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Pu (R) = {n N / r R | input r |u = n} P (N) m Hyperplane of d {1,...,m} in k N over N is defined as:

k m m Hd (N ) {(x1,..., xd,..., xm) / xd = k} P ( N ) Thus, it is considered the grid over R P(R (U,T) ) as:

k H (R) = {h / h = H(u) u U k Pu (R)} m Moreover, D (R) is defined as the partition N in disjoint subsets formed from every hyperplane of the grid H (R). It is named domain D to each one of the elements from partition D (R). Where it is fulfilled:

Knowledge Engineering d =|D (R) | = Pu (R) | < | uU d m N = Di Dj,i, j {1,...,d} i j Dk k=Finally, it is defined representative of D D (R) as (D) = min( {dist(m,(0,...,0)) m D}) Fig. 4 shows an example obtained from values of table for the evolution rules set of figure 3. This table includes a row by each representative of the domains, its values for checking relations and applicable evolution rules subset that corresponds to each domain. Fig. 5 shows the classification tree generated by ID3 algorithm for the corresponding figure 4 values table.

Incorporation of decision trees avoids unnecessary null weights comparisons from algorithm 1 because they are not incorporated as in starting instances. Same, direct way redundancies are avoided, the weight of a symbol is compared with the same value just once. Finally, indirect way redundancies are also avoided due to the optimum decision tree ensured by ID3 algorithm, avoiding relations of transitive comparisons.

Fig. 4. Examples battery for the evolution rules set of Fig. 5. Example of decision tree generated by IDfigure 3: in each row there is representative of each algorithm for the examples battery from figure domain, values it takes for comparison relations and corresponding applicable evolution rules subset.

Applicablity Algorithm based on Decision Trees Previously to the algorithm presentation, we will expose the appropriate data structure for supporting the decision tree.

On the one hand, they are disposed four correlative tables left, symbol, value and right for attribute nodes, with one cell in each table by each attribute node; root node is located in position 0 cells;

On the other, It is disposed a table classes for classification nodes, with one cell for each classification node;

Correlative cells of tables symbol and value determine which object weight from the multiset of objects has to be compared with which weight. Cells of tables left y right indicate, whether or not it is respectively accomplished previous relation comparison, which cell is the following attribute node in, whether index is positive; otherwise, indicate which cell of classification nodes table is the solution in.

Fourth International Conference I.TECH 2006 Figure 6 shows an example of data structures of corresponding generated y decision tree from figure 3. y 1 1 x x Then, the input to applicability algorithm 2 -2 -is, multisets of objects, and the x x -1 --1 -supporting decision tree data structure: left, x x 4 4 symbol, value, right and classes. On the y y 5 -5 -other hand, output is A, an evolution rules y y -2 --2 -subset of R that is applicable over that x x 7 -7 -multiset. Following code processes rows of y y the indexes of branches left or right, 8 -8 -depending on the comparison of symbol y y -3 --3 -indicated by symbol weight with established classes classes {r1,r2,r3,r4} {r2,r3,r4} {r2,r4} {r2} {r2,r3} {r1,r2,r4} {r1} {r1,r2,r3,r4} {r2,r3,r4} {r2,r4} {r2} {r2,r3} {r1,r2,r4} {r1} value on value until it is reached a -1 -2 -3 -4 -5 -6 -7 --1 -2 -3 -4 -5 -6 -7 -classification leaf, indicated by a negative Fig. 6. Data structure for decision tree of figure 5.


(1) f (2) WHILE f 0 DO (3) IF | | (symbol[ f ]) value[f ] THEN -(4) f left[f ] (5) ELSE (6) f right[f ] (7) A applicable[f ] Algorithm 2. Evolution rules applicability based on decision trees.

Fig. 7. Execution time reduction carried out by applicability algorithm based on decision tree respect traditional algorithm.

left left right right symbol symbol value value Knowledge Engineering In the worst case, complexity of algorithm 2 considers to process the longest branch of the decision tree which length will always be lesser than n =| R | | U |. We will reach this conclusion by reduction to the absurd: in order to the longest branch of the decision tree requires n attribute nodes, It must be carried out the following a) every weight of each symbol in the antecedent of evolution rules is not null and different between them and, b) the d existing domain leads to applicable evolution rules different subsets. That is impossible because, in such circumstances, always exist more than one domain that would lead to the empty set. Specifically, a number of |U | domains equal to Pi (R) |- |U | +1.

| i = Comparative This section presents the experimental results obtained from evolution rules applicability using the two algorithms presented here. The test set has been randomly generated and it is composed by 48 different evolution rules sets (composed between 2 and 4 evolution rules composed between 2 and 4 symbols per antecedent), over these tests, it has been calculated the applicability of more than a million of randomly generated symbols multisets.

A first global analysis presents a reduction of execution time of this new algorithm based on decision trees respect to traditional algorithm in an average of 33%, with a variance of 7%.

Particularly, they has been made tests directed to four different situations to analyse the behaviour of new algorithm in extreme cases: with every different weight in antecedents of evolution rules, with every weight of same value, and with presence of 25% and 50% null weights.

In the worst case, with every weight being different between them, it has been reached at least 50% of execution time reduction. With all weights with same value, execution time is reduced to a 15% (for 4 evolution rules with symbols per antecedent). In presence of 25% and 50% of null weights in antecedents of evolution rules, time is reduced to a 35% and a 29%, respectively, always in favor of the new algorithm with decision trees.

Conclusions This work presents a new approach to the calculus of evolution rules applicability over a symbols multiset. This approach is based on decision trees generated from the set of evolution rules of a membrane. This way, they are avoided unnecessary and redundant checking in a direct or indirect way. Consequently, It is always obtained a lesser complexity than the corresponding traditional algorithm. So, execution time is optimized in the calculation of evolution rules applicability over a symbols multiset. All of this has repercussions in global efficiency of the P System evolution, because applicability calculation is carried out in parallel in each membrane in each evolution step.

Bibliography [Fernndez, 2005] L.Fernndez, V.J.Martnez, F.Arroyo, L.F.Mingo, A Hardware Circuit for Selecting Active Rules in Transition P Systems, Workshop on Theory and Applications of P Systems. Timisoara (Rumana), september, 2005.

[Fernndez, 2006] L.Fernndez, F.Arroyo, J.Castellanos, J.A.Tejedor, I.Garca, New Algorithms for Application of Evolution Rules based on Applicability Benchmarks, BIOCOMP06 International Conference on Bioinformatics and Computational Biology, Las Vegas (USA), july, 2006 (accepted).

[Pun, 1998] Gh.Pun, Computing with Membranes, Journal of Computer and System Sciences, 61(2000), and Turku Center of Computer Science-TUCS Report n 208, 1998.

[Pun, 2005] Gh.Pun, Membrane computing. Basic ideas, results, applications, Pre-Proceedings of First International Workshop on Theory and Application of P Systems, Timisoara, Romania, September 26-27, 2005, 1-[Rasoul, 1991] S.R.Safavian, D.Landgrebe, A Survey of Decision Tree Classifier Methodology, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 21, No. 3, pp 660-674, May 1991.

Fourth International Conference I.TECH 2006 Authors' Information Luis Fernandez e-mail: setillo@eui.upm.es Fernando Arroyo e-mail: farroyo@eui.upm.es Ivan Garcia e-mail: igarcia@eui.upm.es Gines Bravo e-mail: gines@eui.upm.es Natural Computing Group of Universidad Politcnica de Madrid (UPM); Ctra. Valencia, km. 7, 28031 Madrid, Spain.

ADVERGAMES: OVERVIEW Eugenio Santos, Rafael Gonzalo, Francisco Gisbert Abstract: Advergame is a new marketing concept that has appeared due to the fact that young people are always connected to the Internet, are using mobile services such as SMS and MMS, or are chatting with instant messenger services and they spend too much time just playing in a stand alone way or in a network game. A new revolutionary service is the advergame one; that is a game with advertisment capabilities. Any company can develop an advergame that is, a game with some kind of advertising process of this company. This paper introduces some idea and concepts when developping an advergame..

Keywords: Advergames, Mobile Computing, Games Development.

ACM Classification Keywords: D.1.m Miscellaneous.

Introduction Online games are the future of the interactive entertainment industry, seeing the convergence between the traditional media, and entertainment industry, and the gaming industry in an effort to develop new and sustainable business models and revenue streams in an increasingly online world. They move the gaming industry into a more functionally rich online environment from which the majority of the revenue stream will come -- an ebusiness environment. But moving to this new model presents a number of challenges to the games developers, the players, and the service providers who ultimately will need to support this new environment.

However, it also presents a number of exciting opportunities for new business models, new markets, and new growth. The main problem faced is a solution integration issue. The player wants to pay for online content with their existing channels, but they also want security and privacy. The developers need cross-platform integration and support for multiple services, channels, and providers. The service providers need to build reusable business function that is robust, efficient, and generic -- it should work for all business models, not just the gaming industries.

Online games come in many forms. Perhaps the most recognized are the highly visual, action-oriented pop-ups familiar to NYTimes.com users. They're primarily used by advertisers for branding purposes and are generally delivered via pop-ups and in various other ad formats on third-party sites. The objective is to attract traffic and acquire new customers.

Instant-win promotions and contests requiring some level of consumer participation are increasingly popular.

Again, their purpose goes beyond branding into acquisition and building databases of customers and prospects.

Knowledge Engineering These games can take many forms, from a roulette-style wheel spun by the user to determine whether she's got a winning game card to an online drag race in which consumers challenge an automated car for a chance to win a related prize.

One marketer specializing in such online instant promotions had noteworthy results with incentive-based online games and contests.

It's hard to say, but most marketers' resistance to the game industry probably has to do with the pimply, geeky gamer stereotype. If we're not in an industry targeted to the teen market, we probably don't believe that games can have any impact on our marketing efforts. That's wrong, and more companies than ever out there are trying to change our collective marketing perceptions -- and convince us to start using games as advertising.

The concept's called advergaming, and regardless of its clunky moniker, it's a concept that has worked well for brands such as Nike (with its Nike Shox email game campaign), Ford (which used a racing game to promote its new Escape), and Pepsi. Companies such as YaYa, WildTangent, and The Groove Alliance have used stunning 3-D technology to create games that rival many commercial desktop and console games. Other companies, such as XI Interactive have brought together some of the finest minds in the gaming industry to create killer sports games. They combine single-player fun with innovative viral techniques that get consumers engaged with brands.

Even now, most of these games can be played over dial-up connections with middle-of-the-road computers. But with higher-speed computers and broadband connections becoming commonplace, these games are destined to become killer marketing vehicles for the future.

Simply put, games engage users for long periods of time, immersing them in an environment where they can develop an affinity for the brand. Rather than merely watching the action (as they do when viewing a sponsored sporting event on TV), advergame consumers actually become part of the action. Also, since the experience can be closely scripted in a near TV-like manner, the action can be interrupted to show TV-like commercials, or the views can be scripted to ensure advertiser messages are seen. It's a great combination of interactivity (for the user) and control (for the advertiser).

Some companies (such as Life Savers) create destination sites (check out Candystand) that host heavily brandidentified games. Others (such as Nike) have created effective viral campaigns in which users can play each other via email, inviting friends to beat their scores. Games have also been incorporated into banners and other rich media ad vehicles.

The market (and audience) for games is huge now and is going to continue to grow in the future as today's kids become tomorrow's sophisticated consumers. It's time to consider games as a viable marketing vehicle.

Advergames The strict definition of an advergame is a Web-based computer game that incorporates advertising messages and images. However, we like to think of it as a tool that adds stickiness to your site as well as a little fun.

Advergames allow you to market your product or brand subtly. Benefits of an Advergame are:

Brand image reinforcement.

Databases created from the advergame can be used for demographics research.

Targeted markets can be reached by your advertising (when the game link is emailed).

Visitors may spend more time on your site.

Increased traffic due to viral marketing.

Fourth International Conference I.TECH 2006 An advergame is not just for kids anymore - many surfers play advergames. These surfers include but are not limited to:

59\% of the boys ages 13 to 17 who go online.

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