Macroscopic Modeling of Aggregation Experiments using Embodied Agents in Teams of Constant and Time-Varying Sizes In this paper, we present discrete-time, nonspatial, macroscopic models able to capture the dynamics of collective aggregation experiments using groups of embodied agents endowed with reactive controllers. The strength of the proposed models is that they have been built up incrementally, with matching between models and embodied simulations verified at each step as new complexity was added. Precise heuristic criteria based on geometrical considerations and systematic tests with one or two embodied agents prevent the introduction of free parameters into the models. The collective aggregation experiments presented in this paper are concerned with the gathering and clustering of small objects initially scattered in an enclosed arena. Experiments were carried out with teams consisting of one to ten individuals, using groups of both constant and time-varying sizes. In the latter case, the number of active workers was controlled by a simple, fully distributed, thresholdbased algorithm whose aim was to allocate an appropriate number of individuals to a time-evolving aggregation demand. To this purpose, agents exclusively used their local perception to estimate the availability of work. Results show that models can deliver both qualitatively and quantitatively correct predictions and they represent a useful tool for generalizing the dynamics of these highly stochastic, asynchronous, nonlinear systems, often outperforming intuitive reasoning. Finally, in addition to discussions of small prediction discrepancies and difficulties in generating quantitatively correct macroscopic models, we conclude the paper by reviewing the intrinsic limitations of the current modeling methodology and by proposing a few suggestions for future work. Swarm Intelligence (SI) [6, 8] is an innovative computational and behavioral metaphor for solving distributed problems that takes its inspiration from the biological examples provided by social insects [8, 9] such as ants, termites, bees, and wasps and by swarming, flocking, herding, and shoaling phenomena in vertebrates [18, 35] . The abilities of such natural systems appear to transcend the abilities of the constituent individual agents. In most biological cases studied so far, the robust and capable high-level group behavior has been found to be mediated by nothing more than a small set of simple low-level interactions between individuals, and between individuals and the environment. The SI approach emphasizes self-organization, distributedness, parallelism, and exploitation of direct (peer-to-peer) or indirect (via the environment) local communication mechanisms among relatively simple agents.. The main advantages of the application of the SI approach to the control of multiple robots are four-fold: (i) scalability: the control architecture can be kept exactly the same from a few units to thousands of units; (ii) flexibility: units can be dynamically added or removed, they can be given the ability to reallocate and redistribute themselves in a selforganized way; (iii) robustness: the resulting collective system is robust in facing a priori unknown environmental and team changes not only through unit redundancy but also through an adequate balance between exploratory and exploitative behavior; (iv) individual simplicity: a simple way to obtain an adequate explorative-exploitative balance and at the same time allow for unit miniaturization and overall system cost reduction is to minimize individual complexity.. Probabilistic modeling -The main motivation for developing a modeling methodology for swarm robotic systems is that, while SI principles are appealing from scalability, robustness, and individual simplicity points of view, they do not provide us with a way to quantitatively predict the swarm performance according to a particular metric or analyze further possible optimization margins and intrinsic limitations of this approach from an engineering point of view. In other words, if we want to achieve coordinated, self-organized group behavior based on local interactions, we need to have appropriate tools for understanding how to design and control individual units so that the swarm can achieve target behaviors and levels of performance. Models allow the engineer to capture the dynamics of these nonlinear, asynchronous, potentially large-scale systems at more abstract levels, sometimes achieving even mathematical tractability. More generally, modeling is a means for saving time, enabling generalization to different robotic platforms, and estimating optimal system parameters, including control parameters and number of agents in a team. There are fundamentally two different categories of models: microscopic and macroscopic models. While in microscopic models each robot has a separate representation, in macroscopic models, such as those presented in this paper, a single probabilistic representation (in our case a Markov chain) summarizes the whole robotic team. Therefore, macroscopic models offer a direct description of the collective group behavior and are computationally more efficient than their microscopic counterparts since, even if they must be solved numerically, their computation time is independent of the number of agents in the system. Although for a long period early in collective robotics research there was relatively little work in modeling of multi-robot systems, recently physicists and engineers have dedicated more attention to this problem (see, for example, related work performed by Kazadi et al. [17] , Lerman and Galstyan [23] , and Sugawara and Sano [36, 37] ). Moreover, modeling methodologies for swarm robotics systems must take into account mobility, individual intelligence, intrinsic stochastic properties of the collective coordination based on SI-principles, and, potentially, several different modalities of interaction among individuals and between an individual and the environment (e.g., mechanical, electromagnetic, chemical). This extremely rich combination of system features has drastically reduced the applicability of modeling techniques developed and commonly used in other fields.. In this paper, we combine the expertise accumulated while building probabilistic microscopic models of aggregation [25, 26] with that from devising macroscopic models [1, 3, 22, 28, 29, 30] for various distributed manipulation experiments including aggregation. In contrast to other classical approaches adopted in robotics, the originality of our models is that instead of being derived first in highly abstracted environmental conditions, where everything is noise-free and accurate, where global information about the world is available, and then moving down to reality by relaxing certain assumptions, we proceed along the path in reverse. Much as natural system scientists do, we start from real experimental data, gradually increasing the level of abstraction of the system description. Unlike biologists and physicists, however, we engineer our artificial systems and can therefore incrementally remove or add system details from a certain description level in order to understand their influence on the metric chosen for evaluating the performance of the swarm. Therefore, in contrast to contributions which traded quantitative prediction accuracy for model simplicity [17, 22] , our research aims to obtain quantitatively correct predictions without free parameters through an incremental development and corresponding validation of models using less abstracted tools (sensor-based, embodied simulator or real robots).. Macroscopic models and division of labor -Generally speaking, we are interested in understanding task allocation and labor division mechanisms exploited in social insect societies that are suitable for artificial, embedded systems such as multiple mobile robot platforms. Recently, several models have been proposed to explain these mechanisms in natural colonies [5] : some of them based on threshold responses b [7, 38] , others focus only on task-switching probabilities [34] . However, none of these publications has attempted to compare the macroscopic description of the system (which matches the experimental data) with a microscopic characterization, for instance by investigating how workers gather the information necessary to decide whether or not to switch task or to engage in a task performance. More specifically, they have not taken into consideration the partial perception in time and space of the demand and the embodiment of the agents. For instance, partial perceptions of the demand combined with real world uncertainties could strongly influence the optimal distribution of thresholds among teammates or the switching mechanism itself (e.g., probabilistic vs. deterministic). Therefore, our task as b In threshold-based systems, the 'propensity' of any agent to act is governed by a response threshold. If the demand is above the agent's threshold then that agent continues to perform the task; conversely, if the demand is below its threshold, then the agent stops performing that particular task. engineers is to use our intuition and engineering knowledge to concretely design individual robots, from software to hardware, which then allows the swarm as a whole to achieve self-organized division of labor.. Our efforts do not necessarily target the mimicking of natural, microscopic mechanisms since the available models of natural systems do not tell us implementation details at lower level and, moreover, natural and artificial hardware substrates show fundamental differences. However, we hope that this paper will not only contribute to the autonomous robotic literature but also stimulate the discussion among biologists about possible low-level mechanisms used by social insect societies for achieving division of labor.. Krieger and Billeter provide us one of the first examples of an engineering interpretation of the macroscopic allocation models presented in the social insect literature in [19] . In this experiment, the individual decision of whether or not to undertake a foraging mission was regulated by an internal threshold. A regulation of the foraging activity translated in this particular setup into a reduction of traffic jams at the nest entrance. The stimulus used for regulating the individual robot's activity was the nest energy, a software value which was assessed by an external supervisor as a function of the foraging success of the robotic colony and globally transmitted to all the robots. By implementing the threshold-based algorithm in this way, each individual robot must be endowed with a different threshold in order to achieve regulation of the overall colony activity. This in turn not only forced the experimenters to select an ad hoc distribution of thresholds but also resulted in a different exploitation of the teammates, the one endowed with the lowest threshold systematically being more active than that with the highest threshold.. In contrast with the engineering interpretation described above, in this paper we propose a threshold-based, distributed, scalable worker allocation algorithm that is based exclusively on the local estimation of the demand by the individuals. The individuals are all characterized by the same threshold but, since the agents do not perceive the demand globally but rather estimate it locally, they do not work or rest all at the same time, a behavior that would arise if the demand was broadcasted from an external supervisor.. The case study -The experiments presented in this article are the follow-up of experiments performed with real robots reported by Martinoli et al. [24, 25, 26] . The task is to collect small objects, referred to as "seeds", in a square arena and to gather them in a single cluster c using simulated Khepera robots [32] equipped with grippers and capable of distinguishing seeds from obstacles (walls, teammates) with their frontal sensors. As the robots have only local sensing capabilities and do not exploit a fully connected communication network, there is neither central nor global coordination among robots. Collective coordination is purely probabilistic and happens based on local interactions, strictly following the SI-principles mentioned above (see the experiment description in Section 2). In the experiments modeled in this paper, robots do not exploit any form of specific wireless peer-to-peer communication; stigmergic communication via the aggregation process is the only way to (indirectly) communicate. Moreover, as the robots do not have a global perception of the environment, they do not know when the task is c Although these experiments are not intended to reproduce a biological system, they present several similarities with the nest cleaning and dead ants clustering performed by some ant colonies [11] .. finished, motivating the need for a distributed task allocation mechanism to allow each individual to stop working based on its own estimate of the availability of work. Robots that decide to stop working can rest in a dedicated parking zone adjacent to the main arena. Allocation algorithms relying on direct peer-to-peer wireless communication have been published elsewhere [2] and are briefly mentioned in Subsection 7.2.. The specific interest for modeling this particular aggregation experiment lies in the fact that, although the control algorithms used for aggregation and individual activity regulation are both deterministic (and therefore easy to model), the whole system depends on and exploits randomness to achieve its final state, i.e., a single cluster and all the robots resting. Indeed, the stochastic nature of the robot-environment interactions combined with noisy sensory readings automatically generates probabilistic transitions between system (i.e., the robots' and environment's) states. As we will see more specifically in the next sections of the paper, first, randomness combined with irreversible elimination of isolated seeds prevents the aggregation process from getting stuck in multiple-cluster configurations, and second, randomness combined with an irreversible decision to rest achieves a self-regulation of the swarm activity which gracefully follows the evolution of the aggregation process.. Paper organization -In Section 2, we give a detailed description of the setup and of the embodied agents' control algorithms. In Section 3, we introduce the modeling methodology and we specifically address how we derived and calibrated the models presented in this paper. In Section 4, we first introduce and analyze two simple systems in which the robots search, avoid obstacles, and eventually interact with objects without, however, manipulating them. We validate model predictions with embodied simulations. In Section 5, we present the full aggregation experiment without worker allocation while in Section 6 we illustrate how the model can be extended for capturing the worker allocation mechanism. In both sections, we validate model predictions with embodied simulations. In Section 7, we discuss problems in building accurate models, strength and limitations of the modeling methodology, and briefly introduce (but do not model) possible, more efficient and/or robust variations of the worker allocation algorithm. Section 8 concludes the paper and presents a few suggestions for future work. In this paper we have presented macroscopic models of incremental complexity from simple examples in Section 4 representing scenarios characterized by no modification of the environment to the scenario presented in Section 6, a model that captures not only environmental modification but also changes in the robotic team size. In each of these sections, we have successfully validated the macroscopic models with embodied simulation results comparing the two levels of implementation based on either state variables in steady-state regimes (Section 4) or more high-level metrics related to the aggregation or worker allocation processes (Sections 5 and 6).. In this section, we discuss the usefulness of macroscopic models for understanding aggregation experiments, generalization to tasks other than aggregation, control optimization, the difficulties encountered in generating quantitatively accurate models, and finally, the intrinsic limitations of such models. With a team of 10 robots (Figure 9 , left), the aggregation process clearly has two phases. In the first phase, the mean cluster size increases steadily from 1 seed to about 15 seeds and in a second phase, the mean cluster size remains, on average, constant around 15 seeds. Similarly, during the first phase, Figure 9 , right, shows that the average number of clusters decreases asymptotically from 20 to about 1 and then remains close to 1 during the second phase of the aggregation process. This is clearly a side effect of the lack of a mechanism to allow workers to stop performing the aggregation task once a single cluster arises, which is confirmed by the fact that 10 hours into the aggregation process, the average cluster size built by the team of 5 robots (see Figure 8 , left) is larger than that obtained with the team of 10 robots.. The results in Figure 8 and Figure 9 can be explained by the fact that, once a single cluster arises only two manipulation sites remain in the environment (i.e., the two tips of that cluster); the seed pick-up and drop-off probabilities (i.e., dec c n p and inc c n p ) are empirically very close, therefore at any given time during the last phase of the aggregation process, on average, half of the active workers will be carrying a seed and the other half will not. This explains why the average cluster size at steady-state (i.e., L * ) as expressed in Equation (32), is a decreasing function of the team size. For instance, L * ≈ 15.2 seeds for the team of 10 robots and Figure 9 shows that after 10 hours of aggregation the average cluster size built by that team is close to this value for both the macroscopic model and the embodied simulator..

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Parameterized linear matrix inequality techniques in fuzzy control system design Abstract-This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems. These PLMI characterizations are, in turn, relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control systems. The advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations.Index Terms-Fuzzy systems, parameterized linear matrix inequality (PLMI). T HE well-known Tagaki-Sugeno (T-S) fuzzy model [13] is a convenient and flexible tool for handling complex nonlinear systems [11] , where its consequent parts are linear systems connected by IF-THEN rules. Suppose that is the state vector with dimension , is the control input with dimension , , and are the disturbance and controlled output of the system with the same dimension , and denotes the number of IF-THEN rules, where each th plant rule has the form is and is H. D. Tuan and T. Narikiyo are with the Department of Control and Information, Toyota Technological Institute, Hisakata 2-12-1, Tenpaku, Nagoya 468-8511, Japan (e-mail: tuan@toyota-ti.ac.jp; n-tatsuo@toyota-ti.ac.jp).. P. Apkarian is with ONERA-CERT, 31055 Toulousse, France (e-mail: apkarian@cert.fr).. Y. Yamamoto is with Aichi Steel Ltd., Arao-machi, Tokai-shi, Aichi 477-0036 Japan. He was also with the Toyota Technological Institute, Hisakata 2-12-1, Tenpaku, Nagoya 468-8511, Japan.. Publisher Item Identifier S 1063-6706(01)02825-9.. the state-space representation of the T-S model is (4) where (5) The simple and natural feedback control for T-S model is the so-called parallel distributed compensation (PDC), whose each th plant rule is inferred similarly to (1) as is and is. The outcome is the state-feedback control law:. where (8) Since in (4) is available online, system (4) also belongs to the more general class of gain-scheduling control systems intensively studied in control theory in the past decade (see, e.g., [12] , [1] , and [2] ). Gain-scheduling is a widely used method for the control of nonlinear plants or a family of linear models. Only recently, however, this technique has received a systematic treatment within the framework and tools based on LMIs [12] , [1] , [2] . LMI characterizations of the gain-scheduling control problem renders the design task both practical and appealing since LMIs can be globally and efficiently solved by interiorpoint methods in semidefinite programming. The representation relation (3) and (4) is often called a polytopic system [7] a class of parameter-dependent systems, which lends itself easily to practical computations. At first glance, it could appear that the additionally restricted structure (8) for PDC fuzzy control incurs conservatism in the synthesis problem in comparison with the most general structure (7) often considered in gain-scheduling control [14] , [15] . In fact, the main contribution of [14] and [15] is to adapt the approach of [7] (for polytopic systems) to design PDC controller (8) . However, by a main result presented in this paper, the existence of a general gain-scheduling freely structured controller (7) is equivalent to the existence of one with PDC structure (8) . In other words, the PDC structure (7) very naturally arises in gain-scheduling control. Moreover, 1063-6706/01$10.00 © 2001 IEEE our presented results based on a general theory of gain-scheduling control [1] , [2] , [12] have the following essential advantages over those of [14] and [15] :. 1) The resulting optimization formulations are much simpler with much fewer variables involved. Therefore, they are much more efficient computationally. In fact, our computational experiments show that the cpu time for solving problems of [14] and [15] are 2-4 times larger than that needed for solving our problems. 2) The controller performance are much better. In fact, our computational experience indicates that our controllers improve the performance by a significant order of magnitude of 10-15 as compared to those of [14] and [15] . It is important to note that the aforementioned advantages are also achieved by our new relaxation results for solving arising parameterized linear matrix inequalities (PLMIs). To see how PLMIs naturally arise in gain-scheduling control including fuzzy logic control, let us consider the stabilization problem where we seek stabilizing (1), i.e., such that system (9) resulting from (1) and (8) by setting is asymptotically stable.. By virtue of the Lyapunov theorem, (9) is asymptotically stable if there exists a quadratic Lyapunov function such that (10). The linearization technique (12) is rather standard and well known in control theory, even before LMI invention (see, e.g., [6] ). Particularly, it is the main tool of [7, Ch. 7] in state-feedback control for polytopic systems. Later, it has been adapted in [14] and [15] for designing PDC of the form (8) . In fact, with the PDC (8), has the form. Therefore, (11) can be rewritten as (14) where (15) i.e., is an affine matrix-valued function of the variable .. Note that (14) is an LMI problem depending on the parameter , i.e., one has to check the LMIs in (14) holds for all , hence, the named PLMI.. As we shall see, PLMIs like (14) also arise in other control problems such as the regulator problem, , control problems and so forth. PLMI problems of the form (14) belong to the class of robust semidefinite programs, which is a very hard optimization problem whose NP-hardness is well known [4] . Therefore, it is natural to derive some convex (LMI) relaxations for (14) (see, e.g., [5] , [3] , and [17] ) to make it computationally tractable. For it is obvious that one such convex (LMI) relaxation for (14) is obtained as [15] (16) Unfortunately, conditions (16) are practically very restrictive and some potential improvements have been discussed in [14] - [16] . Other convex relaxations techniques solving a general PLMI including (14) as a particular case have been proposed in [17] and [3] .. A major target of this paper is to give some new convex relaxation results for PLMI (14) , which include and generalize all previous results in [14] , [15] , [17] , and [3] as a particular case and are less conservative, i.e., they offer much better solutions while are still computationally efficient.. Since the work of [9] , it is known that in many cases the control variable in (11) can be eliminated by using the Projection Lemma [9] or the Finsler's Lemma. Such an elimination procedure not only makes LMI formulations much more appealing for computation but plays a key role for obtaining LMI characterizations in dynamic output feedback problems. In this paper, such elimination technique is adapted to obtain simpler PLMI characterizations with the two aforementioned advantages compared with (14) , (15) and other arising in regulator and control problems.. The structure of the paper is as follows. The main results on LMI relaxation for PLMIs are given in Section II. Then, based on this, different PLMI characterizations for stabilization, regulator, control problems together with their LMI relaxations are considered in Sections III-V. The comparison between these LMI relaxations are illustrated by numerical examples in Section VI.. The notation of the paper is fairly standard. is the transpose of the matrix . For symmetric matrices, ( , respectively) means is negative definite (positive definite, respectively). In symmetric block matrices or long matrix expressions, we use as an ellipsis for terms that are induced by symmetry, e.g.,. Useful instrumental tools such as congruent transformation of matrices, Shur's complement and Finsler's lemma are given in the Appendix.

O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Nash equilibria in graphical games on trees revisited Graphical games have been proposed as a game-theoretic model of large-scale distributed networks of non-cooperative agents. When the number of players is large, and the underlying graph has low degree, they provide a concise way to represent the players' payoffs. It has recently been shown that the problem of finding Nash equilibria in a general degree-3 graphical game with two actions per player is complete for the complexity class PPAD, indicating that it is unlikely that there is any polynomial-time algorithm for this problem. In this paper, we study the complexity of graphical games with two actions per player on bounded-degree trees. This setting was first considered by Kearns, Littman and Singh, who proposed a dynamic programming-based algorithm that computes all Nash equilibria of such games. The running time of their algorithm is exponential, though approximate equilibria can be computed efficiently. Later, Littman, Kearns and Singh proposed a modification to this algorithm that can find a single Nash equilibrium in polynomial time. We show that this modified algorithm is incorrect -the output is not always a Nash equilibrium. We then propose a new algorithm that is based on the ideas of Kearns et al. and computes all Nash equilibria in quadratic time if the input graph is a path, and in polynomial time if it is an arbitrary graph of maximum degree 2. Moreover, our algorithm can be used to compute Nash equilibria of graphical games on arbitrary trees, but the running time can be exponential, even when the tree has bounded degree. We show that this is inevitable -any algorithm of this type will take exponential time, even on bounded-degree trees with pathwidth 2. It is an open question whether our algorithm runs in polynomial time on graphs with pathwidth 1, but we show that finding a Nash equilibrium for a 2-action graphical game in which the underlying graph has maximum degree 3 and constant pathwidth is PPAD-complete (so is unlikely to be tractable). Graphical games were introduced in the papers of Kearns et al. [8] and Littman et al. [9] as a succinct representation of games with a large number of players. The classical normal form (or matrix form) representation has a size that is exponential in the number of players, making it unsuitable for large-scale distributed games. A graphical game associates each player with a vertex of an underlying graph G, and the payoff to that player is a function of the actions chosen by himself and his neighbours in G; if G has low degree, this is a concise way to represent a game with many players.. The papers [8, 9] give a dynamic-programming algorithm for finding Nash equilibria in graphical games where there are two actions per player and G is a tree. The first of these papers describes a generic algorithm for this problem that can be specialized in two ways: as an algorithm that computes approximations to all Nash equilibria in time polynomial in the input size and the approximation quality, or as an exponential-time algorithm that allows the exact computation of all Nash equilibria in G. In [9] , the authors propose a modification to the latter algorithm that aims to find a single Nash equilibrium in polynomial time. This does not quite work, as we show in Section 3, though it introduces a useful idea. The generic algorithm of [8] consists of two phases which we will refer to as the upstream pass and the downstream pass; 1 the former starts at the leaves of the tree and ends at the root, while the latter starts at the root and ends at the leaves. It is assumed that each player has two pure strategies (actions), which are denoted by 0 and 1; it follows that any mixed strategy can be represented as a single number x ∈ [0, 1], where x is the probability that the player selects 1. During the upstream pass, each vertex V computes the set of its potential best responses to every mixed strategy w of its parent W ; a strategy v is a potential best response to w if there is a Nash equilibrium in the graphical game downstream of V (inclusive) given that W plays w (for a more technical definition, the reader is referred to Section 2). The output of this stage can be viewed as a (continuous) table T (w, v), where T (w, v) = 1 if and only if v is a potential best response to w; we refer to this table as the best response policy for V . The generic algorithm does not address the problem of representing the best response policy; in fact, the most important difference between the two instantiations of the generic algorithm described in [8] is in their approach to this issue. The computation is performed inductively: the best response policy for V is computed based on the best response policies of V 's children U1, . . . , U k . By the end of the upstream pass, all children of the root have computed their best response policies.. In the beginning of the downstream pass, the root selects its strategy and informs its children about its choice. It also selects a strategy for each child. A necessary and sufficient condition for the algorithm to proceed is that the strategy of the root is a best response to the strategies of its children and, for each child, the chosen strategy is one of the pre-computed potential best responses to the chosen strategy of the root. The equilibrium then propagates downstream, with each vertex selecting its children's actions. The action of the child is chosen to be any strategy from the pre-computed potential best responses to the chosen strategy of the parent.. To bound the running time of this algorithm, the paper [8] shows that any best response policy can be represented as a union of an exponential number of rectangles; the polynomial time approximation algorithm is obtained by combining this representation with a polynomial-sized grid. The main idea of [9] is that it is not necessary to keep track of all rectangles in the best response policies; rather, at each step of the upstream pass, it is possible to select a polynomial-size subset of the corresponding policy (in [9] , this subset is called a breakpoint policy), and still ensure that the downstream pass can proceed successfully (a sufficient condition for this is that the subset of the best response policy for V stored by the algorithm contains a continuous path from w = 0 to w = 1).

O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Mobile Relay Configuration in Data-Intensive Wireless Sensor Networks Abstract-Wireless Sensor Networks (WSNs) are increasingly used in data-intensive applications such as micro-climate monitoring, precision agriculture, and audio/video surveillance. A key challenge faced by data-intensive WSNs is to transmit all the data generated within an application's lifetime to the base station despite the fact that sensor nodes have limited power supplies. We propose using low-cost disposable mobile relays to reduce the energy consumption of data-intensive WSNs. Our approach differs from previous work in two main aspects. First, it does not require complex motion planning of mobile nodes, so it can be implemented on a number of low-cost mobile sensor platforms. Second, we integrate the energy consumption due to both mobility and wireless transmissions into a holistic optimization framework. Our framework consists of three main algorithms. The first algorithm computes an optimal routing tree assuming no nodes can move. The second algorithm improves the topology of the routing tree by greedily adding new nodes exploiting mobility of the newly added nodes. The third algorithm improves the routing tree by relocating its nodes without changing its topology. This iterative algorithm converges on the optimal position for each node given the constraint that the routing tree topology does not change. We present efficient distributed implementations for each algorithm that require only limited, localized synchronization. Because we do not necessarily compute an optimal topology, our final routing tree is not necessarily optimal. However, our simulation results show that our algorithms significantly outperform the best existing solutions. In this paper, we proposed a holistic approach to minimize the total energy consumed by both mobility of relays and wireless transmissions. Most previous work ignored the energy consumed by moving mobile relays. When we model both sources of energy consumption, the optimal position of a node that receives data from one or multiple neighbors and transmits it to a single parent is not the midpoint of its neighbors; instead, it converges to this position as the amount of data transmitted goes to infinity. Ideally, we start with the optimal initial routing tree in a static environment where no nodes can move. However, our approach can work with less optimal initial configurations including one generated using only local information such as greedy geographic routing. Our approach improves the initial configuration using two iterative schemes. The first inserts new nodes into the tree. The second computes the optimal positions of relay nodes in the tree given a fixed topology. This algorithm is appropriate for a variety of data-intensive wireless sensor networks. It allows some nodes to move while others do not because any local improvement for a given mobile relay is a global improvement. This allows us to potentially extend our approach to handle additional constraints on individual nodes such as low energy levels or mobility restrictions due to application requirements. Our approach can be implemented in a centralized or distributed fashion. Our simulations show it substantially reduces the energy consumption by up to 45%. We review three different approaches, mobile base stations, data mules, and mobile relays, that use mobility to reduce energy consumption in wireless sensor networks. A mobile base station moves around the network and collects data from the nodes. In some work, all nodes are always performing multiple hop transmissions to the base station, and the goal is to rotate which nodes are close to the base station in order to balance the transmission load [4] , [5] , [6] . In other work, nodes only transmit to the base station when it is close to them (or a neighbor). The goal is to compute a mobility path to collect data from visited nodes before those nodes suffer buffer overflows [7] , [8] , [14] , [15] . In [8] , [19] , [20] , several rendezvousbased data collection algorithms are proposed, where the mobile base station only visits a selected set of nodes referred to as rendezvous points within a deadline and the rendezvous points buffer the data from sources. These approaches incur high latencies due to the low to moderate speed, e.g. 0.1-1 m/s [14] , [16] , of mobile base stations.. Data mules are similar to the second form of mobile base stations [9] , [10] , [11] . They pick up data from the sensors and transport it to the sink. In [21] , the data mule visits all the sources to collect data, transports data over some distance, and then transmits it to the static base station through the network. The goal is to find a movement path that minimizes both communication and mobility energy consumption. Similar to mobile base stations, data mules introduce large delays since sensors have to wait for a mule to pass by before starting their transmission.. In the third approach, the network consists of mobile relay nodes along with static base station and data sources. Relay nodes do not transport data; instead, they move to different locations to decrease the transmission costs. We use the mobile relay approach in this work. Goldenberg et al. [13] showed that an iterative mobility algorithm where each relay node moves to the midpoint of its neighbors converges on the optimal solution for a single routing path. However, they do not account for the cost of moving the relay nodes. In [22] , mobile nodes decide to move only when moving is beneficial, but the only position considered is the midpoint of neighbors.. Unlike mobile base stations and data mules, our OMRC problem considers the energy consumption of both mobility and transmission. Our approach also relocates each mobile relay only once immediately after deployment. Unlike previous mobile relay schemes [13] and [22] , we consider all possible locations as possible target locations for a mobile node instead of just the midpoint of its neighbors.. Mobility has been extensively studied in sensor network and robotics applications which consider only mobility costs but not communication costs. For example, in [23] , the authors propose approximation algorithms to minimize maximum and total movement of the mobile nodes such that the network becomes connected. In [24] , the authors propose an optimal algorithm to bridge the gap between two static nodes by moving nearby mobile nodes along the line connecting the static points while also minimizing the total/maximum distance moved. In [25] , [26] , the authors propose algorithms to find motion paths for robots to explore the area and perform a certain task while taking into consideration the energy available at each robot. These problems ignore communication costs which add an increased complexity to OMRC, and consequently their results are not applicable.. Our OMRC problem is somewhat similar to a number of graph theory problems such as the Steiner tree problem [27] , [28] , [29] and the facility location problem [30] , [31] . However, because the OMRC cost function is fundamentally different from the cost function for these other problems, existing solutions to these problems cannot be applied directly and do not provide good solutions to OMRC. For example, there is no obvious way to include mobility costs in the Steiner tree problem.

O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Mathematical model of consumer homeostasis control in plant-herbivore dynamics Consumers must regulate the elemental composition of body tissue at ratios that differ from those of their food. This problem of elemental homeostasis is especially acute for herbivores for which elemental composition of food does not equal that of the consumer and changes widely throughout the lifespan. We extend work of Sterner [1] and Frost & Elser [2] using a dynamic model of homeostatic control within tolerance limits by consumers feeding on unbalanced diets based on nonlinear assimilation as a primary mechanism. Differential assimilation provides a suitable, if incomplete, mechanism for homeostasis where the limiting element defines the accumulation trajectory of nutrients incorporated into the consumer. In this paper, we explicitly incorporate differential assimilation with a variable food supply to examine control of the maintenance of elemental homeostasis in a consumer eating food composed of significantly different elemental ratios. Our model extends those of Sterner [1] and Frost & Elser [2] (see also Sterner & Elser [16] ). By including a tolerance envelope around exact homeostatic control, we show that a consumer can adjust assimilation in response to food the most limiting element. The limiting nutrient defines the trajectory of elemental accumulation constrained by the tolerance envelope, allowing one to predict the biomass accumulation of critical elements (e.g., C, P) depending on the relative abundance of these elements in the food supply. As the food supply ratio changes independent of the action of consumers, assimilation changes accordingly and relative elemental accumulation shifts. In this sense, differential assimilation can effectively act as a nonlinear control mechanism permitting elemental homeostasis in consumers as predicted by Sterner [1] . Finally, this work has further application to the overall nutrient cycling problem in ecosystems, being one essential component in the process (DeAngelis [40] , Daufresne & Loreau [41] , Mueller et al [42] ). Figure 5: Calculated C:P biomass ratio in 0 ≤ t ≤ 10 with a changing food supply: a low quality food supply C f = 48, Q = 1/400 in 0 ≤ t ≤ 2.5,and high quality C f = 48, Q = 1/75 in 2.5 ≤ t ≤ 10. The total growth is C(10) = 3.738.

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Dynamic Shannon coding For dynamic character coding, we are given a string S = s 1 · · · s m , character by character, drawn from an alphabet of size n. We must encode each character before receiving the next. Our goal is to minimize the length of the entire encoding of S.The best known algorithms for dynamic character coding are based on Huffman coding. There is an algorithm due to Faller, Gallager, and Knuth [2] uses at most (H + 2 + r)m + O(n log n) bits [1, 4] is the empirical entropy of S and 0 ≤ r < 1 is a function of the character frequencies in S. Vitter [5] gave an improved version that uses at most (H + 1 + r)m + O(n log n) bits.We present a new algorithm, called dynamic Shannon coding, that uses at most (H + 1)m + O(n log m) bits to encode S. For n ∈ o(m/ log m), including the standard case of a fixed alphabet size, this improves previous upper bounds. Dynamic Shannon coding uses data structures similar to those used by Knuth, but employs background processing to update the weight associated with each character. In addition, our analysis of dynamic Shannon coding is much simpler than the analysis of dynamic Huffman coding.For dynamic length-restricted coding, the length of any codeword used in the encoding must not exceed a given bound. Liddell and Moffat [3] gave an algorithm for this problem, but their algorithm is quite complicated and they did not give bounds on the length of the encoding it produces.We show that dynamic Shannon coding can be easily modified to restrict the maximum length of any codeword in the encoding produced. Specifically, given an integer ≥ 1, our algorithm uses at most 2 log 2 n + bits to encode the first occurrence of each distinct character in S, at most log 2 n + bits to encode each remaining character in S, and at most H + 1 + 1 (2 −1) ln 2 m + O(n log m) bits in total. The key idea is to smooth the relative frequencies of characters when computing their weights.Like the cited algorithms, both versions of our algorithm take O((H + 1)m) time to encode S. 1. R. De Prisco and A. De Santis. On the redundancy achieved by Huffman codes.

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Design and Performance Evaluation of Data Dissemination Systems for Opportunistic Networks Based on Cognitive Heuristics In the convergence of the Cyber-Physical World, user devices will act as proxies of the humans in the cyber world. They will be required to act in a vast information landscape, asserting the relevance of data spread in the cyber world, in order to let their human users become aware of the content they really need. This is a remarkably similar situation to what the human brain has to do all the time when deciding what information coming from the surrounding environment is interesting and what can simply be ignored. The brain performs this task using so called cognitive heuristics, i.e. simple, rapid, yet very effective schemes. In this article, we propose a new approach that exploits one of these heuristics, the recognition heuristic, for developing a self-adaptive system that deals with effective data dissemination in opportunistic networks. We show how to implement it and provide an extensive analysis via simulation. Specifically, results show that the proposed solution is as effective as state-of-the-art solutions for data dissemination in opportunistic networks, while requiring far less resources. Finally, our sensitiveness analysis shows how various parameters depend on the context where nodes are situated, and suggest corresponding optimal configurations for the algorithm. The pervasive and ubiquitous presence in the physical world of devices that are able to interact among themselves and with their own users, is leading to what is called the Cyber-Physical World (CPW) convergence scenario, which is one of the key trends in future Internet research [Conti et al. 2011a [Conti et al. , 2012 Paul et al. 2011] . One of the main characteristics of the CPW convergence scenario will be the presence of a huge number of mobile devices handled by their users, which allow a flow of information from the physical to the cyber world and vice-versa. Mobile devices will then be part of a vast dynamic information environment, where data will come from many, disparate sources. In this scenario, more traditional CDNs or P2P networks [Passarella 2012 ] will be coupled with the data coming from, and spread by, the mobile devices themselves. In fact, increasingly active user participation in the process of data creation and diffusion will create a huge quantity of pervasive information. Moreover, a considerable portion of this data will also be very contextualized, i.e. relevant only at specific times and/or geographic areas, and of interest only for specific groups of users. In such a context, it is reasonable to think of data exchange schemes, where data is exchanged directly between users upon physical contact, rather than relying exclusively on fixed infrastructures, both for communication and data sharing. Opportunistic networking [Conti et al. 2011b; Pelusi et al. 2006 ] is one of the key paradigms for supporting direct communication between devices in such scenarios. In opportunistic networks physical encounter events between nodes are opportunistically exploited to exchange data. No paths are precomputed from source to destination, but nodes evaluate how suitable is another encountered node to bring data to interested users. Thus, opportunistic networks do not suffer from the typical problems that plague mobile ad hoc networking (MANET) solutions related to the instability of mobile topologies.. Since devices moving in the CPW convergence scenario will act on behalf of their users inside the cyber world, they can be regarded as the avatars of their respective users, allowing their holders to explore congested cyber information landscape. They will have to face the challenging task of rapidly reacting to the discovery of new data and assert the relevance of such content in order to select the most interesting information for both their own users and the overall dissemination of data to other interested users. This selection should be performed swiftly, since the contextualized nature of information could make it aged or not available anymore before a complex evaluation process has ended. Furthermore, collecting complete information in order to make optimal choices about which data items to store is typically unfeasible in practice due to excessive overhead and the time to obtain it. Finally, nodes-in general-will contribute limited resources to the dissemination process (e.g. in terms of computing and storage capabilities). Thus the data selection process must be very lightweight and able to perform a sharp distinction between data items, since only a very limited portion of them could be stored.. One approach to address the aforementioned problems is to embed autonomic decision-making capabilities into mobile devices Carreras et al. 2008; Gao and Cao 2011; Ioannidis et al. 2009; Jaho et al. 2010 Jaho et al. , 2012 Krifa et al. 2011; Lenders et al. 2008; Pantazopoulos et al. 2010; Tang et al. 2011] . In this article, we explore a new (to the best of our knowledge) direction in the autonomic networking field, i.e., we exploit results coming from cognitive psychology, by using models of how the human brain assesses the relevance of information under partial knowledge. In fact, human brains are able to swiftly contextualize the stimuli they are subject to, identify the relevant features and knowledge to be considered, assert the relevance of perceived information, and finally select the most useful data, even when only partial information is available. Therefore, as depiceted in Figure 1 , we propose to overcome the problem of traditional ICT information selection processes (left side of the figure) by directly embedding in an ICT system (right side), the rules and procedures for content selection applied by the final user of the ICT system: the human brain.. In order to achieve this goal, we exploit functional descriptions of a set of the most relevant processes used by the brain in the decision-making process, i.e. cognitive heuristics (e.g. [Goldstein and Gigerenzer 1996] ). In computer science, heuristics are computational methods that attempt to optimize a problem by producing stochastically good results. They are obtained by pruning the search space through an iterative improvement of a candidate solution with regard to a given measure of quality. On the other hand, cognitive heuristics are fast, frugal and adaptive strategies of the brain that allow humans to face complex situations by addressing simpler problems. Cognitive heuristics are effective, simple rules, requiring little estimation time and working under incomplete knowledge of the problem space. Hence, despite their simplicity, they are indispensable psychological tools, that are very effective in solving decision-making problems like information selection and acquisition.. In this article, we want to design a data dissemination system in an opportunistic networking scenario by harnessing one of the simplest and most studied of these heuristics: the recognition heuristic [Gigerenzer and Goldstein 2002; Goldstein and Gigerenzer 1996] . This heuristic assumes that merely recognizing an object is sufficient to determine its relevance (see Section 3 for a precise definition). We propose an exploitation of the recognition heuristic to let each node rapidly decide the utility of taking one data item instead of another upon making direct (one-hop) contact with other nodes. First of all, we define the requisites needed to implement the recognition heuristic in an opportunistic environment, by defining the main variables involved in this process. Then, we propose an algorithm, inspired by the Take-the-Best cognitive scheme, which uses the model of Goldstein and Gigerenzer [1996] and exploits the recognition heuristic in order to simplify and limit the complexity of the data selection task. This is done by the recursive creation of small subsets of all the discovered data (consideration sets, see Section 3) from which the relevant data is sorted out. Finally, we evaluate by simulation, the data diffusion process when nodes exploit the proposed solution. Our results show that a solution based on cognitive heuristics is as effective as state-of-the-art solutions for data dissemination in opportunistic networks in delivering to all users the data items they are interested in. However, the proposed solution achieves this result with much lower resource consumption in terms of network traffic. Moreover, our sensitiveness analysis shows how various parameters depend on the context where nodes are situated, and suggests corresponding optimal configurations for the algorithm.. The rest of this article is organized as follows. In Section 2 we briefly survey the state of the art on data dissemination in opportunistic networks. In Section 3 we give a more precise description of the recognition heuristic. In Section 4 we introduce how the recognition heuristic can be implemented by mobile devices, while in Section 5 we define an algorithm that exploits it for the purpose of data dissemination in an opportunistic network. Section 6 presents the experimental results obtained via simulation. Finally, Section 7 concludes the article. In the CPW convergence scenario, devices will act as proxies of their users in a very crowded information landscape. These devices will need efficient mechanisms to select the most relevant information for their users and for a collaborative exchange of information. In this article, we proposed a new approach for trying to directly embed in an ICT system, the rules and procedures for content selection applied by the human brain. These rules are known as cognitive heuristics. Heuristics model how the human brain assesses the relevance of information using only partial knowledge of the problem space and very limited resources. In this article we present how to exploit these models (already established and coded in the cognitive psychology field) to drive data dissemination processes in an opportunistic networking environment.. In particular, we focus on one of the most simple and efficient cognitive heuristics, the recognition heuristic. The recognition heuristic discriminates objects with respect to a given criterion, without requiring the collection of all the information needed to exactly compute the criterion. It assumes that recognized objects have higher value (with respect to the criterion) than nonrecognized objects, and discriminate among them accordingly. We have shown how the recognition heuristic can be implemented in an opportunistic network. Then we have shown how nodes can efficiently combine multiple instances of the recognition heuristic to assess the relevance of available data items, thus deciding what to store and what to drop. This selection is based on a variation of the Take-the-Best algorithm, also originally proposed in the cognitive psychology literature.. Simulation results show that an information dissemination system based on cognitive heuristics is able to achieve the same performance as a more complex, state-ofthe-art algorithm, while needing less than half of the resources. Moreover, we tested our solution in other complex scenarios, with an increasing number of nodes in the network. In a network where subscriptions to topics of interest are distributed unevenly among nodes, the system is able to balance the diffusion of the most and least popular channels, leading them to converge at the same time. Other results show the ability to adapt its behaviour and promptly react to the presence of churning nodes and the sudden insertion of new channels. Results show that a correct tuning of the heuristic parameters has to be evaluated in order to enable the system to achieve its best performance.. In order to further explore the potential of this solution, key topics for future research include the development of analytical models that enable formal understanding of the impact and the interplay of the parameters. Moreover, we wish to investigate how the proposed data dissemination works when additional context information (such as social relationships between users) is exploited. Furthermore, it will also be interesting to understand whether it is possible, in this context, to define an equivalent of the cognitive "adaptive toolbox." In particular, it could be interesting to know whether other heuristics (beyond recognition) can be effectively applied to data dissemination and how they can be exploited in conjunction with the recognition heuristic. Several solutions have been proposed for data dissemination in opportunistic networks. Hereafter we briefly mention the key approaches. A more detailed review is available in Boldrini and Passarella [2013] .. The first work that investigated the problem of content dissemination in an opportunistic network scenario was developed in the PodNet Project [Lenders et al. 2008] . In PodNet, items are arranged in channels, based on their content. Each node is subscribed to a channel and thus tries to retrieve all of its related items. The authors propose four different strategies to decide which data items to store (in addition to those of specific interest for the local users), all based on the items' channel popularities. All the proposed strategies outperform a scenario where nodes keep only the items of the channel they are subscribed to. PodNet does not exploit any social information about nodes. On the other hand, more advanced approaches for data dissemination in opportunistic networks exploit information about users' social relationships to drive the data dissemination process.. In ContentPlace , dissemination is driven by the social structure of the network users, such that nodes store data items that are likely of interest to users they have social relationships with (and who, therefore, are expected to be in touch in the near future). To this end, ContentPlace proposes a set of social-aware dissemination strategies. Each strategy tries to give an approximate optimal solution to a multicostrained knapsack problem, where the goal is to maximize the social utility of fetching an item, and at the same, taking into account the limited resources of a device, by computing the resource consumption of this action. Utility is directly proportional to the number of community users interested in it (access probability) and inversely proportial to the number of community nodes already sharing it (availability). Both of these parameters are estimated as a result of meetings with other nodes. The different strategies proposed give different weights to the utility of each community, thus implementing different dissemination policies. The best results are obtained by strategies that disseminate items on the basis of the probability of future encounters. Another example of social-based approaches is presented in Yoneki et al. [2007] .. Rather than exploiting local optimization policies, as in ContentPlace, in Reich and Chaintreau [2009] , the authors define the content dissemination issue as a global optimization problem. They view all the nodes' shared memories as a unique, global cache. The problem of which item to fetch upon contact is defined as a global optimization problem. The global utility function defines the best possible allocation of items to all the nodes. This is done by considering the items' utilities for each single node, weighted with the actual expected rate of requests for every item. Clearly, the global parameters needed to compute these values cannot be known by each single node. Thus, in practice, each node adopts a simple local approximation policy.. The Push-and-Track system [Whitbeck et al. 2011] proposes a trade-off between an infrastracture-based dissemination approach and pure opportunistic-based solutions. They assume that nodes participating in an opportunistic network are also typically in contact with fixed wireless broadband infrastractures. The authors consider a scenario where content must be delivered to interested users within a given temporal deadline. The central infrastracture sends the content to a small subset of users, which, in turn, start disseminating it with pure opportunistic strategies. Using an ideal dissemination plan, the infrastructure periodically checks whether the content is to be re-injected to another subset of nodes or, when the deadline is approaching, sent to all the remaining users who do not have yet received it.. All these systems use computer-science heuristics. With respect to these approaches, in this article we take a completely new direction, by borrowing models of human cognitive processes coming from the cognitive psychology domain. Due to the characteristics of these cognitive processes, one of the results we expect to achieve is to build a content dissemination mechanism as efficient as other state-of-the-art solutions (able to deliver data to all the requesting nodes) while at the same time, limiting the resources needed to reach this result. As this approach is still totally unexplored, in this article we limit the set of contextual information that we use to the very minimum, and for example, we do not exploit information about users' social structures. This allows us to obtain initial exploratory results about the feasibility of this novel approach.. The work presented in the following sections is an extension of what we presented in Conti et al. [2011b] . The main extensions that we add in this article are a more detailed description of the cognitive concepts behind this work, a more complete illustration of the developed algorithms, and an extensive set of simulation results, including a comparison with another state-of-the-art solutions and tests under various, different scenarios. This article is also complementary to Conti et al. [2013] , where we study how cognitive models of information representation in the human brain can be exploited to track dissemination of semantic information in opportunistic networks.. Since the focus of this article is on the recognition heuristic, in this section we give an overview of the cognitive science background for this heuristic. A more general description of the concept of cognitive heuristic and some examples of these cognitive processes are given in Appendix A.. The interest of the scientific community in the recognition heuristic [Gigerenzer and Goldstein 2002; Goldstein and Gigerenzer 1999] can be evidenced by the three special issues on this topic (from 2010 to 2011) in the official journal of the Society for Judgment and Decision Making, the Journal of Decision Making [Marewski et al. 2010 [Marewski et al. , 2011a [Marewski et al. , 2011b . The recognition heuristic is based on a very simple rule. When choosing between two objects, and one is recognized (the actor is able to recall from memory that she has already heard about that object) and the other is not, the recognition heuristic infers that the recognized object has a higher value with respect to a given evaluation criterion. It can also be used with sets of more than two objects, in order to draw out the subset of the most significant objects [Marewski et al. 2010c] . People tend to rely on this heuristic when the real criterion value is not available, not known or requires further, more complex (and longer and expensive) reasoning to be computed. If the criterion is available, other kinds of processes can be applied. The recognition heuristic is said to be ecologically rational, i.e. effective, when the recognition of objects is highly correlated with the final evaluation criterion (to be inferred). The heuristic adaptively derives this correlation from the surrounding environment.. In order to better explain how the recognition heuristic works, and which are the main elements that are taken into account, Gigerenzer and Goldstein [2002] use, as an example, the estimation of university endowments. In the following example we refer to Figure 2 , which depicts the general elements involved in the recognition heuristic, and the relationships between them. In this example, a person is asked to determine which university has the biggest endowment, choosing between two university names. Hence, the evaluation criterion to be used is the value of the endowment, which is generally not publicly available. It is argued that newspapers could act as mediators, since they periodically publish news related to the most important universities. Thus, the number of times a university appears in the newspapers could be a strong indicator that it has larger endowments than universities that do not ever, or rarely, appear in the media. More generally, the heuristic always exploits the presence in the environment of some mediators that carry information used by the heuristic itself to approximate the value of objects with respect to the criterion. Mediators spread this information in the environment, thus determining which objects are recognized. In other words, the more often information about an object is encountered in the environment (carried by the mediators), the more probable the object will be recognized. The correlation between mediators and the evaluation criterion is called ecological correlation. In the example, newspapers play the role of mediators and the mediator variable related to the criterion is the number of citations. In fact, newspapers influence the recognition of university names, since the more they cite an institution, the more likely that institution name will be remembered, and thus recognized. When a person has to choose which university has the biggest endowments between two institution names, she uses the recognition heuristic and chooses a recognized name against an unknown one. Since the brain evaluates options exploiting the citations in newspapers instead of the real, unknown criterion, the relation between the recognition and the mediators is called surrogate correlation. From this example it is straightforward to see that the effectiveness of the recognition heuristic, i.e. the recognition validity, is continuously reinforced by the stimuli received from the environment.. Critiques have been addressed to this model of the recognition heuristic. In particular, critics point out that other cognitive processes, in addition to recognition, have to be involved in the results reported by the experiments used to validate the recognition heuristic (e.g. Oppenheimer [2003] , Bröder and Eichler [2006] , Pachur et al. [2008] , Hilbig and Pohl [2009] , and Glöckner and Bröder [2011] ). Anyway, none of these critical works give a formal model that allows one to examine whether or not (and in which cases) the recognition heuristic is compensated by other information. Only one paper [Marewski and Mehlhorn 2011] reports tests of the corresponding model of the various cognitive processes associated with recognition-based inference.. While in the previous description the recognition heuristic is used for choosing among pairs of options, it is now starting to be considered as one of the cognitive strategies for the creation of so-called consideration sets when dealing with multi-alternative choices [Marewski et al. 2010c] . The general notion of consideration sets comes from the marketing literature [Alba and Chattopadhyay 1985; Hauser and Wernerfelt 1990; Laroche et al. 2003; Shocker et al. 1991] . Within this field, a consideration set can be defined as the subset of brands that consumers evaluate when making a purchase decision. Since products of many brands can be on display, each having similar features and potentially subject to various price promotions, the brain has to rely on strategies that try to minimize the cost of information search and limit the attention only to a small subset of the available brands. This limited subset of all the available products is termed the consideration set. The final purchase decision will be sorted out from this set. More broadly, a consideration set can be regarded as a smaller subset of all the available information, where only the most relavant data is kept, which contains what will be the final result of the evaluation process.. If needed, items in a consideration set can be further ranked using strategies, like other heuristics. The recognition heuristic permits a sensible reduction of the number of alternatives, and exploits consideration sets to make the decision-making process easier.. The recognition heuristic can be exploited as a support in decision-making processes. As such, it has been successfully used in various fields [Marewski et al. 2010b ], like financial decision-making processes [Monti et al. 2009 ], investment choices [Ortmann et al. 2008] , or even sports events results [Serwe and Frings 2006] , or political election outcomes [Gaissmaier and Marewski 2011] .

B O B O O B I O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O 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Solving the Aerial Fleet Refueling Problem using Group Theoretic Tabu Search The Aerial Fleet Refueling Problem (AFRP) is concerned with the efficient and effective use of a heterogeneous set of tanker (refueling) aircraft, located at diverse geographical locations, in the required operations associated with the deployment of a diverse fleet of military aircraft to a foreign theater of activity. Typically, the "receiving" aircraft must traverse great distances over large bodies of water and/or over other inhospitable environs where no ground based refueling resources exist. Lacking the ability to complete their flights without refueling, each receiving aircraft must be serviced one or more times during their deployment flights by means of in-flight refueling provided by one of the available tanker aircraft. The receiving aircraft, aggregated into receiver groups (RGs) that fly together, have stipulated departure and destination bases and each RG's arrival time is bounded by a stated desired earliest and latest time. The excellence of a suggested solution to this very challenging decision making problem is measured relative to a rigorously defined hierarchical multicriteria objective function. This paper describes how the AFRP for the Air Mobility Command (AMC), Scott AFB, IL is efficiently solved using Group Theoretic Tabu Search (GTTS). GTTS uses the symmetric group on n letters (S n ) and applies it to this problem using the Java TM language.2 Air Refueling, the in-flight transfer of fuel between tanker and receiver aircraft, provides rapid response, increased range, and extended airborne operations for all aircraft. The capability to perform air refueling makes the United States (US) the dominant air power in the world today.. This capability, coupled with the ability to efficiently employ air refueling assets, is essential for the US to maintain this dominance (AFDD 2-6.2 1999). The Air Mobility Command (AMC) of the United States Air Force (USAF) is responsible for determining the use of the US tanker fleet to meet the air refueling needs of the Air Force, Navy, Marines, US allies, and coalition partners.. As part of this responsibility, AMC plans, schedules, tasks, and executes operations involving the use of its forces. Part of AMC's planning encompasses the intertheater movement of forces from the US to areas around the globe. This "deployment" of forces and its accompanied air refueling requirement is known as the Aerial Fleet Refueling Problem (AFRP).. As the agency responsible for air refueling, AMC addresses many questions involving the allocation and use of tankers. During Operations Desert Shield and Desert Storm, approximately 400 tankers off-loaded over 1.2 billion pounds of fuel to over 80,000 aircraft while flying over 30,000 sorties and logging over 140,000 hours of flight time (Gulf War Air Power Survey 1993).. The many planning scenarios, like Desert Shield/Desert Storm, that must be considered create complex sets of questions whose answers demand the use of powerful analytical tools. Among these tools are the Combined Mating and Ranging Planning System (CMARPS), the Quick-Look Tool (QLT), and the Tanker Assignment Planning (TAP) Tool.. CMARPS is a computer program that helps analyze, plan, and schedule deployment of tankers and receiver aircraft in support of immediate and anticipated military operations.. Unfortunately, this tool can take many weeks if not months to produce meaningful results. The QLT is a simple spreadsheet model used for determining gross tanker capabilities for supporting deployments. The TAP Tool is a spreadsheet model used for assigning tankers to refueling points. The simplicity of the QLT and TAP Tool makes them incapable of addressing the problem in required levels of detail. AMC possesses a compelling need for a tool that will provide the detailed analysis of CMARPS within a planning horizon comparable to that required by the QLT. Given a deployment scenario, examples of overview questions that require answers are:. • How many tankers are required to meet the air refueling requirements?. • How quickly can all the receivers be deployed to their final destinations?. • How far do the tankers and receiver aircraft have to travel?. • How much fuel is burned by both tankers and receiver aircraft?. In order to meaningfully answer upper level questions like these, as well as more probing questions relating to the efficiency of planning operations, a great many detailed operational aspects must be addressed.

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