(W)||p(W|Y))], (1)
where KL[q(W)||p(W|Y)) is the Kullback-Leibler divergence between the approximate probability density function (pdf) q and the posterior pdf. In this case,

F (q(W)) = q(W) log p(Y, W) q(W) dW, (2)
is the "negative free energy". As log p(Y) is independent of the approximating density q, minimizing the Kullback-Leibler divergence is obviously equivalent to maximize this negative free energy. The objective of variational Bayesian methods is thus to find

q opt = arg max q F (q(W )). (3)
The negative free energy can also be written as

F (q(W)) = log p(Y, W) q(W) + H(W), (4)
where H(W) is the entropy of W under the distribution q, whereas

log p(Y, W) q(W) = log(p(Y, W))q(W)dW. (5)
represent the expectation of log p(Y, W) under the distribution q(W). Note that as KL is convex, Eq. ( 1) ensures that F is concave relatively to the approximating probability density function q(W), thus we have to solve a convex infinite dimensional optimization problem.

Assuming that q is a separable pdf, i.e. q(W) = i qi(wi), we can obtain an analytic form for qi(wi) (see [START_REF] Choudrey | Variational Methods for Bayesian Independent Component Analysis[END_REF] for details on the variational calculus ):

qi(wi) = 1 Ki exp log p(Y, W) j =i q j (w j ) . (6)
Although this solution is obtained analytically, Eq. ( 6) clearly does not have an explicit form. This solution is hardly tractable in practice, and is thus approximated thanks to iterative methods. These methods impose the use of conjugate prior to obtain a posterior law belonging to a known family. In this context, optimizing the posterior turns out to an optimization of its distribution parameters. As in Eq. ( 6) the calculus of qi imposes the knowledge of all qj for j different from i, this optimization is either performed alternatively or by groups of coordinates, by storing the corresponding covariance matrix.

However, this method increases considerably the computation time. To reduce this drawback, we can only perform the optimization algorithm by group of coordinates. This approach reduces the number of iterations but induces to store and invert a large correlation matrix. Hence for large dimensional problems these methods are not efficient in practice. Our purpose is thus to solve the functional optimization problem given by the Bayesian variational method more efficiently than the approaches induced by Eq. ( 6).

THE PROPOSED ALGORITHM

The optimization problem involved in variational Bayesian method is an infinite dimensional concave problem. It would therefore be convenient to determine the approximating density thanks to classical optimization algorithms, such as the gradient descent method. This is this method which is employed hereafter. However, we have to pay a particular attention to the fact that we stand in an infinite dimensional non-vector space: the space of probability density functions. There are two ways to understand this issue. The first one is to consider that we treat a subspace of the L 1 function space which is an infinite dimensional vector space. In this case the classical gradient descent method is still feasible. However, we thus have to pay a particular attention to the fact that all elements of this subspace have to satisfy f = 1, which induces a projection step at each iteration. The second approach, developed here, is to consider that we stand in a subspace of the probability measures space. The main advantage is that the normalization step is no longer necessary. The main drawback is that a measure space is no longer a vector space (see [START_REF] Billingsley | Convergence of probability measures[END_REF] for details). We thus have to adapt the gradient descent method in this case, taking the structure of the space into account.

Let us define the proposed method. Assume that for k ≥ 0, {q k 1 , . . . , q k N } are constructed and that q k (W) = q k i (wi). As we stand in the space of probability measures, the following step must give a probability density on R N , absolutely continuous with respect to q k dλ, λ being the Lebesgue measure on R N . Such a condition is satisfied, thanks to the Radon-Nikodym theorem, see [START_REF] Rudin | Real and complex analysis[END_REF] for instance, if we consider

q k+1 = hq k (7)
where h ∈ L 1 (q k ) is a positive separable function. As in the gradient descent algorithm, this function h is based on the Gateaux derivatives of F at q k . In order to ensure that h is a positive integrable function we choose to take

h(W) = exp(α∇F (q(W))). (8)
where ∇F stands for the Gateaux derivative of F whereas α > 0 is the algorithm step-size. We take this form for h and we choose α small enough to ensure that the functional F increases at each iteration. Furthermore a calculus similar to those of [START_REF] Choudrey | Variational Methods for Bayesian Independent Component Analysis[END_REF] shows that ∀i = 1, . . . , N ∂F ∂qi = log p(Y, W)

j =i q k j (w j ) -log qi -1. This entails hi(wi) =   1 Ki exp log p(Y, W) j =i q k j (w j ) q k i   α (9)
= q r i (wi)

q k i (wi) α ,
where q r i (wi) = 1 K i exp log p(Y, W) j =i q k j (w j ) is an intermediate density measure.

We thus define q k+1 as q k+1 (W) = q k (W)

  i 1 Ki exp log p(Y, W) j =i q k j (w j ) q k i   α = q k (W) q r (W) q k (W) α . (10)
This algorithm allows to minimize jointly all (qi) unlike the classical Bayesian Variational algorithm. Moreover, the stepsize α can be chosen in order to optimize the convergence rate. Note that with a logarithmic scale we retrieve the classical updating equation of the gradient descent method.

APPLICATION TO SPARSE LINEAR PROBLEMS

In order to have a better understanding of the algorithm defined in section 3, we show how it can be applied to linear inverse problems.

The model

We treat in this section the classical linear problem:

y = Hx + b, ( 11
)
where H is a matrix in MN×M whereas b ∈ R M is a Gaussian white noise. Here the parameter vector X is assumed to be separable. Concerning the prior distribution we choose to take sparsity into account by considering that the distribution of X is a separable Student-t distribution. Indeed, Student-t distributions is a large class of distributions depending on a parameter. For small values of this parameter, they are heavy-tailed distributions, see for instance [START_REF] Grosswald | The student t-distribution of any degree of freedom is infinitely divisible[END_REF] for details. In the following, we use the fact that a Student-t distribution can be modelised as a Gaussian Scale Mixture, that is a Gaussian distribution with an inverse variance given by a hidden variable following a Gamma law, Gamma( a 2 , a 2 ). Thus, for every i = 1, . . . , N , we take

p(xi) = R + √ zi (2π) N/2 |σ 2 1 | 1/2 e - z i x 2 i 2σ 2 1 ( a 2 ) a/2 z a/2-1 i e -az i 2 Γ( a 2 )
dzi.

Hence, we choose to solve an extended problem which takes the hidden vector Z into account. Thanks to this rewriting, the Student-t distribution is conjugate with the Gaussian likelihood.

In this setting, one can easily check that the joint posterior distribution is given by

p(x, z|y) ∝ exp - y -Hx 2 2σ 2 b * i √ zi σ1 exp - zix 2 i 2σ 2 1 ( a 2 ) a/2 z a/2-1 i e -az i 2 Γ( a 2 ) . (12)
This posterior distribution is not tractable analytically due to two main drawbacks. The first issue is the link between X and Z, which is solved by the classical variational Bayesian approach. The second one occurs when the dimension of the vector X increases. In this case, the correlation matrix is too large to be inverted efficiently. This issue is solved by our algorithm presented in section 3. Details are exposed hereafter.

Variational Bayesian algorithm

In this context we apply the algorithm introduced earlier, by taking W = (X, Z). We want to approximate (12) by separable laws, thus by a probability distribution

q(W) = q(X, Z) = i qi(xi)qi(zi),
which maximizes (4).

As we can see in (12), for i = 1, . . . , N , the posterior law of Xi is Gaussian whereas the posterior law of Zi is Gamma. Therefore we determine X thanks to our method and we update afterward the parameters of Z. We choose to initialize our approximating laws by taking q 0 i (xi) as a Gaussian probability density function and the approximate law q0 i (zi) as a Gamma one. Thus, for i = 1, . . . , N we take:

q 0 i (xi) = N (m0(i), σ 2 0 (i)) q0
i (zi) = Gamma(a0, b0). As mentioned in part 2, from the conjugate hypothesis, at each iteration, q k i stays a Gaussian distribution whereas qk i stays a Gamma law. At the next step, the density of q k+1 i which depends of the step size α, is computed with Eq. [START_REF] Rudin | Real and complex analysis[END_REF]. We see that, for i = 1, . . . , N ,

q k+1 i (α) = q k i q r i q k i α
is still a Gaussian law with variance:

σ 2 k+1 (i) = σ 2 r (i)σ 2 k (i) σ 2 r (i) + α(σ 2 k (i) -σ 2 r (i))
where

σ 2 r (i) = (H T H)[i, i] σ 2 b + a k (i) b k (i)σ 2 1 -1 (13)
and the mean of

q k+1 i (α) is m k+1 (i) = m k (i)σ 2 r (i) + α(mr(i)σ 2 k (i) -m k (i)σ 2 r (i)) σ 2 r (i) + α(σ 2 k (i) -σ 2 r (i))
, with

mr(i) = σ 2 r (i) × H T y -(H T H -diag(H T H))m k σ 2 b i
(14) Performances of this algorithm strongly depend on the step size α. For a fixed α small enough, this algorithm indeed converges. However, in order to increase the speed of convergence, we choose to determine an approximation of the optimal step size αopt thanks to a Taylor expansion of our functional. Finally for every i = 1, . . . , N , we take q k+1 i = q k+1 i (αopt). Concerning the approximation of qi we keep the standard variational Bayesian method. We obtain a Gamma function with updating equations:

a k+1 (i) = a 2 + 1 2 , ( 15
) b k+1 (i) = m 2 k (i) + σ 2 k (i) 2σ 2 1 + a 2 . (16)
5. RESULTS

Simulation parameters

In this section we emphasize our approach by comparing it with classical Bayesian methods, i.e. MCMC approach and classical variational Bayesian (VB), and with a classical non bayesian reconstruction method, the filtered Back Projection (FBP method). We choose to treat the linear problem given by Eq. ( 11) with a non invertible matrix H coming from a tomographic problem. From the limitations of MCMC approach, we solve a relatively small inverse problem (image 64 × 64 = 4096 unknowns). The test image is given by a sparse phantom, composed of 7 peaks with a magnitude between 0.5 and 1 (see Fig. 2(a)). We have simulated data in parallel beam geometry. These projections are collected from 32 angles, uniformly spaced over [0, 180[. Each projection is composed of 95 detector cells. We add a white Gaussian noise (iid) with standard deviation equal to 0.3 (see Fig. 1). Data have thus a relatively bad signal to noise ratio and the number of unknowns is larger than the number of data, which leads to an ill-posed inverse problem.

Results and discussion

All the iterative approaches are initialized with a zero mean and a variance equal to one, and the hyper-parameters σ 2 b , σ 2 1 and a are respectively fixed to 1, 0.05 and 0.1. The original image and its different reconstructions are summed up on Fig. 2. A comparison of Fig. 2 (b) with 2 (c), 2 (d) and 2 (e) clearly shows that the analytical inversion of the Radon transform perform using the Filtered Back Projection (FBP) algorithm is less robust to noise than Bayesian approaches. Asymptotically, in Bayesian cases theoretical results are favorable to the MCMC approach, as it does not need any approximation. In practice, the number of samples is too small to fit with asymptotic results of MCMC method, which explains the bad reconstruction observed in Fig. 2(c). Finally, our approach (see Fig. 2(e)) has the same reconstruction quality than the classical variational Bayesian approach (see Fig. 2(d)). However when we compare the execution time (see Tab. 1), we see that our approach is 5 time faster than the VB approach and 370 faster than the MCMC approach for this small inverse problem. Moreover this ratio increases with the size of the problem as both MCMC and classical variational Bayesian need the inversion of a covariance matrix at each iteration. It is not the case of our algorithm. Thanks to this benefit, large dimensional problems can be solved by our fully Bayesian approach.

Fig. 1 .

 1 Fig. 1. Data collected : sinogram composed of 32 angles and 95 detector cells.

Table 1 .

 1 Computing time (s).

	method	FBP	VB	our approach MCMC Gibbs
	CPU time (s) 0.05 586.20	103.55	37079.50

CONCLUSION

In this paper, we have defined a new iterative algorithm based on the descent gradient principle in the space of probability densities. We have also shown how this algorithm can be implemented in the context of variational Bayesian methods. The main interest of this algorithm is that it converges faster than the classical Bayesian methods and allows an use on large dimensional datasets. A small tomographic application allows us to compare our method with classical ones. We see that even in small cases, performances of our algorithm can be better than classical ones. Furthermore its linear structure simplifies an use on large dimensional problems.