Gabriel A L Paillard
email: gabriel@virtual.ufc.br

Felipe M G França
email: felipe@cos.ufrj.br

Christian Lavault
email: lavault@lipn.univ-paris13.fr

A distributed wheel sieve algorithm using Scheduling by Multiple Edge Reversal

Keywords: Distributed Algorithms, Prime Numbers Generation, Wheel Sieve, Scheduling by Edge Reversal, Scheduling by Multiple Edge Reversal

This paper presents a new distributed approach for generating all prime numbers in a given interval of integers. From Eratosthenes, who elaborated the first prime sieve (more than 2000 years ago), to the current generation of parallel computers, which have permitted to reach larger bounds on the interval or to obtain previous results in a shorter time, prime numbers generation still represents an attractive domain of research and plays a central role in cryptography. We propose a fully distributed algorithm for finding all primes in the interval [2 . . . , n], based on the wheel sieve and the SMER (Scheduling by Multiple Edge Reversal ) multigraph dynamics. Given a multigraph M of arbitrary topology, having N nodes, an SMER-driven system is defined by the number of directed edges (arcs) between any two nodes of M, and by the global period length of all "arc reversals" in M. The new prime number generation method inherits the distributed and parallel nature of SMER and requires at most n + √ n time steps.

Introduction

This article takes up the generation of prime numbers smaller than a given bound n, by using the wheel sieve distributively. Wheel sieve algorithms can be very efficient to determine the primality of integers which belong to a given finite interval [2 . . . , n], for sufficiently large values of n and when the test of primality is carried out on all numbers of the interval. The paper designs a fully distributed wheel sieve algorithm using scheduling by multiple edge reversal (SMER).

The main purpose of a parallelization of such kind of algorithm is to increase the bounds of the generation of prime numbers, and to reach these bounds in a shorter execution time. The first parallelization of a sieve algorithm was realized in 1987 [START_REF] Bokhari | Multiprocessing the sieve of Eratosthenes[END_REF], who parallelized the sieve of Eratosthenes. This work was motivated by testing a new parallel machine (the Flex/32 ), because this kind of algorithm is ideal to test the performances of a new architecture (of a sequential or parallel machine) as a benchmark.

The sieve of Eratosthenes was the first prime sieving algorithm, and it consists in eliminating all non prime numbers in the interval [2 . . . , n]. First, the algorithm takes the first number of the interval and generates all its multiples (by adding its own value to himself), which are thus eliminated. The next (non eliminated) number is the one (the next prime number) which sieves the interval, and this process is pursued until all intervals has been sieved. Various parallelizations of this algorithm can be found, e.g. in [START_REF] Sorenson | An introduction to prime numbers sieves[END_REF][START_REF] Sorenson | Parberry Two Fast Parallel Prime Number Sieves[END_REF].

However, the main drawback of the practical sieve of Eratosthenes is clearly the fact that it imposes to go through all the entries of the multiples of each number during the sieving process. For instance, if the current entry corresponds to p, then any entry at locations 2p, 3p, 4p is changed to zero, and so on, until the stop criteria is reached, i.e., p 2 > n. The basic sieve of Eratosthenes proceeds in the same way on any other entry. It is easy to see that some numbers will be generated more than once, for example 6 is generated twice (from 2 and 3), and 12 is generated three times (from 2, 3 and 4). The entries that are already zeros are left unchanged, but each entry must nevertheless be checked throughout the sieving process.

The main idea consists then in trying to prevent all numbers from being sieved "too many times". Sieving the multiples of any given number more than once must be avoided, as much as possible. All efficient sieving algorithms are based on similar techniques. So, the complexity O(n ln ln n) of the sieve of Eratosthenes may be somewhat improved by several clever arguments that are carried out by the above methods. Such sieve algorithms achieve a linear [START_REF] Gries | A linear sieve algorithm for finding prime numbers[END_REF][START_REF]Mairson Some new upper bounds on the generation of prime numbers[END_REF][START_REF] Sorenson | An introduction to prime numbers sieves[END_REF] or even a sublinear (step) complexity [START_REF]Mairson Some new upper bounds on the generation of prime numbers[END_REF][START_REF] Pritchard | A sublinear additive sieve for finding prime numbers[END_REF]. So far, the best algorithm known is the "wheel sieve", designed in 1981 [START_REF] Pritchard | A sublinear additive sieve for finding prime numbers[END_REF][START_REF] Pritchard | Explaining the wheel sieve[END_REF]. It requires only O(n/ log log n) steps to find the set of primes in the interval [2, . . . , n] (with n > 4), where each step is either for bookkeeping or an addition with integers at most n. Basically, the algorithm relies on the central result on the number of primes in arithmetic progressions. More precisely, Dirichlet's theorem states that if a, b are coprime integers (gcd(a, b) := (a, b) = 1) and b > 0, then the arithmetic progression a, a+b, a+2b, . . . = a mod (b) contains infinitely many primes [START_REF] Hardy | An introduction to the theory of numbers[END_REF]Thm. 15]. (See [START_REF] Crandall | Prime Numbers: a computational perspective[END_REF] for more details on the analysis of the wheel sieve algorithm.)

The present paper presents a new kind of fully distributed algorithm that finds all primes by sieving in a given interval [1 . . . , n], using the properties of the wheel sieve using the SMER [START_REF] Pritchard | Explaining the wheel sieve[END_REF]. Some other distributed algorithms gen-erating all prime numbers can be found in [START_REF] Cosnard | Génération de nombres premiers en parallèle[END_REF][START_REF] Cosnard | Discovering new parallel algorithms. The sieve of Eratosthenes revisited[END_REF], which use the properties of Dirichlet's theorem. In [START_REF] Paillard | A SMER-based distributed prime sieving algorithm[END_REF] another kind of distributed prime number generation is presented, based only on scheduling by multiple edge reverse framework [START_REF] Barbosa | An atlas of edge-reversal dynamics[END_REF].

In Sect. 2, the wheel sieve algorithm is introduced. In Sect. 3 and 4, the framework of the scheduling by edge reversal (SER) and the scheduling by multiple edge reversal (SMER) mechanisms are both introduced. Sect. 5 is devoted to the design of our distributed algorithm for sieving primes by using the SMERbased method applied to the wheel sieve. The worst-case complexity analysis of the algorithm is achieved in Sect. 6. The final Sect. 7 draws a short conclusion and offers some perspectives.

The Wheel Sieve

The wheel sieve derived from Pritchard's algorithm [START_REF] Pritchard | A sublinear additive sieve for finding prime numbers[END_REF] operates basically by generating a set of numbers that are not multiples of the first k prime numbers. The sieve, applied on the resulting set from the wheel, eliminates the non prime numbers that remain in the set. This is the basic idea of the wheel which were employed as a reduced residue class mod (Π k ), where Π k denotes the product of the first k prime numbers [START_REF] Pritchard | Explaining the wheel sieve[END_REF]. W k denotes the k-th wheel, which is defined as

R(x) = x / 1 ≤ y ≤ x and (y, x) = 1 , (1)
where (x, y) := gcd(x, y) is the greatest common divisor of the integers x and y.

The sieve introduced by the wheel sieve consists basically, after having generated the next wheel W k+1 , in using the prime number k + 1 to sieve the new wheel, generating all its multiples and removing them from W k+1 . For more clarity this new set will denoted S k+1 . It is clear that after S k+1 is obtained the algorithm proceeds to another sieving process, and eliminate the remaining composite numbers. The wheels are thus patterns that are repeated every Π k times. In Fig. 1 we use Π 2 in the first step of the wheel sieve as the product of the first two prime numbers (2 and 3) figured by the small circle; this generates all "pseudo-primes" numbers4 between 1 and the new bound contained in the new wheel W 3 = R(30), that is the actual bound Π 2 multiplied by the next prime p 3 = 5. The next prime is the first number after 1 which belongs to the interval being sieved [START_REF] Pritchard | Explaining the wheel sieve[END_REF] in the second wheel which contains now a value equal to 5.

Within the small wheel, Fig. 2 shows that all the pseudo-prime numbers of the big wheel {1, 5, 7, 11, 13, 17, 19, 23, 25, 29} are generated. In Fig. 3 the process of generating the big wheel is going on, and the number 7 is generated, from the number 1 of the small wheel, which can be interpreted as if we were "rolling" the small circle inside the big one. This means that starting from a wheel W k , we can generate the next wheel W k+1 in a graphical way. The points where the elements of the wheel W k touch the circle featuring W k+1 are the new pseudo-primes. More precisely, W k+1 is defined as

W k+1 = W k ∪ xΠ k + y / x ∈ {1, . . . , p k+1 -1} and y ∈ W k .
(2) Fig. 4 shows the final phase of the wheel sieve, where the multiples of the previous p k+1 (in that case, the number 5) are eliminated from the set R(Π 3 ). According to the definition of W k+1 in Eq. ( 2), we also define

S k+1 = W k+1 \ y × p k+1 / y ∈ W k+1 . (3)
The previous wheel W k is put in the center of the new wheel S k+1 (See Fig. 4).

Then drawing a radius from the center of the small circle containing each pseudoprime number of this circle, each one of the prolongations of such radii touches the big circle at every pseudo-prime that will be eliminated in the new wheel W k+1 . Thus, the prime p k+1 will be put in the set P of all prime numbers. In [START_REF] Paillard | Lavault Le crible de la roue en distribué[END_REF] a distributed version of the wheel sieve is proposed. It is implemented via a message passing interface specification (lam-mpi 7.0.6 library) [START_REF] Burns | An Open Cluster Environment for MPI[END_REF] and the time measurements of a sequential and a distributed implementation of the wheel sieve are compared, together with a sequential and distributed implementation of the sieve of Eratosthenes. In [START_REF] Paillard | A fully distributed prime numbers generation using the wheel sieve[END_REF] a fully distributed version of the wheel sieve is also presented.

Scheduling by Edge Reversal (SER)

Consider a neighbourhood-constrained system composed by a set of processing elements (PEs) and a set of atomic shared resources represented by a connected directed graph G = (V, E), where V is the set of PEs and E the set of its directed edges (or arcs), stating the access topology (directed edges are henceforth refered to as arcs). The latter is defined in the following way: an arc exists between any two nodes if and only if the two corresponding PEs share at least one atomic resource. SER works as follows: starting from any acyclic orientation ω on G, there is at least one sink node, i.e., a node such that all its arcs are directed to itself; all sink nodes are allowed to operate while other nodes remain idle.

This obviously ensures mutual exclusion at any access made to shared resources by sink nodes. After operation, a sink node will reverse the orientation of its arcs, becoming a source and thus releasing the access to resources to its neighbours. A new acyclic orientation is defined and the whole process is then repeated for the new set of sinks. Let ω = g(ω) denote this greedy operation. SER can be regarded as the endless repetition of the application of g(ω) upon G.

Assuming that G is finite, it is easy to see that eventually a set of acyclic orientations will be repeated defining a period of length P . This simple dynamics ensures that no deadlocks or starvation will ever occur since in every acyclic orientation there exists at least one sink, i.e., one node allowed to operate. Also, it is proved that inside any period, every node operates exactly the same constant number of times (denoted M ) [START_REF] Barbosa | Gafni Concurrency in heavily loaded neighborhoodconstrained systems[END_REF].

SER is a fully distributed graph dynamics in which the sense of time is defined by its own operation, i.e., the synchronous behavior is equivalent to the case where every node in G takes an identical amount of time to operate and also an identical amount of time to reverse arcs. Another interesting observation to be made here is that any topology G will have its own set of possible SER dynamics [START_REF] Barbosa | An atlas of edge-reversal dynamics[END_REF].

As an example of SER's applicability, consider Dijkstra's paradigmatic Dining Philosophers problem [START_REF] Edsger | Dijkstra Hierarchical Ordering of Sequential Processes[END_REF] under heavy load, i.e., in the case philosophers are either "hungry" or "eating" (no "thinking" state). Such system can be represented by a set P 1 , . . . , P N of N PEs, in which each PE shares a resource both with its previous PE and its subsequent PE. Thus, taking the original configuration where N = 5 and setting an acyclic orientation over the 5 nodes ring, the resulting SER dynamics where P = 5 and M = 2 is illustrated in Fig. 5.

Operating nodes

Scheduling by Multiple Edge Reversal (SMER)

SMER is a generalization of SER in which pre-specified access rates to atomic resources are imposed to processes in a distributed resource-sharing system represented by a multigraph M = (V, E). In contrast with SER, multiple edges can exist between any two nodes i and j (i, j ∈ V ) in the SMER dynamics: there can exist e i,j ≥ 0 undirected edges connecting nodes i and j; such connected nodes are called "neighbours".

Let r i denote the "reversibility" of node i, as defined in [START_REF] Barbosa | Sharing resources at nonuniform access rates[END_REF]. More precisely, reversibility r i is the number of arcs that shall be reversed by i towards each of its neighbouring nodes at the end of each operation step (access to shared resources). Node i is called a r-sink if at least r i arcs are directed to itself from each of its neighbours. In the SMER dynamics, each r-sink node i operates by reversing r i arcs towards all of its neighbours, next a new set of r-sinks operates in turn, and so on. Similarly to sinks under SER, only r-sink nodes are allowed to operate under SMER. Unlike SER, nodes may operate more than once consecutively in SMER dynamics.

Let µ 0 , µ 1 , . . . be the sequence of orientations produced by SMER over M from the initial orientation µ 0 . As infinite sequences are of our interest (originally motivated by the Dining Philosophers with rates (DPPr) problem [START_REF] Barbosa | Sharing resources at nonuniform access rates[END_REF]), let a ij s denote the greatest multiple of gcd(r i , r j ) of r i and r j , which does not exceed the number of edges oriented from i to j in µ s , s ≥ 0. Orientations µ s , such that f ij = a ij s + a ji s , s ≥ 0, remaining constant as a consequence of the two terms changing by a certain multiple of gcd(r i , r j ) (arcs reversed between neighbouring nodes i and j). Let M i,j be the submultigraph of M induced by a pair of neighbouring nodes i and j. Moreover, let µ ij 0 , µ ij 1 , . . . the sequence of orientations of M i,j produced by SMER from µ ij 0 . The following Lemma 1 states a basic topology constraint towards the definition of the multigraph M. Lemma 1. ( [2, 10]) If max{r i , r j } ≤ e i,j ≤ r i + r j -1, aplication of SMER from µ ij 0 on M i,j solves the instance of DPPr given by neighbouring nodes i and j, r i and r j , if and only if f ij = r i + r j -gcd(r i , r j ). In this case, the sequence µ ij 0 , µ ij 1 , . . . µ ij s (s ≥ 0) includes all orientations of M ij that are legal for i and j given µ ij 0 . n a given arbitrary multigraph M. If no deadlock arises for any initial orientation of the arcs between i and j, then

It is important to know that there is always at least one SMER solution for any target system's topology having arbitrary pre-specified reversibilities at any of its nodes [START_REF] Franc | Scheduling weightless systems with self-timed boolean networks[END_REF]. According to Lemma 1, since e i,j = r i + r j -1, either i or j is in a r-sink condition, independently of µ s , s ≥ 0. It may also be seen that, between all pairs of neighbouring nodes i and j in M, any SMER dynamics produces one unique period, given by the relation P i,j = (r i + r j )/ gcd(r i , r j ) [START_REF] Barbosa | Sharing resources at nonuniform access rates[END_REF][START_REF] Franc ¸a | Neural networks as neighbourhood-constrained systems[END_REF]. This periodic property of SMER can be observed in Fig. 6,where P i,j = 8 and the nodes in M share values that are pairwise coprime integers: such pairs (r i , r j ) have no common divisors (but 1). Operating nodes Arcs to be reversed by operating nodes Arcs that can be reversed in the next steps Fig. 6. An example of SMER, with period Pi,j = 8. Oriented arcs are represented by tokens.

5 The Distributed Wheel Sieve Algorithm using SMER Let M = (V, E) be an arbitrary multigraph having N nodes. For the sake of simplicity, the distributed algorithm is actually assumed to sieve the restricted interval {2} ∪ {odd integers from [3, . . . , n]}, according to the parity of n. Such a SMER-based sieving algorithm is called Semi-SMER; this in contrast with the SMER dynamics described in Section 3, which considers the whole neighbourhood of any given node. The procedure Semi-SMER is designed for any current node process i ∈ V , and it uses local variables, defined as follows:

-The interval I is set to an exclusive value in {1, 7, 11, 13, 17, 19, 23, 29}. For example, when we employ the third wheel W 3 in the algorithm, the interval J is set to a value of Π 3 extended to 30, 60, 90 (2 × 3 × 5, 2 × 3 2 × 5 and 2 × 3 3 × 5). -Neigh i denotes the set of neighbours of process i, and the number of incoming arcs oriented from every j ∈ Neigh i to the current process i is denoted by the variable incoming i [j]; r i [j] denotes the required number of arcs that shall be reversed by i towards every j ∈ Neigh i , independently. Variable r i [j] takes its values in the interval I, and variable r j [i] takes its values in the interval J; e i [j] denotes the number of undirected edges (both outgoing and incoming arcs) connecting every pair of neighbours (i, j) in M (see Fig. 6); a i [j] denotes the number of incoming arcs oriented from each j ∈ Neigh i to i in the initial orientation;

In order to sieve all primes from the interval [2 . . . , n], the only fundamental operations explicitly used in the algorithm Semi-SMER are comparisons, additions and the sending and receiving of messages (arc reversals). Besides, a send-receive event and one comparison operation are assumed to take O(1) number of time slots.

The number of steps required by the algorithm is proportional to the period involved between any two nodes of M during the algorithm. Now, the largest period P i,j follows from Lemma 1 and [START_REF] Barbosa | Sharing resources at nonuniform access rates[END_REF]: P i,j = r i + r j , when (r i , r j ) = 1. Since r i ≤ √ n and r j ≤ n, for any pair of nodes (i, j), the procedure Semi-SMER(n) requires at most n + √ n steps. Similarly, for any current pair of nodes (i, j) of M smaller than √ n, the number of messages exchanged in the while loop is proportional to P i,j × deg i , with deg i = #Neigh i . Hence, if we let P := sup (i,j)∈V 2 P i,j denote the largest period between all pairs (i, j) ∈ V 2 , the maximum message complexity of the algorithm is proportional to P × ∆ N , where 1 ≤ ∆ N ≤ N -1 is the maximum multidegree of M. Finally, the message complexity achieves at most n∆ N + √ n ∆ N . The maximum amount of memory space required per process is O(n) bits.

Conclusion and Perspectives

This paper introduced a totally new kind of SMER-based distributed sieve algorithm that generates all primes in a given interval [2 . . . , n]. Apart from observing that the fundamental operation of the Semi-SMER algorithm is a local comparison, it is also worth noticing that no gcd computation is needed. Moreover, no precomputation is assumed in the Semi-SMER complexity analysis (precomputation would take O n log log Π k , where Π k denotes the product of the first k prime numbers, in the wheel sieve). This approach seems also general enough to compute some of the elementary arithmetic functions in number theory. For instance, via the gcd and inverse, the least common multiple of integers, and various basic multiplicative arithmetic functions, e.g. Euler's totient function φ(n), Möbius function µ(n) and divisor functions: d(n), σ(n), ω(n), Ω(n), etc.

Finally, it stems also from both computer-driven and theoretical results that the number of steps T (n) executed by the algorithm stays always "very close" to the maximal number of steps. More precisely, T (n) = n + √ n -ϕ(n), where ϕ(n) is a positive non periodic arithmetic function with rather small fluctuations when n ≥ 4: we conjecture that ϕ(n) < 5 for "almost every" n ≥ 4. Hence, for every n ≥ 4, ϕ(n) should yield an expected ϕ(n) = 2.47 . . . ± ε n for all 0 ≤ ε n < 1, and the average number of steps required by the algorithm should then be expected to achieve T (n) ≈ n + √ n -2.47 . . ..

Fig. 1 .

 1 Fig. 1. Example of the generation of a wheel W k+1 starting from the preceding wheel W k

Fig. 2 .

 2 Fig. 2. Generation of the new "pseudo-prime" numbers

Fig. 3 .

 3 Fig. 3. Here we can see the generation of another new pseudo-prime (number 7)

Fig. 4 .

 4 Fig.[START_REF] Bokhari | Multiprocessing the sieve of Eratosthenes[END_REF]. The sieve being applied on the new wheel W k+1 to generate S k+1

Fig. 5 .

 5 Fig. 5. SER dynamics for the Dining Philosophers under heavy load.

Numbers that are not multiples of the first k prime numbers.

Acknowledgements

Support has been provided by the Brazilian agency Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico -FUNCAP.

-Process i also maintains the boolean variables rev arc i [j] and end period i [j].

If, at the end of the Semi-SMER period, rev arc i [j] is true for j ∈ Neigh i , then r i [j] and r j [i] are coprime ((r i , rj) = 1). The value of end period i[j] checks whether the Semi-SMER between two nodes ended its execution or not; -P seudoP rimes contains the numbers generated by the extended wheel that consists in the remaining prime numbers.

Procedure WheelSieve-SMER(N) var P i,j = 0 ( P i,j contains the size of the period of the SMER between two nodes ) P; ( P is the set of the first k prime numbers ) P seudoP rimes = 0; p k+1 ; ( p k+1 is initialized with the next prime number ) prime: boolean init true; incoming i [j]: integer; rev arc i [j]: boolean init false; end period i [j]: boolean init false; ( r i [j] and r j [i] are initialized with the values of I and J, respectively. )

EndIf EndWhile P seudoP rimes = P i,j ; end period i [j]: boolean init false; ( r i [j] and r j [i] are initialized with the values of p k+1 and P seudoP rimes, respectively. )

Then P ∪ P i,j ; EndIf Return P ( P is the set of primes in the interval [2 . . . , n] ) end.

As pointed out, if we start initially the sieve with the third wheel there are eight processes, whose values are the numbers {1, 7, 11, 13, 17, 19, 23, 29}, that represent the values of I. The set J is started in accordance with N ; for example, if N = 230, eight processes are needed, one for each value ∈ J. These values represent the multiples of Π 3 = 30. Beginning with these values (we consider that at the beginning, each process knows its identity), and after executing the WheelSieve-SMER, we obtain a set (P seudoP rimes) composed with the values of all periods spread in between the values of I and J. There remains the operation of sieving the P seudoP rimes set with p k+1 in order to obtain P.


François Cluzel
email: francois.cluzel@ecp.fr

Bernard Yannou

Dominique Millet

Yann Leroy

Identification and selection of eco-innovative R&D projects in complex systems industries

Keywords: Eco-design, eco-innovation, complex industrials system, R&D project portfolio, creativity, eco-design strategy wheel

An eco-innovation process is proposed to identify and select at a strategic level and with limited time and resources eco-innovative R&D projects for complex industrial systems. First, an ecoideation stage is performed with a multidisciplinary working group. Then the group qualitatively assesses the projects with a multicriteria approach that takes into account the individual expertise on each topic. An application is proposed on complex electrical substations. It is further validated according to its ability to generate R&D ideas in terms of their quantity, quality, variety and novelty.

Introduction

Environmental concerns become more and more important as the awareness of human activities impact towards environment increases. It results for companies in a need to answer to new environmental requirements and regulations. In this perspective, eco-design permits to consider, manage and improve the environmental performance of products, processes and services.

However if this approach is now recognized and well deployed in competitive mass-consumer goods producers (B-to-C), the situation is not so advanced in B-to-B industries, in particular for complex industrial systems. They are characterized by a very long and uncertain life cycle, a high number of subsystems and components or strong interactions with their environment. The technological and regulatory constraints associated with these systems may slow down the ability to innovate, as reliable and long-term proven technologies are often favoured. Nevertheless the need for eco-innovation is clearly present, as these systems are often associated with strong environmental impacts.

However to eco-innovate on complex industrial systems is a hard task. R&D projects in complex systems industries are often driven by technological and not environmental considerations. These project need to be identified really early in the design process, with few information. On the other hand everybody agrees that environmental-oriented R&D projects are necessary, but the product complexity makes the initiation of an eco-innovation approach tricky. Furthermore only few R&D decision-makers are trained in eco-design or Life Cycle Assessment (LCA) and know how to manage eco-innovation. That is why a simple and effective eco-innovation method is necessary, with little necessary preliminary environmental knowledge and stimulating the collaboration.

Thus we propose in this paper such an intuitive eco-innovation process. It permits to identify at a strategic level and with limited time and resources eco-innovative R&D projects through a multidisciplinary working group. The eco-design strategy wheel [START_REF] Brezet | Ecodesign: A Promising Approach to Sustainable Production and Consumption[END_REF]] is used at the ecoideation stage to comprehend the whole system and share environmental strategies with non-experts people. It is also used to assess the environmental performance of the projects in an original way. Other dimensions like feasibility and customers' value are also qualitatively considered to position the project and select a powerful eco-innovative portfolio with a multicriteria view. The competence levels of the working group members allow weighting their individual evaluations of each project to obtain reliable results. In this way the top management of the company is able to select a pertinent and wellbalanced set of eco-innovative R&D projects that will be performed in the next months or years. The whole eco-innovation process is deployed at Alstom Grid on complex electrical substations. It is further validated according to its ability to generate R&D ideas in terms of their quantity, quality, variety and novelty.

Section 2 presents a literature study about eco-innovation on the one hand and R&D projects evaluation and selection for complex industrial systems on the other hand. It permits to introduce the adapted eco-ideation process in section 3. Section 4 deals with the application of this process at Alstom Grid. Finally, some concluding remarks and perspectives are presented in section 5.

How to eco-innovate in complex systems industries?

Complex industrial systems in eco-design

This paper focuses on complex industrial and technological systems whose specificities have not really been taken into account in eco-design and eco-innovation: these are industrial systems where complexity induces major issues in terms of modelling, prediction or configuration. Adding an environmental dimension to the classical definition of an engineered system, we define a complex industrial system in the sense of eco-design as:

A large-scale system in terms of subsystems and components, mass and resource usage, A system whose life cycle is hardly predictable at the design level in the long-term, in particular its lifetime, upgrades, maintenance and end-of-life, A system whose subsystems may have different life cycles and different obsolescence times, A system in close interaction with its environment (super system, geographic site…), A system supervised by human decisions and management.

Concerning eco-innovation, the main problem of such systems is that the clients' specifications or the regulations and standards largely limit the ability to radically innovate, as only long-term proven technologies are used. Thus the challenge associated to an eco-innovation approach is whether to identify a set of reliable incremental eco-innovative projects, and/or to be able to make possible radical eco-innovations acceptable to the clients.

To deploy an adapted eco-innovation approach, a literature review is first performed on eco-innovation and R&D projects portfolio management. It permits to identify the limits associated to the current practices and to select the most efficient methods for complex industrial systems.

Eco-innovation

Definition

Eco-innovation has been associated with numerous definitions during the last years. Carrillo-Hermosilla et al. lists for example 16 definitions [START_REF] Carrillo-Hermosilla | Diversity of eco-innovations: Reflections from selected case studies[END_REF]. Taking them into account, the authors propose their own: an eco-innovation is "an innovation that improves environmental performance, in line with the idea that the reduction in environmental impacts (whether intentional or not) is the main distinguishing feature of eco-innovation". This includes in particular radical and incremental innovations. Considering the hierarchical nature of complex industrial systems, as well as the fact that radical changes are often hardly acceptable for clients in complex systems industries, we consider that the eco-innovation framework defined by Carrillo-Hermosilla et al. is well adapted to complex industrial systems.

An eco-innovation approach implies two major activities: the identification of eco-innovative ideas (or eco-ideation), and the evaluation and selection of the most promising ideas. These two fields are explored in the next paragraphs. Bocken et al. shows that eco-ideation has not been widely explored and proposes to separately study ideation and eco-design [START_REF] Bocken | Development of an eco-ideation tool to identify stepwise greenhouse gas emissions reduction options for consumer goods[END_REF]]. However, different tools have been designed to support an eco-innovation process. The most known are explained with some details in the next paragraph.

Eco-ideation

Concerning the eco-ideation process in itself, experts groups are largely used through creativity sessions [START_REF] Bocken | Development of an eco-ideation tool to identify stepwise greenhouse gas emissions reduction options for consumer goods[END_REF]]. Researches performed in the last decade have identified some best practices to perform an effective creativity session in eco-innovation. Collado-Ruiz and Ostad-Ahmad-Ghorabi advise to diffuse only 'soft' environmental information to the group because 'hard' environmental information may restrict the creativity [START_REF] Collado-Ruiz | Influence of environmental information on creativity[END_REF]. Pujari shows that the multidisciplinarity in the working group is an eco-innovation success factor [START_REF] Pujari | Eco-innovation and new product development: understanding the influences on market performance[END_REF]].

Finally, eco-ideation processes in companies are often performed as classical creativity sessions supported by an eco-innovation tool. These tools are studied in the next paragraph.

Eco-innovation tools

Different eco-innovation tools are well known or regularly used in the literature. We distinguish in this paper two main types: simple tools allowing guiding the creativity process like the eco-design strategy wheel, and TRIZ-based tools that are more focused on the ideation process.

The eco-design strategy wheel (also known as the LiDS wheel) [START_REF] Brezet | Ecodesign: A Promising Approach to Sustainable Production and Consumption[END_REF]] is a very simple tool that proposes eco-design guidelines divided in 8 axes on a graphic wheel. 7 axes cover the whole life cycle of the product, whereas the last one aims at identifying new concepts. According to Tyl, its appropriation is really easy. It does not imply specific knowledge and the graphic representation is very clear. It is ideal for a multidisciplinary working group in a company. But as a simple tool, the ecodesign strategy wheel may become simplistic, and the pre-defined guidelines hardly allow going further than product-level considerations [START_REF] Tyl | L'apport de la créativité dans les processus d'éco-innovation -Proposition de l'outil EcoASIT pour faciliter l'éco-idéation de systèmes durables[END_REF]].

Concerning TRIZ-based tools for eco-innovation, several examples exist in the literature, like EcoASIT proposed by Tyl [START_REF] Tyl | L'apport de la créativité dans les processus d'éco-innovation -Proposition de l'outil EcoASIT pour faciliter l'éco-idéation de systèmes durables[END_REF]]. TRIZ is known as a really effective ideation tool, but it is also perceived as a complex approach. Tyl also states that the initial TRIZ innovative principles do not really fit the ecoinnovation principles and need to be reworked [START_REF] Tyl | L'apport de la créativité dans les processus d'éco-innovation -Proposition de l'outil EcoASIT pour faciliter l'éco-idéation de systèmes durables[END_REF]].

These tools are able to support an eco-ideation process. However they do not ensure an effective and multicriteria evaluation and selection step of the most promising ideas. The next section considers general methods in the field of R&D projects portfolio evaluation and selection.

Evaluation and selection of R&D projects

Overview of the methods

Once eco-innovation projects have been generated, it is then necessary to identify the best mix of R&D projects to perform. Actually the number of projects selected by a working group may be too high compared to the available resources in the company. This issue deals with the field of R&D projects evaluation and selection and R&D portfolio management. Cooper et al. proposes a classification of the portfolio management techniques [START_REF] Cooper | New product portfolio management: practices and performance[END_REF]]: financial models, strategic approaches, scoring models and checklists, analytical hierarchy approaches, behavioural approaches and mapping approaches. Cooper et al. also states that mathematical models are not really deployed in companies, because they need a large amount of precise data and they are hard to manage. Another interesting point highlighted by Bitman and Sharif [START_REF] Bitman | A Conceptual Framework for Ranking R&D Projects[END_REF]] is that the methods only based on financial aspects do not give the best results. The relevance of a hybrid approach is also emphasized by [START_REF] Cooper | New product portfolio management: practices and performance[END_REF]].

Finally, Cooper et al. shows that a good method should allow to identify the right number of projects, to avoid gridlocks, to highlight high values projects, to ensure a balanced portfolio (for instance long term versus short term), and to be aligned with the company strategy [START_REF] Cooper | New product portfolio management: practices and performance[END_REF]]. Among all the methods, scoring models and mapping approaches are very popular, mainly because they are easy to use and give good performance results [START_REF] Cooper | New product portfolio management: practices and performance[END_REF]]. We focus in the two next sections on these models.

Scoring models

The scoring models are simple, direct, effective and flexible [START_REF] Bitman | A Conceptual Framework for Ranking R&D Projects[END_REF]]. They show a good ratio between rigor and time spent on the study. Projects are rated and scored according to several qualitative or quantitative indicators. The weighting of the criteria permits to customize the model for special needs [START_REF] Cooper | New product portfolio management: practices and performance[END_REF]].

One of the main forces of a scoring model is its ability to be easily implemented in companies. Actually, and contrarily to mathematical or financial models, the use of qualitative scales allows a large diffusion of the tools, for example through an Excel sheet or even a paper questionnaire.

However, the success of a scoring approach is clearly linked to the selection of sound variables and indicators [START_REF] Mikkola | Portfolio management of R&D projects: implications for innovation management[END_REF]]. References from the existing literature often propose some categories to consider. However environmental aspects are sometimes mentioned, but never analyzed in depth.

Mapping approaches

Historically the BCG (Boston Consulting Group) and the McKinsey matrices are the most familiar mapping approaches [START_REF] Mikkola | Portfolio management of R&D projects: implications for innovation management[END_REF]]. Highlighting the particular needs for R&D projects selection, Mikkola introduces the R&D Project Portfolio Matrix [START_REF] Mikkola | Portfolio management of R&D projects: implications for innovation management[END_REF]]. Two dimensions are considered: competitive advantage and benefits to client. The positioning of the candidate R&D projects (see Figure 1) permits to define four quadrants: FLOP projects are unlikely to generate positive returns and should be removed; SNOB projects often characterize first generation innovations; FAD projects often characterize imitation or mass production of existing products; Finally STAR projects characterize successful breakthrough innovations.

Mikkola clearly states that a balanced R&D project portfolio should include of course STARs, but also SNOBs and FADs, and in some cases FLOPs [START_REF] Mikkola | Portfolio management of R&D projects: implications for innovation management[END_REF]].

Figure 1. The R&D Project Portfolio Matrix [Mikkola 2001]

Nevertheless if the two dimensions do not seem adapted to our needs, we notice that this representation type involving two (or more) dimensions may be powerful.

But as for scoring models, eco-innovation aspects, or more generally environmental concerns have not really been considered in the past. One single example is proposed by [START_REF] Millet | How to identify the most promising areas of environmental improvement at the early stages of the design process?[END_REF]]. Three dimensions are considered: technico-economic feasibility, functional attractiveness (clients' values), and environmental impacts through an Environmental Improvement Rate (EIR). The latter is represented thanks to bubbles whose size is proportional to the EIR value.

Requirements for an adapted eco-innovation process

Considering the constraints associated to complex industrial systems as well as the previous literature review, an adapted and effective eco-innovation process needs to:  Consider the different system levels, as incremental innovations are easier at a component or subsystem level, and radical innovations easier at a system level;  Be very simple, as multidisciplinary knowledge is mandatory to consider all the aspects of such a large scale system, i.e. the process mainly involves non-environmental experts;  Be performed in a short time and with limited resources, to be easily accepted by the management and the involved experts,  Be very efficient, to reach the best possible ratio between used resources and results;  Build a strong basis for future eco-design works, to maximize the success rate of the identified R&D projects;  Be multicriteria, by considering technical, financial and marketing aspects, to be accepted;  Provide strong proofs in terms of feasibility and interest for the clients, to be successful on the markets.

Considering these requirements, it does not seem possible to give to a working group an in-depth training, whether it concerns eco-design or creativity tools. For this reason we do not consider TRIZbased tools. The ideal tool to assist creativity should give predefined stimuli based on checklists or guidelines. That is why we consider and adopt the eco-design strategy wheel in the next section.

However this tool does not propose any post-processing filter treatment of the ideas, i.e. any process to follow up the group work to evaluate and select the most promising ideas. The R&D projects associated with complex industrial systems may be long-term studies. It is thus essential to ensure a multicriteria assessment of each project, even if it is mainly based on qualitative evaluations. A multidisciplinary group appears as the best solution to obtain a complete knowledge of the system.

Consequently we propose in the next section an adapted eco-innovation process for complex industrial system, based on a multidisciplinary working group, supported by the eco-design strategy wheel and using a hybrid scoring/mapping model for R&D projects evaluation and selection.

Proposition of an adapted methodology for complex industrial systems

Prerequisites and general approach

The eco-innovation process for complex industrial systems presented is this paper is part of a larger methodology described in [START_REF] Cluzel | Proposition of an adapted management process to evolve from an unsupervised LCA of complex industrial systems towards an eco-designing organisation[END_REF]]. It is built on the following hypothesis:

 The eco-innovation is deployed in a company providing complex industrial systems (as defined in section 2.1), but with no specific knowledge in eco-design/eco-innovation,  The approach is supported by at least one eco-design expert leading the process,  A primary environmental evaluation (Life Cycle Assessment or simplified LCA) of the considered complex technological system has permitted to identify the most impacting elements of the complete system life cycle, Considering that the global vision of a complex industrial system is necessarily shared by several persons with different knowledge, the main departments of the company need to be represented.

The objective of the eco-innovation process is to identify a set of pertinent environmental improvement projects (incremental or radical eco-innovations) ready to be assessed by the decision-makers. Once the working group has been defined, the eco-innovation consists in two main steps: eco-ideation, and eco-innovation R&D projects evaluation and selection, detailed in the next sections.

Generation of eco-innovative projects

The eco-ideation phase is divided in three sessions, supported by the eco-design strategy wheel.

The first session is called 'introduction session'. As the members of the working group are for most of them not familiar with environmental concerns and eco-design principles, it aims at introducing during a short meeting (1 to 2 hours) the main eco-design concepts, the previous environmental assessments as well as the eco-innovation approach. As stated in [Collado-Ruiz 2010], the diffusion of 'soft' environmental information is favoured.

The second session is called 'creativity session' and may be performed as a half-day meeting. A short introduction is first necessary to remind the objectives and the scope of the study and to put the participants in good creativity conditions. Then a divergent creativity phase is launched. During this phase, only environmental considerations are taken into account (technical, economic or clients' aspects are voluntary omitted). Each of the 8 axes of the eco-design strategy wheel is separately considered during a short workshop (15 to 30 minutes) in a two-step approach:

 A brainwriting phase, where each participant individually generates a maximal number of ideas in accordance with the considered axis using Post-it® papers,  Followed by a common brainstorming, where all ideas are read and grouped. The participants are encouraged to orally propose new ideas. All the ideas are stuck on pre-defined supports.

The divergent phase is followed by a convergent phase, where all ideas are discussed and sorted out. Technical, economic or clients' aspects are now considered. This phase aims at identifying a first set of promising ideas or ideas groups which are from now called eco-innovative projects.

These projects are synthesized in standardized sheets that include a description of the project, its objectives, its potential environmental benefits, and its technical and economic feasibility. Of course this information is not well known at this step, so only qualitative or estimated data are available. The standardized sheets are then deepened during a few weeks by sharing them out between the working group members according to their own competencies.

The last session is called 'synthesis session'. It consists in a discussion on each eco-innovative project in order to clarify the different design aspects and to ensure that a common vision emerges.

At that point, a first set of promising projects has been identified. But they are generally too numerous to be all considered as R&D projects. Thus the last step concerns the prioritization of the projects.

Prioritization of eco-innovative projects

The objective of this step is to evaluate and select a portfolio of eco-innovative R&D projects. It has been previously shown that scoring and mapping models are well adapted to our requirements. We propose in this paragraph an assessment grid based on five dimensions, assimilated to a simple scoring model without any prioritization of the projects. We consider that these five dimensions allow a good perception of the performance of an eco-innovative project inside and outside the company. Each dimension is measured by one or several indicators, as a two-level structure is preferable [START_REF] Bitman | A Conceptual Framework for Ranking R&D Projects[END_REF]]:

 Potential environmental benefits: the environmental benefits of the project are compared to the environmental performance of the existing solution thanks to the eight axes of eco-design strategy wheel [START_REF] Brezet | Ecodesign: A Promising Approach to Sustainable Production and Consumption[END_REF]] on a six-level qualitative scale (0 to 5, see Table 1). A final score on 20 points is then calculated (average score on the eight axes).  Feasibility explores both the technical and the economic feasibility thanks to 4 indicators resulting from an expert debate at Alstom Grid: ease of implementation (in terms of time and resources), financial return of investment, technical feasibility (in terms of knowledge), and internal level of control (is the company able to internally manage the entire project or not?).

Each indicator is assessed thanks to a six-level qualitative scale (0 to 5) that permits to obtain a final feasibility on 20 points (sum of the four scores).  Clients' value: this dimension assesses the benefits for the clients associated with each project. It uses 4 indicators proposed in [START_REF] Kondoh | Analysis of key success factors for ecobusiness through case studies in Japan[END_REF]]: cost reduction, avoidance of risks, improvement of service quality, and improvement of image. As previously each indicator is assessed thanks to a six-level comparative and qualitative scale (0 to 5) that permits to obtain a final clients' value on 20 points (sum of the four scores).  Time horizon: this fourth dimension gives information concerning the term of the studies associated to each project, which is often considered as important to get a balanced project portfolio [START_REF] Cooper | New product portfolio management: practices and performance[END_REF]]. It simply consists in a four-level textual indicator: short term, middle term, long term, prospective (i.e. at a very long term and with high uncertainties).  Project perimeter: this last dimension concerns the system level considered in each project.

It also consists in a four-level textual indicator inspired by Carrillo-Hermosilla's typology [Carrillo-Hermosilla 2010]: component, subsystem, system, super system.

Moreover for each project we have added an expertise indicator that expresses the self-assessment of a user expertise on each project, with four possible levels (from non-expert to expert).

The four first dimensions are formalized in an evaluation sheet, and each member of the working group evaluates each eco-innovative project. By weighting each evaluation with the member's level of expertise, we give more value to the assessments performed by an expert rather than by a nonexpert. Finally an average score is obtained on the five dimensions and for each project.

The last dimension (project perimeter) is not assessed as we assume that each project is clearly linked to one level without ambiguity. This information is simply given to the decision-makers.

We then use a mapping model to draw an overview of the performance of the eco-innovative projects.

The most powerful graph involves potential environmental benefits, feasibility and clients' value on a 'bubble diagram', but other graphs are possible to consider the five dimensions. By defining different quadrants inspired by [START_REF] Mikkola | Portfolio management of R&D projects: implications for innovation management[END_REF]], we give to the decision-makers the ability to identify a powerful and pertinent set of eco-innovative projects according to their available resources.

Table 1. Qualitative scale used to measure potential environmental benefits on each eco-design strategy wheel axis. The scales used for the other dimensions are based on the same principle.

Score Description 0

The project highly deteriorates the environmental performance of the current solution. 1

The project significantly deteriorates the environmental performance of the current solution. 2

The project does not bring any benefit or damage compared to the current solution. 3

The benefits brought by the considered project are weak. 4

The benefits brought by the considered project are significant. 5

The benefits brought by the considered project are very important.

Validation criteria

The validation of such a process is not easy, because it involves subjective and qualitative elements. We consider in this paper the four criteria proposed by [START_REF] Shah | Metrics for measuring ideation effectiveness[END_REF]], who combines variety and novelty with quantity and quality. We associate the following indicators with those criteria:

 Novelty: two questions are added in the assessment grid: 1) Do you think that this project already exist before the eco-innovation approach in the mind of one or several persons in the company, in a subliminal way? 2) Do you think that this project would have emerged, been formalized and seriously considered by the decision-makers without this process?  Variety considers the balance between short/middle/long term and prospective projects, the balance between component/subsystem/system/super system related projects, and the balance of the nature of the projects (technological, organisational or methodological projects).  Quantity is assessed by the total number of ideas generated during the divergent creativity phase and the total number of eco-innovative projects proposed after the convergent phase.

The time spent on the different phases of the eco-innovation process is also considered.  Quality is assessed thanks to the three dimensions: potential environmental benefits, feasibility and clients' value.

These four criteria permit to assess the global performance of the eco-innovation process proposed in this paper. In the next section, we propose a case study performed at Alstom Grid.

Case study: application at Alstom Grid

AC/DC conversion substations for the aluminium industry

Alstom Grid PEM (Power Electronics Massy) designs, assembles and sells substations for the electrolysis of aluminium worldwide. These are large electrical stations designed to convert energy from the high voltage network to energy usable for aluminium electrolysis, which is a particularly environmentally impacting and energy-consuming activity. A substation represents thousands of tons of power electronics components and transformers, costing tens of millions of Euros.

These substations are considered to be complex industrial systems because the number of subsystems and components is considerable, and the lifetime of a substation is really long, up to 35 or 109 ideas were generated during the creativity sessions. Each axis of the eco-design strategy wheel provided between 10 and 23% of theses ideas. Each active member of the working group proposed between 8 and 35 ideas. Relatively to the time spent in the divergent session (1 hour and 45 minutes), it is really satisfactory. After the convergent session, 16 eco-innovative projects were identified.

Variety

Considering the 16 eco-innovative projects, 2 of them were judged to deal with short-term studies (less than 6 months), 9 with middle-term studies (6 months to 2 years), 3 with long-term studies (more than 2 years). For two projects no consensus was found (in particular one was judged between longterm and prospective, i.e. more than 5 years with high uncertainties).

Concerning the project perimeter, one project concerns a component, whereas 5 projects deals with the subsystem level. 9 projects involve the whole system, and only one the super system.

Finally, concerning project nature, 8 projects concern methodological aspects, 12 projects include technological considerations, and 2 projects organisational aspects (a hybrid nature is possible).

These results are considered as really satisfactory, as the portfolio including the 16 projects is well balanced on the three criteria. All categories are represented. A consensus is almost always found for the 'time horizon' criteria, which was the only one evaluated by the working group.

Novelty

5 projects were judged by the majority of the working as being already present in the mind of one or several persons in the company (but not formalized), whereas one project was judged as not being present. It was not possible to find a consensus for the 10 other projects.

But even if some project ideas were already present in some people's mind, only one project was considered as possibly formalized without the eco-innovation process. Moreover the working group estimated that 10 out of the 16 projects would not have emerged without the eco-innovation process.

These results clearly show that a lot of eco-innovative ideas may be present in the company employees' mind but would never emerge without the proposed method. It also shows that new ideas could appear thanks to this method, and that it is a good way to stimulate designer's creativity.

Quality

The quality of the process is assessed thanks to the designer's evaluation of the 16 projects according to three criteria (environmental benefits, feasibility, client's value).

The results for the environmental benefits shows that the average score is 10.8 (out of 20), but with a low standard deviation (0.98). It means that the 16 projects propose environmental improvements on some axes of the eco-design strategy wheel, but no generalized environmental improvements. This clearly characterises incremental eco-innovations. But it also shows that the environmental qualitative scales are not sensitive enough to assess in a good way the differences between the projects.

For the feasibility criteria, the average score is 12.2 and the standard deviation is clearly higher (2.70).

The projects are well ranged on the scale (from 4.5 to 15.2) showing that the proposed qualitative indicators are sufficient to distinguish the projects.

Finally, the results for the client's value criterion show that the average score reaches 10.9 with a standard deviation at 1.34. As for environmental benefits, it is hard to distinguish the 16 projects. But if we consider that only incremental eco-innovations have been identified, it could be explained by the fact that the projects would only bring little benefits for the client's value.

Concluding remarks

Starting from the statement that eco-innovation methods are not adapted to complex industrial and technological systems, we have proposed an adapted eco-innovation process. This process includes two main stages:

An eco-ideation phase involving a multidisciplinary working group and a creativity session in order to identify powerful eco-innovative projects involving the complete life cycle of the system and its subsystems,

A multicriteria assessment phase performed by the working group, considering environmental, but also technical and economic feasibility, client's value, project perimeter and time horizon. This original assessment stage ensures the selection of an optimized eco-innovative R&D projects portfolio.

This process has been applied at Alstom Grid on large electrical substations. The results are very satisfactory as we have that this method permits to obtain a high number of ideas with limited time and resources. From these ideas a balanced eco-innovative R&D projects portfolio is identified, mainly composed of ideas that would not have emerged without the method, but also of some new ideas. The assessment grid seems satisfactory for the feasibility and client aspects. However the sensitivity of the environmental indicators does not seem sufficient to assess the projects, as the constraints associated with complex industrial systems favour incremental eco-innovations.

That is why further works need to be performed to assess the potential environmental benefits associated to the projects, in order to give to the decision-makers powerful information through the proposed mapping approach. Two perspectives will be considered. The first one consists in performing a new assessment of the environmental performance of each project with eco-design experts. This process would permit to refine environmental evaluations and to study if the low variability between the projects is due to the participation of non-expert people or is inherent in these projects. The second perspective concerns the development of a more sophisticated model based on LCA to quantitatively assess at an early stage the environmental performance of the R&D projects.

Acknowledgement

We gratefully thank Joël Devautour and François Puchar from Alstom Grid for their full support, as well as Frankie Rico Sanz and all the working group members for their contribution.

40 years with high uncertainties. Furthermore the substation is only a part of the aluminium plant. Their processes are closely connected. Finally no standard design exists: the substation is tailor-made for each client, even though the general design is often the same.

In this context, Alstom Grid PEM wishes to minimise the environmental impacts of its products. A first global Life Cycle Assessment has been performed on an entire substation [START_REF] Cluzel | Proposition of an adapted management process to evolve from an unsupervised LCA of complex industrial systems towards an eco-designing organisation[END_REF]]. This LCA is the basis for the eco-innovation process described in the next parts.

Eco-innovation process deployment

A working group was built with complementary knowledge of a substation, including two persons from the R&D department, one from the Engineering department, one from the Commercial department, two from the R&D department of another Alstom Grid unit providing the transformers, and one academic eco-design expert. The animation was managed by one junior eco-design expert assisted by one eco-design trainee, who were not proposing ideas during the creativity session. So the ecoinnovation process involved 9 persons. The whole process lasted about 10 weeks (see Figure 2).

Figure 2. Time line of the eco-innovation process at Alstom Grid PEM

After the creativity session, 16 eco-innovative projects were selected and assessed by the working group thanks to the assessment grid presented in section 3.3.

The next part presents the results obtained according to the four validation criteria.

Results and discussion

Quantity

Creativity session

Working group creation

Introduction session

Introduction


Review of Bernecker, Sven (2010).Memory. A philosophical Study. OUP, New York.

Reviewed by Marina Trakas, Macquarie Centre for Cognitive Science, Macquarie University, Australia & Institut Jean Nicod, Ecole des Hautes Etudes en Sciences Sociales, France Finding an entire philosophy book dedicated to memory is rare, when clearly memory is not even close to becoming a hot topic in philosophy of mind (which paradoxically contrasts with the enormous interest that it stirs up in other fields, such as cognitive science or sociology). That is a very good reason to welcome and read Bernecker´s new book Memory: A Philosophical Study, which is a kind of renewed and improved version of his previous book The Metaphysics of Memory (2008) 1 .

The book is a wide, punctilious and analytic exposition of the causal theory of memory, which had already been advocated in an article full of ideas written in 1966 by Martin and Deutscher called "Remembering"2 .

The main principles of Bernecker's account are the same as those expounded in "Remembering"; for a present propositional representation to be a genuine memory of a past event, three objective conditions must be met: a continuous causal relationship between the past representation of that event and the present one via a memory trace, a similarity of content between the two, and the truth of the memory representation. Let´s see how Bernecker develops and argues in favor of these conditions.

The causal condition, which constitutes the core of the causal theory of memory, is discussed in chapter 5. In order to exclude from the category of memory both cases of epistemic luck (like suggestion) and cases of relearning, the causal condition establishes that the relationship between the past and present representations must be guaranteed by a persisting memory trace or a contiguous series of memory traces that derives from the past representation and that causes the present one. According to Bernecker, memory representations are brought about by mental memory traces, which are dispositional beliefs that preserve the mental content through time, or subdoxastic states if the content stored is non-conceptual, and which supervene on neurobiological memory traces. From the reading of this section, we find out that mental memory traces are not mere epiphenomena without causal power because they give rise to representations and behavior, that they are opaque to the subject, and that they are not structural analogues of the event represented by the past experience (as Martin and Deutscher had advanced). We also find out that memory traces can be removed from the biological body and thus can be intra and interpersonally transplanted, and even replicated, and continue to give rise to authentic memories. This is compatible with Bernecker'sdefence in chapter 3 of the notion of quasi-memory and therefore of a psychological theory of personal identity, that is, that memory can be used as a criterion to define personal identity because memory does not imply it. Nonetheless, these eight pages about memory traces in a book of 250 pages seem too schematic and synthetic to fully characterize the core of the causal theory of memory. Bernecker is not an exception; most of the philosophers who have written about memory never analyzed memory traces in depth, maybe due to the force of the metaphorical image which is very easy to grasp. However, this kind of transparent analogy should not justify the omission of a proper characterization of memory traces, especially in a book entirely dedicated to the defence of the causal theory.

The last part of chapter 5 sheds light on the other central notion of the causal theory, that is, on the relation between the different elements involved in the causal bond. On this subject, Bernecker explains the causal dependence between the past representation and the present one in terms of counterfactual dependency, whereas the causal dependence of memory states on memory traces vis-à-vis retrieval cues is analyzed in terms of necessary and sufficient conditions.

The second condition of the causal theory, the content condition, is developed in chapters 6, 7 and 8. The first two chapters constitute a defence of pastist externalism about memory content, that is, the idea that the content of both the past and the present representations is fixed by and so supervenes on the same past environment, and that is why they are similar. Bernecker's argument resorts to different world-switching scenarios, which allows him to rule out internalist accounts and other possible content externalisms, like presentist and futurist versions (as well as the extended mind thesis). Chapter 8 addresses the kind of relationship between the content of the two representations: Bernecker rejects the idea that memory simply duplicates a past experience (what he calls the identity theory but which in fact very few philosophers defend), but he also disapproves strong forms of constructivism about memory, because they lose sight of the first function of memory that according to his view is the "preservation of the content". But this rejection of constructivism is clearly at odds with the social and pragmatic main functions that the current psychology literature attributes to memory: planning for the future, decision-making, construction of personal identity, guiding present and future actions, are now more associated with the concept of memory than the idea of preservation of the past3 . Furthermore, we could ask to what extent the implicitly assumed preservationist view about memory content differentiates his position from the identity theory. Although Bernecker calls himself a "moderate generativist", his generativism only applies to the justification of knowledge: memory is a generative source of justification because memory can remove defeaters. But memory cannot generate anything new: it cannot bring about new elements of justification or generate new content. In fact, in regard to memory content, his position is incontrovertiblypreservationist: the content of the memory representation must be entailed (in the relevance sense of "entailment") by the content of the past representation without the need of additional premises, which certainly forbids any enrichment or increase of content. So the "changes" allowed are minimal: substitutions of synonyms, adjustments of verb tenses seem all that can be done. Even if Bernecker did not mention these "principles of semantic similarity" developed in his previous book (pages 158-163), they seem nonetheless to be implicitly assumed here. And unfortunately, together with the omission of these principles, Bernecker omitted a remarkable conception that he should definitely have continued to develop: the contextdependence or pragmatic sensitivity of these principles, that is, the idea that what counts as an accurate or veridical memory representation is defined to some degree relative to the interests and intentions of the remembered and the attributors of the conversational context (chapter 10 of his previous book).

Finally, the truth condition is mentioned in chapter 8 and chapter 3. The requirement is that the memory representation must be true in a correspondence sense. However, the past representation need not be true at the moment of forming it. Probably, one reason that motivates Bernecker to defend this conception is his intention to distinguish his theory from the epistemic theory of memory, which considers that memory representations are states of knowledge. To this idea, Bernecker responds in chapter 3: memory does not imply past or present justification, memory does not imply past or present belief, and memory does not imply a true past representation. Nonetheless, it implies a true memory representation, which seems to lead to the anti-Fregean consequence that a change in the world can convert a false memory into a true one, or a true memory into a false one, even if the causal and the content conditions are met. One example: I formed at t 1 the justified but false belief that John has borrowed a blue book from the library; if I remember this at t 2 my memory is false, but if at t 3 without my knowledge John effectively borrowed a blue book from the library, when I remember at t 4 the representation I formed at t 1 my memory is true. Once again, this use of the sense of "false memory" moves Bernecker away from the conception of falsity common among psychologists which mainly refers tomemory distortion and intrusion, false recognition, delusional memory, confabulation, etc4 . In psychology, there are three cases in which a memory representation can be false: a. the past representation was never formed; b. the past representation was false due for example to a perceptual error; c. the past representation was true but during the retrieval process there were some errors on the "editing" functions or on the temporal context or other source monitoring. Therefore, in the example given above, on standard use in psychology my memory would be false not only at t 1 but also at t 4 because my past representation, even if justified at t 1 , was false. Unlike Bernecker, for psychologists the false/true distinction of memory representations is not reduced to the truth value of the propositions implied on those memory representations.

The truth condition is required for factive attitudes, like knowing, but not for memories that are "introversive", that is, memories that represent an attitude toward a content, like memories of beliefs, desires, doubts. The only requirement in this last case is the authenticity of the memory representation, which is defined in terms of functional identity (direction of fit and polarity). The distinction between introversive and extroversive memories is outlined in chapter 1, as well as other non-traditional distinctions between different types of memories. In my opinion these distinctions constitute the weakest point of Bernecker's proposal. Bernecker's two main typologies are guided by a grammatical criterion: first, extroversive memories are divided according to the grammatical complement of the verb "remember", which gives rise to four types of memories: memories of objects, memories of properties, memories of events (gerundive construction) and propositional memories (that-clauses). Only these last cases, that is, when the verb "remember" is followed by a that-clause, require the possession of concepts, and are the object of analysis in the book. This distinction however is problematic. Beyond this grammatical taxonomy these four types of memory do not seem to correspond to psychological kinds. If we take these three examples: a. remembering visiting the Colosseum; b. remembering that I visited the Colosseum; c. remembering that Paris is the capital of France, according to the grammatical criterion a and b would correspond to different memory kinds, i.e. event-memory and propositional memory respectively, even if the content remembered is the same: an event of my life, whereas b and c would belong to the same kind, even when in one case I remember an event experienced before and in the other case a simple fact of the world. Moreover, I could remember a without having any concept, but it seems that I could not remember b without having the concepts of "self", "visit", "Colosseum" and "time". This shows that not only the distinction between gerundive constructions and that-clauses is problematic to establish by itself different kinds of memory, but what is more, this grammatical distinction seems to be implicitly based on other criteria that go beyond grammar, that is the different modalities in which a subject can experience a memory: experiential memory vs detached memory (or episodic memory vs semantic memory according to the most recent distinction made by Tulving5 , which is not centred on the type of content: events vs facts, but on the phenomenology). This would be the only way to explain why a andb differ, while b and c belong to the same memory type. But even if we leave these problems behind, Bernecker's grammatical criterion is exclusively based on the analysis of English, leaving aside the fact that some other languages don't have the same kind of constructions, especially in what concerns the gerundive form.

On the other hand, the second main distinction, that is between extroversive and introversive memories, is also grounded in a grammatical difference: while one contains only a simple thatclause, the other one also contains a second order that-clause: I remember that I (past tense of an attitude verb) that p. But again there seems to be some difficulties with this criterion: in the case of some verbs, like "believe", the type of memory depends exclusively on the omission or presence of this verb. So, if I decide to say that "I remember that I believed that p", the truth or falsity of p is irrelevant to state a genuine memory, but if I instead omit the verb "believe" and say "I remember that p", p has to be true for my memory to be true; so in this case, the applicability of the truth condition would depend on the arbitrariness of the linguistic choice of the remember.

These problems show that grammar cannot be used by itself as a criterion to establish different psychological kinds of memory; it can only be used as an analytical tool to designate different kinds of memory that differ according to other criteria, such as their content (events vs facts), phenomenological properties (knowing vs recalling with rich sensory detail and mentally time travelling) and/or source (perception vs thought vs emotion). In fact, surprisingly Bernecker himself says that "memory reports are sometimes not reliable indicators of whether a given state is a propositional or non-propositional memory" (p. 23) or an extroversive or introversive memory, so it is hard to understand why he creates a memory taxonomy based on a criterion that himself recognized as unreliable, especially when he dismissed the phenomenological criterion for this same reason, for not been "sharp". He owes us at least a positive argument in favor of the grammatical taxonomy, as well as why that-clauses constitute a single memory kind. This focus on the objective conditions and not on the phenomenological aspect of the mental representations does not provide a criterion to distinguish between dreams, imaginings, explicit memory, familiarity (know experience), etc. Even if Bernecker reduces his analysis to conscious explicit propositional memories as he announces in chapter 1, if the field of application of the causal account is extended, it can be deduced that provided all these mental representations have the same kind of content (namely propositional content) and fulfill the conditions enumerated before, the subject is in the same mental state, that is, in a genuine memory state, regardless of the different ways in which the subject experiences it. So a person who read Don Quixote in the past might be remembering that he read Don Quixote, or imagining that he read Don Quixote, or he might know that he read it but not remember any details associated with the episode, or he might be doubting whether he read it; and any of these conscious mental states would satisfy the necessary conditions for being a genuine memory state. As we can see, the causal, content and truth conditions cannot account for the specificity of memory states that make them different from other mental states. This clearly constitutes a gap in the causal theory of memory, a gap that seems to be even more outstanding when in return Bernecker proposes a grammatical typology that is blurred. Furthermore, Bernecker reduces his analysis to conscious explicit propositional memories that are non-inferential, that is, that they are not the result of a reasoning based on additional premises. But the problem is that in everyday life, non-inferential memories occur only rarely, like memories of shopping lists, telephone numbers and "someone told me that" or "I left my glasses on the desk". Because most of our memories are inferential, as Bernecker himself recognizes (p. 25), an account exclusively focused on non-inferential memory has limited explanatory power.

At this point, we can ask ourselves why this causal account of memory phenomena should be assumed. Chapter 4 tries to give an answer to this question, arguing that the causal theory of memory offers the most viable explanation of memory processes, because it provides a comprehensive account of the kind of process that is responsible for the capacity to retain and represent again something represented in the past. This ability is expressed througha counterfactual relationship between the past and present representation and can be summarized in the intuitive conditional: If S hadn´t represented at t 1 that p he wouldn´t represent at t 2 that p*. However, the problem is not just that Bernecker again does not give any argument in favor of the theory (he dismisses three possible objections but also two possible arguments in favor), but that the only opponent theory that he evaluates and rules out, the retention theory, that is, the idea that once we represent something we only acquire a disposition to represent it again, is an old-fashioned idea that nobody explicitly or implicitly defends, because as Bernecker notices himself, it does not explain the essential point: how we retain this disposition over time. That is why the retention theory is not a real opponent to the causal theory, and that is why finally nothing convinces the reader that the causal explanation is more plausible than other "non-existent" theories. We just have to accept it. And decidedly, it is not hard to do so, because the causal theory is highly intuitive. At least at first glance. But if we take a look to the cognitive science literature, reconstructivism in memory seems to be the new dogma. And reconstructivism not only claims that "retrieving a memory is like reconstructing a dinosaur from fragments of bone" 6 but that memories cannot be "simple, countable connections between two well-defined moments of consciousness" 7 because the content of memories is not determined at encoding alone, due to the fact that the continual processing of new information transforms the old information stored and, what is more, that the overall context of retrieval (present thoughts, interests, expectations) also contributes to the determination of the content of memory 8 . As we can see, reconstructivism in memory seems to be in tension with the two main principles of the causal theory: the causal condition and the content condition, which at the same time arouses some doubts about the truth of the counterfactual relationship. Maybe it is possible to represent something at t 2 and have a genuine case of memory without having represented something similar at a past time. More in this direction should be explored, because here could lie a potential and respectable opponent of the causal explanation of the memory phenomena.

To round up, I personally would like to have found a battle-hardened defence of the causal theory of memory, including some arguments in favour. Unfortunately, this is absent in this book: we have to assume the causal theory because there does not seem to be any better option. Despite this absence and other weaknesses, Memory: A Philosophical Study is worth it because while inviting us to discuss with the author, it reminds us how many questions about memory deserve a deeper debate among the philosophical community, questions whose answers are indispensable for a better understanding of the mind.

  Further readingFredAdams (2011). Husker Du?Philosophical Studies, 153 (1):81-94. Sanford Goldberg (2010).The Metasemantics of Memory.Philosophical Studies, 153 (1):95-107. MaryaSchechtman (2010). Memory and Identity.Philosophical Studies, 153 (1):65-79. Sven Bernecker (2011). Further Thoughts on Memory: Replies to Schechtman, Adams, and Goldberg. Philosophical Studies, 153 (1):109-121.

 Bernecker, S. (2008). TheMetaphysics of Memory. Dordrecht, Springer.

Martin, C. B. &Deutscher, M. (1966).Remembering. ThePhilosophicalReview, 75(2),

See for example,Bluck, Alea, Habermas& Rubin (2005). A tale of three functions:the self-reported uses of autobiographical memory.Social Cognition,23 (1), pp. 91-117.

See for example,Kopelman, M. (1999). Varieties of False Memory.CognitiveNeuropsychology, 16 (3/4/5),

Tulving, E.(2005). Episodic Memory and Autonoesis: Uniquely Human? In H. S. Terrace & J. Metcalfe (Eds.), The Missing Link in Cognition. New York, Oxford University Press, pp. 4-56.

 Schacter, D.L. (1996). Searchingformemory: Thebrain, themind, and thepast. New York:Basic Books, page 69.

 Schechtman, M. (1994). Thetruthaboutmemory. PhilosophicalPsychology, 7(1), page

8 Campbell, S.(2004). Models of mind and memoryactivity. In P. DesAutels& M. Urban Walker (Eds.), Moral psychology: feministethics and social theory. Maryland, Rowman&Littlefield.


Individual and Colllective Consolidation. Analogous Processes on Different Levels. Cambridge, MIT

The authors of this erudite booka neuroscientist and three PhD students coming from diverse fields-defend the thesis that even if individual and collective memories may differ in their intrinsic structures, the processes through which both memories are formed are analogous, and that is why a single theory can explain both of them. In neuroscience literature, memory formation is known as the process of consolidation, which more specifically refers to the progressive post-encoding process of stabilization of labile memory items held in the short-term memory buffer until they become stable and long-term memory representations ready to use. Because the aim of the authors is to expand this concept to humanities, the book mainly centres on the formulation of a comprehensive model of memory consolidation. The description of this model is developed after a brief review of the history of the concept of memory consolidation (Chapter 2) and a working definition of collective memory -which is basically considered as an emergent phenomenon that is more complex and broader than the sum of the memories of the individuals who compose the collective (Chapter 3).

Chapter 4 provides an overview of their model of consolidation. Their model is inspired by [START_REF] Mcclelland | Why there are complementary learning systems in the hippocampus and neocortex: Insights from the successes and failures of connectionist models of learning and memory[END_REF] two-box model which consists of a buffer, which temporarily holds memory items over the short term for further processing, and a generalizer that clusters similar items together and categorizes them. This model, however, presents a limitation: it cannot explain why certain memory items are or are not retained because it does not consider the content of memories, that is, their meaning. That is why Anastasio et al reformulate it and propose a "three-in-one" model, which adds a third component between the buffer and the generalizer: the relater. The relater selects items from buffered storage and establishes relationships between memory items imbuing them with meanings while connecting them with other new and old items. In order to capture the full range of influences on the consolidation process, a fourth element is introduced: the entity in which the consolidation process takes place. It can be an individual person, or a particular social group, or even a nation. The entity represents the non-mnemonic factors such as the goals, plans, emotions and desires of the individual or collective that can influence all the three stages of the memory consolidation process. An important feature of Anastasio's model is recursion: all the components of the model are interconnected in a two-way direction, so that already consolidated memories can influence which items to attend in the buffer, which ones to draw from the generalizer, or direct the way in which the relater relates the selected items.

Anastasio et al dedicate one chapter to the development of each of the four components of the model (chapters 5, 6, 7 and 8) . Each chapter not only deepens their description but also gives plenty of concrete examples at the collective level with the purpose of providing evidence for the usefulness of this conceptual framework for humanities. In a society, for example, the material culture -like documents, pictures, monuments, etcprovides unconsolidated and "raw" material. Archives (through archivists) and mass media would correspond to the collective buffer because they are characterized by the attentional tagging. The "relaters" or social hippocampi (making an analogy with the hippocampus which is the brain structure that plays a key part in identifying and creating associations between memory items at the individual level) would be historians, journalists, and other social groups who try to place an event in context and determine its features and meaning. Analytic and popular history, as well as narratives and collective identities (like national identity, or class consciousness) would be forms of generalization, and so, forms of collective memory that once formed, recur to influence further memory consolidation. The goals, emotions, desires and other nonmnemonic properties of the collective entity, like the establishment of truth as a desire of the historical scientific entity (but other political factors and personal goals and desires of scientists too), also influence each stage of the consolidation process.

However, the main evidence the authors pretend to provide in favor of the functional analogy between individual and colective memory consolidation is presented in the last part of the book (Chapters 9, 10 and 11). In this section, Anastasio et al analyse the Chinese Cultural Revolution as a social trauma that produced in mainland Chinese people a collective retrograde amnesia for literature and literary figures that were well represented as labile memory items at the time of the Communist takeover, but not for religious personages, tenets and practices which had been consolidated generations before and were already ingrained in the society.

Overall, Individual and Collective Memory Consolidation is a good reading for varied readers. Even if it clearly and mainly constitutes an invitation for social scientists to analyse collective memory in a more systematic way using a model borrowed from cognitive science, it is also of interest for neuroscientists and cognitive psychologists who can find a novel reformulation of the process of consolidation of individual memories. Furthermore, because of its clarity, erudition and constant use of examples, it is apt and very informative for a general public interested in memory issues. Historians concerned with 20th century Chinese history will also enjoy reading the last section of the book.

Just some words to end: the proposal developed by Anastasio et al makes me wonder until what extent it is fruitful to apply one single model to different levels of analysis, like the individual and the collective levels, the last one which in turn includes various and different collectives, like couples, families, communities, nations, etc. Because of the interactions between individual and collective memory -interactions that are deliberately omitted from the book to focus exclusively on the analogy-the collective memory level seems far more complex than the individual one. Taking one example mentioned in the book, the consolidation of historical knowledge not only can be influenced by goals and desires of the collective entity -the community of historians-, but also by the goals and desires of the particular historians (page 176). That happens because even if collectives can be considered as more than the sum of the individual parts, collectives are also composed by individuals and, in some cases, by other collectives. And this points to a fundamental difference between individuals and collectives. In Anastasio et al's proposal, it seems that the emphasis on the analogy and the systematisation of the collective memory consolidation has been done at the expense of a reduction of the complexity of the collective memory phenomenon. Anyway, social scientists will be the adequate public to judge the utility of this innovative conceptual framework to study collective memory formation, and maybe to continue to enhance and broaden this original proposal.