Francesca Barigozzi
email: francesca.barigozzi@unibo.it.

Izabela Jelovac
email: izabela.jelovac@cnrs.fr.

David Bardey

Paula Gonzalez

Robert Nuscheler

Lorenzo

Research funding and price negotiation for new drugs *

Keywords: Pharmaceutical innovation, drug prices, negotiation, basic research, applied research Pharmaceutical innovation, drug prices, negotiation, basic research, applied research. JEL codes. D8

Pharmaceutical innovations result from the successful achievement of basic research, produced by an upstream lab, and applied research, produced by a downstream lab. We focus on the negotiation process to finance basic research by setting public and private grants and to agree on the final price of a new drug. We show that exclusive funding of basic research is desirable. To increase consumers' surplus and reduce negotiated prices for new drugs, basic and applied research should be integrated if the lab producing applied research has a relatively large bargaining power. When instead the health authority has the larger bargaining power, integration with the producer of basic research increases negotiated prices for new drugs and should be avoided, unless the gain in bargaining power after the integration is extremely high.

Introduction

Pharmaceutical innovations result from the successful achievement of basic and applied research. Basic research generally precedes applied research, which makes use of the fundamentals from basic research to develop tradable innovations and, doing so, translates basic research into operational medical knowledge. Applied research mostly lies in the hands of private companies, precisely because they lead to tradable innovations, while basic research is traditionally financed by the government or is developed in the public sector. Aghion et al. (2008) provides a powerful argument to justify public early-stage research and private applied research. They show that, by serving as a pre-commitment mechanism that allows scientists to freely pursue their own interests, academia can be indispensable for early-stage research. At the same time, the private sector's ability to direct scientists towards higher-payoff activities makes it more attractive for later-stage research. Gonzalez et al. (2016) provide another interesting argument to discuss the pros and cons of private research. They distinguish between breakthrough and incremental innovations. They show that pharmaceutical firms' incentives for conducting R&D activities searching for breakthrough drugs are inferior to those socially optimal and that firms devote too many resources to R&D activities that lead to incremental innovations. But the authors disregard the different roles played by basic and applied research labs.

Nowadays, private forms of basic research are emerging so that basic research takes place no more only in public universities and institutes. In the United States, for example, where basic research was funded mainly by federal government and done mainly at universities and institutes, the government funding has diminished in the 2010s and private funding is increasingly important (see Broad, 2014). Independent spin-offs, startups, joint ventures appear and independent basic research labs are sometimes integrated in the research department of big private corporations such as pharmaceutical firms (see Billette de Villemeur and Versaevel, 2017, among others).

The changing organization of basic research is concomitant with the public debate about the fast rising prices of innovative drugs. It is not our goal to question the patent system and the corresponding market power for the innovators. However, the existence of public insurance for drug consumption justifies this public concern for such rising prices. In 2015, 118 US cancer physicians co-signed a commentary in Mayo Clinic Proceedings (Tefferi, Ayalev et al. 2015) to raise concerns about fast-increasing prices of innovative cancer drugs. They report the following: "In 2014, all new US Food and Drug Administration (FDA)-approved cancer drugs were priced above $120,000 per year of use. The average annual household gross income in the United States is about $52,000. For a patient with cancer who needs one cancer drug that costs $120,000 per year, the outof-pocket expenses could be as high as $25,000 to $30,000-more than half the average household income and possibly more than the median take-home pay for a year." They advocate, among other actions, to allow Medicare to negotiate drug prices. Recently, the US administration has adopted the Medicare Prescription Drug Price Negotiation Act of 2017, which "amends title XVIII (Medicare) of the Social Security Act to require the Centers for Medicare and Medicaid Services (CMS) to negotiate with pharmaceutical companies regarding prices for drugs covered under the Medicare prescription drug benefit." Until then, the law prohibits CMS from doing so.

In France, cancer physicians led by Maraninci and Vernant (2016) have followed their US pairs by launching a petition against rising cancer drug prices. Even if in France, drug prices are negotiated and patients are protected against catastrophic out-of-pocket expenses, prices of innovative drugs are high and increasing. The Cour des Comptes (2017), a French administrative court charged with conducting financial and legislative audits of most public institutions, recommends to provide the Comité Économique des Produits de Santé, which is the public authority in charge of drug price negotiations, with increased financial and legal resources to raise its negotiation power. On top of this, Maraninci and Vernant (2016) recommend to take into account not only private R&D expenses when negotiating drug prices, but also the costs of public R&D that contributed to the production of such drugs. In different words, in countries with public provision of health insurance, one should avoid that taxpayers first pay basic research for the development of a new drug and then pay the full price of the new drugs by financing the health authority when the latter purchase the drug from the pharmaceutical firm.

We offer a contribution to this debate by proposing a very simple three-side negotiation model where the health authority, the lab producing basic research and the one producing applied research interact and agree on the investments in basic and applied research and on the final price of the drug. In our interpretation, basic research represents an intermediate input necessary to finalize a new drug so that it is produced upstream. Applied research is instead produced downstream. This implies that the decision about the amount invested in basic research is always made before the decision about the amount invested in applied research. In addition, the downstream lab negotiates with the health authority the price of the drug. The collectivity attaches some social value to the innovation that enters the payoff of the health authority. The monopoly power of the unique pharmaceutical firm (i.e., the downstream lab) is justified by some guaranteed protection (patent) of the innovation. Our setting is suited to describe the current situation in many NHS-type countries: the public sector can actually influence drug prices because it partially or totally pays these prices to the pharmaceutical firms. [START_REF] Aghion | Academic freedom, private-sector focus, and the process of innovation[END_REF] When we analyze the funding of basic research, we consider both public and private research grants, which are also negotiated. The health authority negotiates public grants with the basic research lab and the pharmaceutical firm negotiates private grants with the same lab. We also investigate integration, either private or public, as an alternative to research grants. Private integration reflects the possibility of a merger between the basic research lab and the firm. Public integration illustrates the case of basic research within the public sector.

Surprisingly, we find that the interest of the regulator and of the downstream lab are aligned: both agents are better off when the one with the higher bargaining power is the unique funder of basic research. As an intuition, the timing of the game favors both the health authority and the downstream firm (i.e. the final negotiators), at the expense of the upstream research lab that would prefer to negotiate a grant with the least powerful negotiator.

Moving to integration and considering the likely situation in which the bargaining power does not display very important 'increasing returns to merger', we show that integration with the lab producing basic research impairs the merging decision makers and benefits the decision maker remaining independent. Combining results with and without integration, we observe that the health authority can benefit from the interaction / merger of the two labs and, in the same way, the downstream lab can benefit from the interaction / merger of the health authority and the upstream lab. The intuition is that the decision-makers at the two extremes of the negotiation chain are able to obtain a larger share of the surplus when they leave negotiation with the intermediate decisionmaker (the lab producing basic research) to the stronger one of the two. However, in case of very important 'increasing returns to merger', the previous results are reversed and we are back to the intuitive case in which the merging decision-makers are better off.

Our policy implications are the following. When the bargaining power does not display very important 'increasing returns to merger' and the bargaining power of the health authority (alone) is relatively high, the latter should be the unique funder of basic research but should not integrate with the lab producing it. When instead the bargaining power of the health authority is relatively low, it should leave the full funding of basic research to the downstream lab and would benefit from the integration of the labs producing basic [START_REF] Aghion | Academic freedom, private-sector focus, and the process of innovation[END_REF] The recent legislative change in the US in favor of drug price negotiation is likely to influence prices downwards. This effect would be even stronger with higher Medicare reimbursements. Indeed, considering that drugs are listed for insurance reimbursement only if prices are negotiated, the (public) health insurer and a drug producer would negotiate lower prices the higher the health insurance reimbursements (Jelovac, 2015). Moreover, as mentioned above, the drug price should not only compensate for the applied research undertaken by the pharmaceutical firm itself, but it should also be discounted for all of the basic research outside the firm. and applied research. This strategy assures the highest share of the surplus to the health authority and the lowest negotiated price paid by the health authority to the downstream lab.

The remaining of the note is organized as follows. The next section describes our theoretical setting. Section 3 shows the general case where drug price, private and public grants for basic research are negotiated. Section 4 introduces the possibility of integrating basic research into either the public sector or the private pharmaceutical firm. Section 5 concludes.

The Model

Consider three decision makers: A public health authority, H; a laboratory B producing basic research b; and a lab A producing applied research a. In our interpretation, basic research b represents an intermediate input necessary to finalize a new drug (see also Aghion et al. 2008). Thus, lab B produces upstream whereas lab A produces downstream. This implies that the decision about the amount b invested in basic research is always made before the decision about the amount a invested in applied research. In addition, lab A commercializes the new drug. Hence, it negotiates with the health authority H the final price of the drug P , which the public health authority pays to the lab. Given that lab A sells the new drug in the market, we will refer to it as 'lab A' or 'firm A' interchangeably.

The basic research lab B can negotiate some compensation, X H , with the public health agency, which corresponds to a public research grant. Lab B can also negotiate some compensation X A from firm A, which is equivalent to a private grant or to outsourcing of basic research.

We assume that a and b represent research activities as well as their costs. The value of innovation to the public health authority depends on the investments in both basic and applied research and we denote it V (a, b). We reasonably assume that the variable cost of producing the pharmaceutical innovation is null and the demand for it is part of its social value. The monopoly power of firm A is justified by some guaranteed protection (patent) of the innovation.

The objectives of the health authority, labs A and B are as follows:

W H = V (a, b) -X H -P ; (2.1)
Π B = X H + X A -b; (2.2) Π A = P -X A -a; (2.3)
where X H , X A ≥ 0 and at least one of the two payments is positive, meaning that basic research must be financed. We define β H , β B and β A the negotiation power of the three decision makers. In any bargaining stage, the relative negotiation powers of any two bargaining decision makers must sum at one. The total surplus is thus T S = V (a, b) -a -b. The resulting efficient investment in basic and applied research maximizes this total surplus by equating marginal cost and marginal benefit :

V a (a, b) = V b (a, b) = 1.
We consider that payments X H and X A for basic research and P for applied research, are negotiated after the corresponding investments b and a have been chosen. This guarantees that all participants choose the efficient investments in basic and applied research. This is easy to show along the whole analysis and we decided to skip these steps.

How should basic research be funded?

The timing of the game is as follows. The research lab B first plans her investment in basic research b. Then, lab B simultaneously negotiates a transfer X H with the public health authority H and a transfer X A with the downstream lab A to finance basic research. In a third step, the downstream lab A decides to invest a in applied research. Last, H and A negotiate the final price, P .

Solving the game backwards, we start deriving the final negotiated price, which is the solution to the following Nash Bargaining Program.

max P β H ln(V (a, b) -X H -P ) + β A ln(P -X A -a). (3.1)
The Nash Bargaining Solution provides the following negotiated final price:

P = β H (a + X A ) + β A (V (a, b) -X H ) β H + β A . (3.2)
The negotiated price thus positively depends on the contribution to innovation from firm A, a and X A , and it negatively depends on the contribution from the health authority, X H . If price setting was not regulated, the pharmaceutical firm, owner of a patent for the final innovation, would set a price close to the social value of the innovation net of the public investment in research, so as to fully extract the surplus from pharmaceutical consumption. If instead, the health authority is the unique price decision maker, it would set a price that compensates the pharmaceutical firm for its research investment but leave to the firm only limited profits. The negotiated price lies between the before mentioned two extreme values, at a level that depends on the respective negotiation powers of both negotiating parties. The total surplus from this transaction is shared between the health authority and the downstream research lab according to their respective negotiation power:

W H = β H β H + β A (V (a, b) -X A -X H -a); (3.3)
Π A = β A β H + β A (V (a, b) -X A -X H -a). (3.4)
The total surplus so far still depends on the grants X A and X H , decided two step backwards. In the meanwhile, firm A decides its investment in applied research a so as to maximize its profit and the resulting investment equates marginal cost and marginal benefits:

V a (a, b) = 1.
In the preceding step, lab A and lab B negotiate their transfer X A according to the following Nash Bargaining Program:

max X A β A ln β A β H + β A (V (a, b) -X A -X H -a) + β B ln(X A + X H -b). (3.5)
The resulting best-reply private transfer is:

X A = β A β B + β A b + β B β B + β A (V (a, b) -a) -X H . (3.6)
Simultaneously, lab B and the health authority H negotiate their transfer X H according to the following Nash Bargaining Program:

max X H β H ln β H β H + β A (V (a, b) -X A -X H -a) + β B ln(X A + X H -b). (3.7)
The resulting best-reply private transfer is:

X H = β H β B + β H b + β B β B + β H (V (a, b) -a) -X A . (3.8)
Solving the system of equations given by (3.6) and (3.8) for the transfers X A and X H , we have either X A = 0 or X H = 0. Specifically: Lemma 1 (Exclusive financing of basic research). If the health authority H has a larger bargaining power than the downstream lab (β H > β A ), then X A = 0, i.e., basic research is exclusively financed by the health authority. If the health authority H has a lower bargaining power than the downstream lab (β A > β H ), then X H = 0, i.e., basic research is exclusively financed by the downstream lab.

Given quasilinear payoff functions, we obtain a corner solution: the agent with the largest bargaining power is the only one to finance basic research. If the health authority has a comparative advantage in negotiating with the upstream lab, then basic research is financed by the public body; otherwise basic research is financed by the downstream firm. This depends on the fact that the health authority and the downstream lab negotiate price P in the last stage of the game and basic research is an intermediate input in the innovation process.

We are now going to study the two possible situations in turn.

Basic research financed by the public sector

Here the basic research lab receives a grant from the public health authority only. Given that β H > β A and X A = 0, the decision makers payoff functions simplify to:

W H = V (a, b) -X H -P ; (3.9) Π B = X H -b;
(3.10)

Π A = P -a. (3.11)
Now the payoff functions of the two labs are isomorphic. However the distinction between basic and applied research labs is still captured by the timing: the decision about the amount b invested in basic research is always made before the decision about the amount a invested in applied research. In addition, recall that firm A commercializes the new drug and negotiates with the health authority the final price of the drug P .

Substituting X A = 0, into (3.2) and (3.8), then solving for drug price P and public grant X H , we obtain the following solution holding when β H > β A :

P (1) = a + β H β A (β H + β A )(β H + β B ) (V (a, b) -a -b). (3.12) X (1)
H = β H β B + β H b + β B β B + β H (V (a, b) -a). (3.13) X (1)
A = 0. (3.14)
Superscript (1) refers to the solution to the present case where the lab B receives a grant from the health authority only.

The resulting total expenses for the health authority are:

P (1) + X (1)
H = V (a, b) - (β H ) 2 (β H + β A )(β H + β B ) (V (a, b) -a -b). (3.15)
Each participant then obtain, respectively:

W (1) H = (β H ) 2 (β H + β A )(β H + β B ) (V (a, b) -a -b); (3.16) Π (1)
B = β B β H + β B (V (a, b) -a -b); (3.17) Π (1)
A = β H β A (β H + β A )(β H + β B ) (V (a, b) -a -b). (3.18)
Finally, in the first stage, lab B decides its investment in basic research b so as to maximize its profit and the resulting investment equates marginal cost and marginal benefits:

V b (a, b) = 1.
The comparative statics of the payoff functions show very intuitive relationships between solution and parameters. The only unexpected result relates to the role of the health authority negotiation power with regards to the payoff of firm A. Indeed, we can show that ∂Π

(1) A ∂β H > 0 ⇐⇒ (β H ) 2 < β A β B . (3.19)
Recalling that this case 1 occurs when β H > β A , (β H ) 2 < β A β B implies that the following chain of inequalities holds:

(β H ) 2 < β A β B < β H β B . Hence, for Π (1)
A to be increasing in β H it must be:

(β H ) 2 < β H β B or β B > β H . To sum up, a necessary condition for Π (1)
A to be increasing in β H is that negotiating powers are such that β B > β H > β A (see Lemma 2 below).

Basic research financed by the pharmaceutical firm

Here basic research is funded by the downstream firm only. Given that β H < β A and X H = 0, the decision makers payoff functions simplify to:

W H = V (a, b) -P ;
(3.20)

Π B = X A -b; (3.21) Π A = P -X A -a. (3.22)
Substituting X H = 0, into (3.2) and (3.6), then solving for drug price and funding of basic research X A , we obtain the following solution holding when β A > β H :

P (2) = V (a, b) - β H β A (β H + β A )(β B + β A ) (V (a, b) -a -b). (3.23) X (2)
A = β A β B + β A b + β B β B + β A (V (a, b) -a). (3.24) X (2)
H = 0. (3.25)
The superscript (2) refers to the solution to the present case where basic research is exclusively financed by the downstream lab. The total expenses for the regulator are given by the final negotiated price, P [START_REF] Billette De Villemeur | One Lab, Two Firms, Many Possibilities: On R&D Outsourcing in the Biopharmaceutical Industry[END_REF] in (3.23). Each participant then obtain, respectively:

W (2) H = β H β A (β H + β A )(β B + β A ) (V (a, b) -a -b); (3.26) Π (2) B = β B β B + β A (V (a, b) -a -b); (3.27) Π (2)
A = (β A ) 2 (β H + β A )(β B + β A ) (V (a, b) -a -b). (3.28)
Finally, in the first stage, lab B decides its investment in basic research b so as to maximize its profit and the resulting investment equates marginal cost and marginal benefits:

V b (a, b) = 1.
Again, the comparative statics of the payoff functions show intuitive relationships between solution and parameters except for the effect of the downstream lab's negotiation power β A on the health authority payoff W

H . Proceeding as before, we can show that

∂W (2) H ∂β A > 0 ⇐⇒ (β A ) 2 < β H β B . ( 3
, β A } > min{β H , β A })
, then the payoff of the downstream lab (of the health authority) can increase with the bargaining power of the health authority (downstream lab) when

β H > β A (β A > β H ).
Hence, a 'strong' lab producing basic research has unexpected effects on the negotiation between the health authority and the downstream lab, irrespective of whether the former or the latter decision maker finances basic research. When basic research is financed by the health authority (β H > β A ), the payoff of the downstream lab can benefit from an increase in the negotiation power of the health authority. When instead basic research is financed by the downstream lab (β A > β H ), the payoff of the health authority can benefit from an increase in the negotiation power of the downstream lab, provided that the latter remains low relative to the negotiating power of the upstream lab.

Comparing health expenditures of the public agency H in the two scenarios we observe that H pays P [START_REF] Aghion | Academic freedom, private-sector focus, and the process of innovation[END_REF]

+ X (1)
H when it finances basic research, while it pays P [START_REF] Billette De Villemeur | One Lab, Two Firms, Many Possibilities: On R&D Outsourcing in the Biopharmaceutical Industry[END_REF] when basic research is financed by the downstream lab. Comparing public expenses using (3.15) and (3.23), we show that: P (1) + X

(1)

H ≶ P (2) ⇐⇒ β H ≷ β A , (3.30)
which is precisely the case. We can generalize the comparison as follows:

P (1) + X (1)
H ≶ P [START_REF] Billette De Villemeur | One Lab, Two Firms, Many Possibilities: On R&D Outsourcing in the Biopharmaceutical Industry[END_REF] ⇐⇒ W

(1)

H ≶ W (2)
H ⇐⇒ Π

(1)

B ≷ Π (2)
B ⇐⇒ Π

(1)

A ≶ Π (2)
A ⇐⇒ β H ≷ β A .

(3.31) The previous chain of inequalities shows that the downstream lab is better off when the health authority has high bargaining power and funds basic research. In the same way, the health authority is better off when the downstream lab is 'strong' and negotiates with the upstream lab. Despite the fact that they negotiate price P together and thus have conflicting objectives in the last stage of the game, H and A have aligned payoffs in the whole negotiation.

From the discussions above we conclude that:

Proposition 1. (i)
The objectives of the health authority and of the downstream lab are perfectly aligned: the two agents are better off when the one with the higher bargaining power is the unique funder of basic research. (ii) The objective of the upstream lab is conflicting with that of the health authority and that of the downstream lab. Exclusive funding of basic research is detrimental to the upstream lab. (iii) These outcomes are exacerbated when the upstream lab is the 'strongest' among the three agents.

To understand Part (i) and (ii) of the proposition consider that the final negotiators H and A are determinant as to how basic research is funded, at the expense of the upstream lab. Indeed, when β H > β A , then both the health authority and the pharmaceutical lab are better off with public financing of basic research, while the basic research lab would prefer to negotiate a grant with the least powerful negotiator, i.e., the downstream firm in this case (see inequalities 3.31). Conversely, when β H < β A , then the upstream lab would prefer to negotiate with the health authority. However, both the latter and the downstream lab prefer to have exclusive funding of basic research by the 'stronger' A. The outcome from the three negotiations favors both the health authority and the downstream firm, because of the timing of negotiations. Part (iii) of the proposition is a direct consequence of Lemma 2 stating that

β B > β A > β H (β B > β H > β A
) is a necessary condition such that the payoff of H (respectively A) is increasing in the bargaining power of A (respectively H).

Integration of basic research

In this section, we ask the following questions. Is integration between the health authority and the basic research lab desirable from the perspective of the three decision makers? Should basic research be done in public institutions?

Recall that financing is always efficient in our model so that integration only affects the negotiation process and how the surplus is shared between the different decisionmakers. Integration can be of two different kinds. When the health authority and the upstream lab merge (public integration), basic research takes place in a public lab or in a public funded research center. According to our results in the previous section, we expect integration to be public when β H > β A , or when the health authority finances basic research by exclusively negotiating with the upstream lab (see Lemma 1). When the two labs merge (private integration), the applied research lab acquires the basic research lab. This is relevant when β H < β A , or when the downstream lab finances basic research.

Public integration of basic research

Suppose that β H > β A so that, absent integration, the health authority finances basic research by exclusively negotiating with the upstream lab.

When the public health authority and the basic research lab are integrated, they jointly decide on the investment in basic research and on its internal compensation (that will be such that X H = b). They also negotiate the final price P with the pharmaceutical lab. Therefore, the objectives of the integrated public body and of the downstream lab are as follows:

W HB = V (a, b) -P -b; (4.1)
Π A = P -a. (4.2)
We prefer to simplify our expressions omitting X A . In the unlikely case in which the downstream lab directly contributes to basic research with a payment X A > 0, then the price P paid by the integrated body has to be interpreted as a total price incorporating such contribution. The timing of the game is as follows. The integrated public research entity, HB, decides its investment in basic research, b. Then, lab A decides on her investment in applied research a. Last, the integrated public research entity HB and the downstream lab A negotiate the price of the drug P . Solving the game backwards, we start deriving the final negotiated price, which is the solution to the following Nash Bargaining Program, where β HB is the negotiation power of the integrated public research entity, and β A is the negotiation power of the lab:

max P β HB ln(V (a, b) -P -b) + β A ln(P -a). (4.3)
The Nash Bargaining Solution provides the following negotiated price:

P (3) = β HB a + β A (V (a, b) -b) β HB + β A . (4.4)
That is, the higher the public agency's negotiation power, the smallest the difference between price and private research costs. Conversely, the higher the firm negotiation power, the lower the difference between the price and the value of the innovation net of the public research investment. The total surplus is split between the integrated public research entity and the lab according to their respective negotiation powers:

W (3) HB = β HB β HB + β A (V (a, b) -a -b); (4.5) Π (3)
A = β A β HB + β A (V (a, b) -a -b). (4.6)
In the preceding steps, the public integrated agency and the pharmaceutical lab efficiently decide on their investment, as described before.

Proceeding as before, the Nash Bargaining Solution provides price P as follows:

P (4) = V (a, b) - β H β H + β AB (V (a, b) -a -b). (4.9)
The total surplus is shared between the health authority and the integrated research firm according to their respective negotiation power:

W (4) H = β H β H + β AB (V (a, b) -a -b); (4.10) Π (4) AB = β AB β H + β AB (V (a, b) -a -b). (4.11)
Comparing the health authority payoff W

H with the one obtained without integration when β A > β H (that is, the payoff

W (2)
H in Section 3.2), results in the following lemma: Lemma 4. Suppose that β A > β H so that, without integration, we would observe exclusive financing of basic research by the downstream lab (case 2). With respect to case (2), integration of the two labs implies (i) an increase in the final surplus of the health authority if

β AB < β A + β B + β H β B
β A , (ii) a decrease in the final surplus of the health authority if the opposite condition holds.

As before, points (ii) and (iii) show that the change in the payoffs of the decision makers depends on the bargaining power of the new integrated body. In the likely case (ii), where the bargaining power of the integrated firm is not too high, the health authority is better off after the integration between the two labs.

The intuition is the same as before: integration reduces the number of negotiations. The total surplus is unchanged because efficiency is granted anyway, the only difference is the sharing of the total surplus between the health authority and the integrated labs. The health authority gains from the integration between the two labs if the bargaining power of the integrated pharmaceutical firm is not too high. The integrated lab instead is worse off.

Combining results of Lemmas 3 and 4:

Proposition 2. In the plausible situation in which the bargaining power does not display very important increasing returns to merger, integration with the lab producing basic research impairs the merging decision makers and benefits the decision maker remaining independent.

Proposition 2 complements and extends Proposition 1. The health authority benefits from the interaction / integration of the two labs and, in the same way, the downstream lab benefits from the interaction / integration of the health authority and the upstream lab.

The following directly follows from Propositions 1 and 2:

Corollary 1. In the plausible situation in which the bargaining power does not display very important increasing returns to merger, (i) if β H > β A , the health authority benefits from being the unique funder of basic research but not from integrating with the lab producing it. (ii) If β A > β H , the health authority benefits from leaving the full funding of basic research to the downstream lab and from the integration of the labs producing basic and applied research.

Indeed, in the model a higher share of the surplus for the health authority always goes hand in hand with a reduction of the negotiated price P. Hence the previous corollary takes the perspective of the health authority and indicates the strategy that increases consumers' welfare and reduces the negotiated price paid to the downstream lab.

Corollary 1 provides a new rationale for the public financing of basic research. Our argument focuses on the negotiation process to set public and private grants for basic research and to agree on the final price of a new drug. Even in the absence of efficiency gains, in order to increase consumers' surplus and reduce negotiated prices for new drugs, the two labs should merge if the downstream lab has a relatively large bargaining power (β A > β H ). When instead the health authority is relatively stronger (β H > β A ), integration with the producer of basic research increases negotiated prices for new drugs, unless the gain in bargaining power after the integration is extremely high

(β HB > β H + β B + β A β B β H ).

Conclusion

We presented an extremely simple and parsimonious model of price and research grant negotiations. We disregarded efficiency motives and focused on the bargaining process between the health authority and the downstream lab when basic research is produced by an upstream lab. We show that basic research is financed with public (private) grants if the health authority has more (less) negotiation power than the pharmaceutical firm and that the exclusive financing of basic research benefits both the health authority and the downstream lab. This shows that, in the three-side negotiation analyzed in this note, the 'intermediate negotiator' (i.e. the upstream lab) is always worse off while the payoff of the 'extreme negotiators' (i.e. the health authority and the downstream lab) are fully aligned.

The disadvantaged position of the upstream lab is confirmed in the case of vertical integration. Specifically, the upstream lab looses from integration (either upstream or downstream), unless the bargaining power after integration displays very high 'increasing returns to integration'.

From the point of view of the regulator, results can be interpreted as follows. When the bargaining power does not display very important 'increasing returns to merger' and the bargaining power of the health authority (alone) is relatively high, the latter should be the unique funder of basic research but should not integrate with the lab producing it. When instead the bargaining power of the health authority is relatively low, it should leave the full funding of basic research to the downstream lab and would benefit from the integration of the labs producing basic and applied research. This strategy assures the highest share of the surplus to the health authority and the lowest negotiated price paid by the health authority to the downstream lab.

Our results are specific to the use of negotiations to determine pharmaceutical prices and the grants to finance basic research. In the real world we observe different possible arrangements as for the financing and the production of basic research; however, basic research is mainly financed by the government in many countries or is directly developed in the public sector. In our model, this corresponds to vertical integration between the health authority and the lab producing basic research. Our results suggest that this arrangement increases consumers' surplus and reduces negotiated prices for new drugs only if the bargaining power of the health authority is lower than the one of the firm commercializing the innovation, provided the public contribution to basic research is appropriately accounted for. In our setting, accounting for the public contribution to basic research translates in the explicit negotiation of the public grant X H (which is equal to b in the case of vertical integration between health authority and basic research lab). Unfortunately, in the real world, health authorities do not seem to internalize the public contribution to public research when negotiating prices of innovations, which could in part explain the dramatic increase in drug prices in past decades. [START_REF] Broad | Billionaires with big ideas are privatizing American science[END_REF] The model also highlights some unexpected complementarities between the payoff of the 'extreme negotiators' (i.e. the health authority and the downstream lab) in the negotiation process.

Drug price negotiations have been adopted in many countries and the US has just started expanding their use. Given the dominant position of the US in the international pharmaceutical market, the impact of negotiations on the price of drugs may become more relevant in a near future. The setting we propose in this note offers an appropriate framework to study the effects of different arrangements in the financing of basic research on negotiated prices for new drugs. It shows how public contributions to basic research should be properly taken into account by the regulator when negotiating prices with the downstream lab.

Notice that we are comparing here the final payoff of the decision-maker that is not merging (lab A in this section) with and without vertical integration of the other two decision-makers (H and B in this section). This allows us to reach clear conclusion about who benefits from the integration.

In practice, the regulator seems to behave according to a model in which, when the negotiation for the final price of the drug is tackled, the payment X H is fully disregarded.

The resulting total expenses for the public integrated body are:

The comparison between the firm's payoff without integration when β H > β A (that is, the payoff Π (1)

A in Section 3.1) and Π

(3)

A leads to the following lemma: 2 Lemma 3. Suppose that β H > β A so that, without integration, we would observe exclusive financing of basic research by the health authority (case 1). With respect to case (1), integration of basic research by the health authority implies (i) an increase in the final surplus of the downstream lab if

β H , (ii) a decrease in the final surplus of the downstream lab if the opposite condition holds.

How the payoffs of the decision makers change with integration depends on the bargaining power of the new public body. Specifically, unless β HB increases dramatically and

β H , the downstream lab is better off after the integration of the health authority with the basic research lab. Lemma 3(i) represents the most plausible instance in our view, indicating that the bargaining power of the new public body is larger than the one of the 'stronger' merging agent but not larger than the sum of the bargaining power of H and B.

As an explanation for this counterintuitive result consider that two negotiations were necessary in the case of independent basic research, whereas we have only one negotiation with integration. The total surplus is unchanged because efficiency is granted anyway thanks to the final price negotiation. The only difference is the sharing of the total surplus among two entities, i.e., the integrated public body and the downstream firm, instead of three. The downstream pharmaceutical firm gains from the integration between the health authority and the basic research lab if the bargaining power of the integrated body is not too high. The public integrated body thus obtains a lower share of the total surplus than if basic research was independent.

Private integration of basic research

Suppose now that β A > β H so that, absent integration, the downstream lab finances basic research by exclusively negotiating with the upstream lab.

When both upstream and downstream labs are integrated, the objectives of the regulator and of the integrated labs are as follows:

Π AB = P -a -b.

The labs A and B jointly decide their investments in upstream basic research X A = b first, and then in downstream applied research a. Last, A and B jointly negotiate with H the final price P .


Chahinez Benkoussas
email: chahinez.benkoussas@lsis.org

Patrice Bellot
email: patrice.bellot@lsis.org

Anaïs Ollagnier
email: anais.ollagnier@lsis.org

The Impact of Linked Documents and Graph Analysis on Information Retrieval Methods for Book Recommendation

Keywords: Document retrieval, InL2, language model, book recommendation, PageRank, graph modeling, Social Book Search

A new combination of multiple Information Retrieval approaches are proposed for book recommendation based on complex users' queries. We used different theoretical retrieval models: probabilistic as InL2 (Divergence From Randomness model) and language models and tested their interpolated combination. We considered the application of a graph based algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of CLEF Labs precisely Social Book Search track. We established a specific strategy for queries searching after separating query set into two genres "Analogue" and "Analogue" after analyzing users' needs. Series of reranking experiments demonstrate that combining retrieval models and exploiting linked documents for retrieving yield significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

I. INTRODUCTION

There has been much work both in the industry and academia on developing new approaches to improve the performance of retrieval and recommendation systems over the last decade. The aim is to help users to deal with information overload and provide recommendation for books, restaurants or movies. Some vendors have incorporated recommendation capabilities into their commerce services, such as Amazon.

Existing document retrieval approaches need to be improved to satisfy users' information needs. Most systems use classic information retrieval models, such as language models or probabilistic models. Language models have been applied with a high degree of success in information retrieval applications [START_REF] Song | A general language model for information retrieval[END_REF]- [START_REF] Zhai | Statistical Language Models for Information Retrieval[END_REF]. This was first introduced by Ponte and Croft in [START_REF] Ponte | A language modeling approach to information retrieval[END_REF]. They proposed a method to score documents, called query likelihood in two steps: estimate a language model for each document and then rank documents according to the likelihood scores resulting from the estimated language model. Markov Random Field model, proposed by Metzler and Croft in [START_REF] Metzler | A markov random field model for term dependencies[END_REF] considers query term proximity in documents by estimating term dependencies in the context of language modeling approach. Alternatively, Divergence From Randomness model, proposed by Amati and Van Rijsbergen [START_REF] Amati | Probabilistic models of information retrieval based on measuring the divergence from randomness[END_REF], measures the global informativeness of the term in the document collection. It is based on the idea :"The more the term occurrences diverge from random throughout the collection, the more informative the term is" [START_REF] Robertson | Probabilistic models of indexing and searching[END_REF]. One limit of such models is that the distance between query terms in documents is not considered.

Users' queries differ by their type of needs. In book recommendation, we identified two genres of queries : "Analogue" and "Analogue" that we describe in the following sections. In this paper, the first proposed approach combines probabilistic and language models to improve the retrieval performances and show that the two models act much better in the context of book recommendation.

In recent years, an important innovation in information retrieval is the exploitation of relationships between documents, e.g. Google's PageRank [START_REF] Page | The pagerank citation ranking: Bringing order to the web[END_REF]. It has been successful in Web environments, where the relationships are provided by hyperlinks between documents. We present a new approach for linking documents to construct a graph structure that is used in retrieving process. In this approach, we exploit the PageRank algorithm for ranking documents with respect to users' queries. In the absence of manually-created hyperlinks, we use social information to create a Directed Graph of Documents (DGD) and argue that it can be treated in the same manner as hyperlink graphs. Our experiments will show that incorporating graph analysis algorithms in document retrieval improves the performance in term of the standard ranked retrieval metrics.

Our work focuses on search in the book recommendation domain, in the context of CLEF Labs Social Book Search track. We tested our approaches on collection contains Amazon/LibraryThing book descriptions and set of queries, called topics, extracted from the LibraryThing discussion forums.

II. RELATED WORK

This work is first related to the area of document retrieval models, more specially language models and probabilistic models. The unigram language models are most often used for ad hoc Information Retrieval work but several researchers explored the use of language modeling for capturing higher order dependencies between terms. Bouchard and Nie in [START_REF] Bouchard | Modles de langue appliqus la recherche d'information contextuelle[END_REF] showed significant improvements in retrieval effectiveness with a new statistical language model for the query based on completing the query by terms in the user's domain of interest, reordering the retrieval results or expanding the query using lexical relations extracted from the user's domain of interest.

Divergence From Randomness (DFR) is one of several probabilistic models that we have used in our work. Abolhassani and Fuhr have investigated several possibilities for applying Amati's DFR model [START_REF] Amati | Probabilistic models of information retrieval based on measuring the divergence from randomness[END_REF] for content-only search in XML documents. [START_REF] Abolhassani | Applying the divergence from randomness approach for content-only search in XML documents[END_REF].

There has been an increasing use of techniques based on graphs constructed by implicit relationships between documents. Kurland and Lee performed structural reranking based on centrality measures in graph of documents which has been generated using relationships between documents based on language models [START_REF] Kurland | PageRank without hyperlinks: Structural reranking using links induced by language models[END_REF]. In [START_REF] Lin | Pagerank without hyperlinks: Reranking with pubmed related article networks for biomedical text retrieval[END_REF], Lin demonstrates the possibility to exploit document networks defined by automatically-generated content-similarity links for document retrieval in the absence of explicit hyperlinks. He integrates the PageRank scores with standard retrieval score and shows a significant improvement in ranked retrieval performance. His work was focused on search in the biomedical domain, in the context of PubMed search engine. Perhaps the main contrast with our work is that links were not induced by generation probabilities or linguistic items.

III. INEX SOCIAL BOOK SEARCH TRACK AND TEST COLLECTION

Social Book Search (SBS) task1 aims to evaluate the value of professional and user's metadata for book search on the Web. The main goal is to exploit search techniques to deal with complex information needs and complex information sources that include user profiles, personal catalogs, and book descriptions.

The SBS task provides a collection of 2.8 million book description crawled by the University of Duisburg-Essen from Amazon2 [START_REF] Beckers | Overview and results of the INEX 2009 interactive track[END_REF] and enriched with content from LibraryThing3 , which is an online service to help people catalog their books easly. Books are stored in XML files and identified by an ISBN. They contains information like: title information, Dewey Decimal Classification (DDC) code (for 61% of the books), category, Amazon product description, etc. Amazon records contain also social information generated by users like: tags, reviews, ratings (see Figure 1. For each book, Amazon suggests a set of "Similar Products" which represents a result of computed similarity based on content information and user behavior (purchases, likes, reviews, etc.) [START_REF] Koolen | Overview of the INEX 2014 social book search track[END_REF].

SBS task provides a set of queries called topics where users describe what they are looking for (books for a particular genre, books of particular authors, similar books to those that have been already read, etc.). These requests for recommendations are natural expressions of information needs for a large collection of online book records. The topics are crawled from LibraryThing discussion Forums.

A. InL2 of Divergence From Randomness

We used InL2, Inverse Document Frequency model with Laplace after-effect and normalization 2. This model has been used with success in different works [START_REF] Amati | Probabilistic models of information retrieval based on measuring the divergence from randomness[END_REF]- [START_REF] Guilln | Gir with language modeling and dfr using terrier[END_REF]. InL2 is a DFR-based model (Divergence From Randomness) based on the Geometric distribution and Laplace law of succession.

B. Sequential dependence Model of Markov Random Field

Language models are largely used in Document Retrieval search for book recommendation [START_REF] Benkoussas | Collaborative filtering for book recommandation[END_REF], [START_REF] Bonnefoy | Do social information help book search?[END_REF]. Metzler and Croft proposed Markov Random Field (MRF) model [START_REF] Metzler | Combining the language model and inference network approaches to retrieval[END_REF], [START_REF]A markov random field model for term dependencies[END_REF] that integrates multi-word phrases in the query. Specifically, we used the Sequential Dependence Model (SDM), which is a special case of MRF. In this models co-occurrence of query terms is taken into consideration. SDM builds upon this idea by considering combinations of query terms with proximity constraints which are: single term features (standard unigram language model features, f T ), exact phrase features (words appearing in sequence, f O ) and unordered window features (require words to be close together, but not necessarily in an exact sequence order, f U ).

Finally, documents are ranked according to the following scoring function:

SDM (Q, D) = λT q∈Q fT (q, D)+ +λO |Q|-1 i=1 fO(qi, qi + 1, D) +λU |Q|-1 i=1 fU (qi, qi + 1, D)
Where feature weights are set based on the authors recommendation (λ T = 0.85, λ O = 0.1, λ U = 0.05) in [START_REF] Bonnefoy | Do social information help book search?[END_REF]. f T , f O and f U are the log maximum likelihood estimates of query terms in document D, computed over the target collection using a Dirichlet smoothing. We applied this model to the queries using Indri4 Query Language 5 .

C. Combining Search Systems

Combining the output of many search systems, in contrast to using just a single one improves the retrieval effectiveness as proved in [START_REF] Belkin | Combining the evidence of multiple query representations for information retrieval[END_REF] where Belkin combined the results of probabilistic with vector space models. On the basis of this approach, In our work, we combined the probabilistic model, InL2 with language model SDM. This combination takes into account both the informativeness of query terms and their dependencies in the document collection. Each retrieval model uses different weighting schemes therefore the scores should be normalized. We used the maximum and minimum scores according to Lee's formula [START_REF] Lee | Combining multiple evidence from different properties of weighting schemes[END_REF]. normalizedScore = oldScore -minScore maxScore -minScore

It has been shown in [START_REF] Benkoussas | Collaborative filtering for book recommandation[END_REF] that InL2 and SDM models have different levels of retrieval effectiveness, thus it is necessary to weight individual model scores depending on their overall performance. We used an interpolation parameter (α) that we varied to improve retrieval effectiveness.

V. GRAPH MODELING

In [START_REF] Lin | Pagerank without hyperlinks: Reranking with pubmed related article networks for biomedical text retrieval[END_REF], the authors have exploited networks defined by automatically-generated content-similarity links for document retrieval. We provided document analysis to find new way to link them. In our case, we exploited a special type of similarity based on several factors. This similarity is provided by Amazon and corresponds to "Similar Products" given generally for each book. The degree of similarity depends on social information like: number of clicks or purchases and contentbased information like book attributes (book description, book title, etc.). The exact formula used by Amazon to combine social and content based information to compute similarity is proprietary. The idea behind this linking method is that documents linked with such type of similarity, the probability that they are in the same context is higher than if they are not connected.

To perform data modeling into DGD, we extracted the "Similar Products" links between documents in order to construct the graph structure. Once used it to enrich results from the retrieval models, in the same spirit as pseudo-relevancefeedback. Each node in the DGD represents document (Amazon description of book), and has set of properties:

• ID: book's ISBN
• content : book description that include many other properties (title, product description, author(s), users' tags, content of reviews, etc.)

• M eanRating : average of ratings attributed to the book

• P R : book's PageRank
Edges in the DGD are directed and correspond to Amazon similarity, so given nodes {A, B} ∈ S , if A points to B, B is suggested as Similar Product to A. In the Figure 3

A. Our Approach

The DGD network contains useful information about documents that can be exploited for document retrieval. Our approach is based, first on results of a traditional retrieval engine, then on the DGD network to find new documents. The idea is to suppose that the suggestions given by Amazon can be relevant to the user queries.

Algorithm 1 takes as inputs: D init returned list of documents for each topic by the retrieval techniques described in Section 3, DGD network and parameter β which is the number of the top selected StartingN ode from D init denoted by D StartingN odes . We fixed β to 100 (10% of the returned list for each topic). The algorithm returns a list of recommendations for each topic denoted by "D f inal ". It processes topic by topic, and extracts the list of all neighbors for each StartingN ode. It performs mutual Shortest Paths computation between all selected StartingN ode in DGD. The two lists (neighbors and nodes in computed Shortest Paths) are concatenated after that all duplicated nodes are deleted. The set of documents in returned list is denoted by D graph . A second concatenation is performed between initial list of documents and D graph (all duplications are deleted) in new final list of retrieved documents, D f inal reranked using different reranking schemes.

VI. EXPERIMENTS AND RESULTS

In this section, we describe the experimental setup we used for our experiments. Furthermore, we present the different reranking schemes used in previously defined approaches. We discuss the results we achieved by using the InL2 retrieval model, its combination to the SDM model, and retrieval system proposed in our approach that uses the DGD network.

A. Experiments setup

For our experiments, we used different tools that implement retrieval models and handle the graph processing. First, we used Terrier (TERabyte RetrIEveR) 6 Information Retrieval framework developed at the University of Glasgow [START_REF] Ounis | Research directions in terrier: a search engine for advanced retrieval on the web[END_REF]- [START_REF] Ounis | Terrier Information Retrieval Platform[END_REF]. Terrier is a modular platform for rapid development of large-scale IR applications. It provides indexing and retrieval functionalities. It is based on DFR framework and we used it to deploy InL2 model described in section 4.1. Further information about Terrier can be found at http://ir.dcs.gla.ac.uk/terrier. A preprocessing step was performed to convert INEX SBS corpus into the Trec Collection Format 7 , by considering that the content of all tags in each XML file is important for indexing; therefore the whole XML file was transformed on one document identified by its ISBN. Thus, we just need two tags instead of all tags in XML, the ISBN and the whole content (named text).

Secondly, Indri8 , Lemur Toolkit for Language Modeling and Information Retrieval was used to carry out a language model (SDM) described in section 4.2. Indri is a framework that provides state-of-the-art text search methods and a rich structured query language for big collections (up to 50 million documents). It is a part of the Lemur project and developed by researchers from UMass and Carnegie Mellon University. We used Porter stemmer and performed Bayesian smoothing with Dirichlet priors (Dirichlet prior µ = 1500). In section 5.1, we have described our approach based on DGD which includes graph processing. We used NetworkX9 tool of Python to perform shortest path computing, neighborhood extraction and PageRank calculation.

To evaluate the results of retrieval systems, several measurements have been used for SBS task: Discounted Cumulative Gain (nDCG), the most popular measure in IR [START_REF] Järvelin | Ir evaluation methods for retrieving highly relevant documents[END_REF], Mean Average Precision (MAP) which calculates the mean of average precisions over a set of queries, and other measures: Recip Rank and Precision at the rank 10 (P@10).

B. Reranking Schemes

Two approaches were proposed. The first one (see section 4.3) merges the results of two different information retrieval models which are the Language Model (SDM) and DFR model (InL2). For topic t i , the models give 1000 documents and each retrieved document has an associated score. The linear combination method uses the following formula to calculate final score for each retrieved document d by SDM and InL2 models:

S f inal (d, t i ) = α * S InL2 (d, t i ) + (1 -α) * S SDM (d, t i )
Where S InL2 (d, t i ) and S SDM (d, t i ) are normalized scores. α is the interpolation parameter set up at 0.8 after several tests on the 2014 topics.

The second approach (described in 5.1) uses the DGD constructed from the "Similar Products" information. The document set returned by the retrieval model are fused to the documents in neighbors set and Shortest Path results. We tested many reranking methods that combine the retrieval model scores and other scores based on social information. For each document in the resulting list, we calculated the following scores:

• PageRank, computed using NetworkX tool. It is a well-known algorithm that exploits link structure to score the importance of nodes in a graph. Usually, it was been used for hyperlink graphs such as the Web [START_REF] Page | The pagerank citation ranking: Bringing order to the web[END_REF]. The values of PageRank are given by the following formula.

P R(A) = (1 -d) + d(P R(T 1 )/C(T 1 ) +... + P R(T n )/C(T n ))
Where document A has documents T 1 ...T n which point to it (i.e., Similar products). The parameter d is a damping factor set between 0 and 1 (0.85 in our case). C(A) is defined as the number of links going out of page A.

• Likeliness, computed from information generated by users (reviews and ratings). It is based on the idea that more the book has a lot of reviews and good ratings, the more interesting it is (it may not be a good or popular book but a book that has a high impact).

Likeliness(D) = log(#reviews(D))× r∈R D r #reviews(D)
Where #reviews(D) is the number of reviews attributed to D, R D is the set of reviews of D.

The computed scores were normalized using this formula: normalized score = old score /max score . After that, to combine the results of retrieval systems and each of normalized scores, an intuitive solution is to weight the retrieval model scores with the previously described scores (normalized PageRank and Likeliness). However, this would favor documents with high PageRank and Likeliness scores even though their content is much less related to the topics.

C. Results

We used two topic sets provided by INEX SBS task in 2014 (680 topics). The systems retrieve 1000 documents per topic. We assessed the narrative field of each topic and provided automatic classification of the topic set into 2 genres. Analogue topics (261) in which users give the already read books (generally, titles and authors) to have similar books. In the second genre Analogue (356 topics), users describe their needs by defining the thematic, interested field, event, etc. without citing other books. Notify that, 63 topics are ignored because of their ambiguity.

In order to evaluate our IR methodologies described in sections IV-C, V we performed retrieving for each topic genre individually. The experimental results, which describe the performance of the different retrieval systems on Amazon/Li-braryThing document collection, are shown in Table I.

As illustrated in Table I, the system that combines probabilistic model InL2 and the Language Model SDM (InL2 SDM) achieves a significant improvement for each topic set comparing to InL2 model (Baseline) but the improvement is highest for Analogue topic set where the content of queries are more explicit than the other topic set. This improvement is mainly due to the increase of the number of relevant documents that are retrieved by both systems.

The results of run InL2 DDG PR using the Analogue topic set confirm that exploiting structured documents and performing reranking with PageRank improves significantly performances but in contrast, it lowers the baseline performances when using the Analogue topic set. This can be explained by the fact that Analogue topics contain examples of books (Figure 6) which require the use of graph to extract the similar connected books. Using Likeliness scores (in InL2 DGD MnRtg) to rerank retrieved documents decreases significantly the baseline efficiency for the two topic sets. This means that ratings given by users don't provide any improvement for the reranking performances. Fig. 7: Histograms that demonstrate and compare the number of improved, deteriorated and same results' topics using the proposed approaches for MAP measure. (Baseline: InL2) Figure 7 compares the number of improved, deteriorated and same results' topics between the baseline (InL2) and the proposed retrieval systems in term of MAP measure. The proposed systems based on DGD graph provide the highest number of improved topics compared with the combination of IR systems. More precisely, using PageRank to rerank document produces better results in term of improved topics. This results prove the positive impact of linked structure on document retrieval systems for book recommendation.

The depicted results confirm that we are starting with competitive baseline, suggesting that improvements contribute by combining output retrieval systems and social link analysis are indeed meaningful.

VII. CONCLUSION AND FUTURE WORK

In this paper, we proposed and evaluated approaches of document retrieval in the context of book recommendation. We used the test collection of CLEF Labs Social Book Search track and the proposed topics in 2014 divided into two classes Analogue and Analogue.

We presented the first approach that combines the outputs of probabilistic model (InL2) and Language Model (SDM) using a linear interpolation after normalizing scores of each retrieval system. We have shown a significant improvement of baseline results using this combination.

A novel approach was proposed, based on Directed Graph of Documents (DGD) constructed from social relationships. It exploits link structure to enrich the returned document list by traditional retrieval model (InL2). We performed a reranking method using PageRank and Likeliness of each retrieved document.

In the future, we would like to test our methodology on another test collection, that of the OpenEdition Portal dedicated to electronic resources in the humanities and social sciences. We would like to explore citation links between scientific documents extracted using Bilbo [START_REF] Kim | Automatic annotation of bibliographical references in digital humanities books, articles and blogs[END_REF]. Using the traversal algorithms we will develop a new way to retrieve documents. Another interesting extension of this work would TABLE I: Experimental results. The runs are ranked according to nDCG@10. ( * ) denotes significance according to Wilcoxon test [START_REF] Croft | Organizing and searching large files of document descriptions[END_REF]. In all cases, all of our tests produced two-sided p-value, α = 0.05. be using the learning to rank techniques to automatically adjust the settings of re-ranking parameters.

VIII. ACKNOWLEDGMENT

Fig. 1 :

 1 Fig. 1: Example of book from the Amazon/LibraryThing collection in XML format

Fig. 2 :

 2 Fig. 2: Example of topic, composed with multiple fields to describe user's need(s)

  , we show an example of DGD, network of documents. The DGD network contains 1 645 355 nodes (89.86% of nodes are within the collection and the rest are outside) and 6 582 258 edges.

Fig. 3 :

 3 Fig. 3: Example of Directed Graph of Documents

Fig. 4 :

 4 Fig. 4: Architecture of document retrieval approach based on graph of documents

Algorithm 1 D

 1 Retrieving based on DGD feedback 1: D init ← Retrieving Documents for each t i ∈ T 2: for each D ti ∈ D init do 3: StartingN odes ← first β documents ∈ D ti 4: for each StartingN ode in D StartingN odes do 5: D graph ← D graph + neighbors(StartingN ode, DGD) 6: D SP nodes ← all D ∈ ShortestP ath(StartingN ode, D StartingN odes , DGD) 7: D graph ← D graph + D SP nodes 8: Delete all duplications from D graph 9: D f inal ← D f inal + (D ti + D graph ) 10: Delete all duplications from D f inal 11: Rerank D f inal

Figure 5

 5 Figure5shows an illustration of the document retrieval approach based on DGD feedback.

Fig. 5 :

 5 Fig. 5: Book retrieval approach based on DGD feedback. Numbers on the arrows refer to the instructions in the Algorithm 1

Fig. 6 :

 6 Fig. 6: Examples of narratives in Analogue topics

http://social-book-search.humanities.uva.nl/

http://www.amazon.com/

http://www.librarything.com/

http://www.lemurproject.org/indri/

http://www.lemurproject.org/lemur/IndriQueryLanguage.php

http://terrier.org/

http://lab.hypotheses.org/1129

http://www.lemurproject.org/indri/

https://networkx.github.io/

This work was supported by the French program Investissements d'Avenir FSN and the French Région PACA under the projects InterTextes and Agoraweb.