Stochastic Traffic Engineering in Multihop Cognitive Wireless Mesh Networks Abstract-In this work, the stochastic traffic engineering problem in multihop cognitive wireless mesh networks is addressed. The challenges induced by the random behaviors of the primary users are investigated in a stochastic network utility maximization framework. For the convex stochastic traffic engineering problem, we propose a fully distributed algorithmic solution which provably converges to the global optimum with probability one. We next extend our framework to the cognitive wireless mesh networks with nonconvex utility functions, where a decentralized algorithmic solution, based on learning automata techniques, is proposed. We show that the decentralized solution converges to the global optimum solution asymptotically. T HE past decade has witnessed the emergence of new wireless services in daily life. One of the promising techniques is the metropolitan wireless mesh networks (WMN), which are envisioned as a technology which advances toward the goal of ubiquitous network connection. Fig. 1 illustrates an example of wireless mesh network. The wireless mesh network consists of edge routers, intermediate relay routers as well as the gateway node. Edge routers are the access points which provide the network access for the clients. The relay routers deliver the traffic aggregated at the edge routers to the gateway node, which is connected to the Internet, in a multihop fashion.. While the current deployed wireless mesh networks provide flexible and convenient services to the clients, the performance of a mesh network is still constrained by several limitations. The first barrier is due to the multihop nature of the wireless mesh network, where the nodes in geographic proximity generate severe mutual interference among each other and thus the network performance is devastated. To address this problem, several scheduling schemes have been proposed in the literature [1] . Recently, a novel coding-based scheme which may produce an interference-free wireless mesh network, is proposed [2] . Another example of the interference-free network is the CDMA-based wireless mesh networks [3] where by assigning orthogonal codes for each link, the network throughput is remarkably improved.. The second hindrance for the network performance is the limited usable frequency resource. In current wireless mesh networks, the unlicensed ISM bands are most commonly adopted for backbone communications. Not surprisingly, the wireless mesh network is largely affected by all other devices in this ISM band, e.g., nearby WLANs and Bluetooth devices. Moreover, the limited bandwidth of the unlicensed band cannot satisfy the increasing demand for the bandwidth due to the evolving network applications. Ironically, as shown by a variety of empirical studies [4] , the current allocated spectrum is drastically underutilized. As a consequence, the urge to explore the unused white space of the spectrum, which can significantly enhance the performance of the wireless mesh networks, attracts tremendous attention in the community [5] , [6] , [7] , [8] , [9] .. Cognitive radios are proposed as a viable solution to the frequency reuse problem [1] . The cognitive devices are capable of sensing the environment and adjusting the configuration parameters automatically. If the primary user, i.e., the legitimate user, is not using the primary band currently, the cognitive devices, namely, secondary users, will utilize this white space of the spectrum. Incorporating with the established interference-free techniques such as [2] and [10] , the throughput of the wireless mesh network can be dramatically enhanced. The protocol design for cognitive wireless mesh networks (CWMN), or more generally, multihop cognitive radio networks, is an innovative and promising topic in the community [11] and has been less studied in the literature. In this paper, we consider a cognitive wireless mesh network where the unlicensed band, e.g., ISM band, is utilized by the mesh routers for the backbone transmission. Moreover, each router is a cognitive device and hence is capable of sensing and exploiting the unused primary bands for transmissions whenever the primary users are absent.. In this paper, we investigate an important yet unexplored issue in the cognitive wireless mesh networks, namely, the stochastic traffic engineering (STE) problem. More specifically, we are particularly interested in how the traffic in the multihop cognitive radio networks should be steered, under the influence of random behaviors of primary users. It is worth noting that given a routing strategy, the corresponding network's performance, e.g., the average queuing delay encountered, is a random variable. The reason is that the available bandwidth for a particular link depends on the appearance of all the affecting primary users. If all the primary users are vacant, a link can utilize all available frequency trunks collectively by utilizing advanced physical layer techniques, e.g., OFDMA. However, if all the primary users are present, the only available frequency space is the unlicensed ISM band and thus the traffic on this link will experience longer delay than the previous case. In other words, the performance of a traffic engineering solution hinges intensely on the unpredictable random behaviors of the primary users. We emphasize that in multihop cognitive radio networks, this distinguishing feature of randomness, induced by the random behaviors of primary users, must be taken into account in protocol designs. Due to the location discrepancy, it is possible that some node is affected by many primary users while others are not. As a consequence, if we route the traffic via this particular node, the transmissions are more likely to be corrupted by the returns of the primary users. Apparently, a favorable solution is more inclined to steer the traffic from those "severely affected area," to the paths which are less affected by the primary users. We will make this intuitive approach precise and rigorous in this paper. To our best knowledge, this paper is the first work on the traffic engineering problem in multihop cognitive radio networks, with a special focus on the impact of random behaviors from the primary users.. The rest of this paper is organized as follows: The related work is reviewed in Section 2, and Section 3 provides the system model of our work. The stochastic traffic engineering problem with convexity is investigated in Section 4. In Section 5, we extend our framework to the nonconvex stochastic traffic engineering problem. Performance evaluation is provided in Section 6, followed by concluding remarks in Section 7. In this paper, we investigate the STE problem in cognitive wireless mesh networks. To harness the randomness induced by the unpredictable behaviors of primary users, we formulate the STE problem in a stochastic network utility maximization framework. For the cases where convexity holds, we derive a distributed algorithmic solution via the stochastic primal-dual approach, which provably converges to the global optimum solution. For the scenarios where convexity is not attainable, we propose an alternative decentralized algorithmic solution based on the learning automata techniques. We show that the algorithm converges to the global optimum solution asymptotically, under certain conditions.. In our work, we restrict ourself in a single gateway scenario. The extension to the multiple gateway scenario seems interesting and needs further investigation. In addition, in this paper, we consider a cooperative case where all 5. By utilizing diminishing parameters, a tradeoff between the performance and the convergence speed can be achieved by tuning the decreasing speed [46] . the edge routers attempt to maximize the overall network performance. In the cases where the edge routers are noncooperative, each player is interested in its own utility rather than the social welfare. Stochastic game theory provides a feasible tool to address the noncooperative case, which remains as future research. We also assume a negligible delay for the feedback signal while in a more general case, the impact of feedback delay needs further investigation. One feasible solution is to utilize the distributed robust optimization framework [49] where the worst case performance is maximized given that the feedback delay/error is within a reasonable range. Our work initiates a first step to investigate the impact of unpredictable returns of primary users, on the stochastic traffic engineering problem in cognitive wireless mesh networks. Traditional traffic engineering (TE) algorithms are proposed as the solution to the traffic management of the network in a cost-efficient manner. Different from the traditional quality of service (QoS) routing, the traffic engineering solution not only guarantees a certain QoS level for each flow, but also optimizes a global performance metric over the whole network, by splitting the ingress traffic optimally among several available paths. The multipath routing is usually supported by the Multiprotocol Label Switching (MPLS) techniques where the explicit routing path for a packet is predetermined rather than being computed in a hop-by-hop fashion. For a pair of source and destination nodes, the set of available paths, a.k.a., label switched paths (LSP), are established and managed by signaling protocols such as RSVP-TE [12] and CR-LDP [13] or manual configuration. The traditional traffic engineering solution evolves to the STE solution when uncertainty exists in the network, e.g., the random returns of the primary users in our scenario. TE solutions require consistent route changes which are unfavorable in that the network will be overwhelmed by the oscillations induced by the unpredictable behaviors of the primary users. In light of this stability concern, STE solution alternatively pursues an optimum multipath routing strategy such that the expected utility of the network is maximized. The stochastic traffic engineering with uncertainties are discussed in the literature such as in [14] and [15] . However, the previous works usually assume a probability distribution of the uncertainty, while in our scenario, the behaviors of the primary users are completely unpredictable from the mesh network's point of view. Distinguishing from the previous works, we propose an algorithmic solution which requires no prior knowledge about the distribution of the uncertainty, in a stochastic network utility maximization framework. It is worth noting that our work differs from the traditional state-dependent traffic engineering solution as well. For example, in [16] , a state-dependent traffic engineering solution is proposed. However, the authors assume that the system state, i.e., the current value of uncertainty, is fully observable. In our approach, we do not assume that the ingress node has the perfect knowledge of the current appearance of the network. We will discuss this issue in detail in Section 4.. Recently, CWMN have attracted great attention in the literature. In [5] , the channel assignment is discussed in a CWMN. In [6] , a cluster-based cognitive wireless mesh network framework is proposed. The infrastructure-based cognitive network is discussed in [7] with a focus on the cooperative mobility and the channel selection schemes. The spectrum sensing and channel selection are jointly considered in a unified framework in [8] . In addition, the IEEE 802.16h is in the process of incorporating the cognitive radios into the WiMAX mesh networks [9] . However, none of the previous works considers the stochastic traffic engineering problem. Therefore, a systematic study of the impacts of the random returns from the primary users, on the network routing performance is lacking in the existing literature. In [17] , the joint congestion control and traffic engineering problem is considered. He et al. propose a distributed algorithm to balance the user's utility and the system's objective. However, the authors assume the environment is fixed and does not consider the randomness which is the distinguishing yet usually overlooked feature in cognitive radio networks. Wang and Zheng [18] and Xin et al. [19] discuss the routing issue in cognitive radio networks yet the impact of random returns of primary users is not investigated. Hou et al. [20] , [21] , [22] , [23] formulate the joint routing, power and subband allocation problem in cognitive radio networks as a mixed-integer programming. However, the channels' bandwidths are assumed to be fixed, i.e., the random behaviors of primary users are still neglected. Our work is partially inspired by Lee et al. [24] . However, our paper differs from theirs in three crucial aspects. First, by targeting the stochastic traffic engineering problem, our model differs from the joint power scheduling and rate control work in [25] . Second, in [24] , [25] , Lee et al. only consider a single-path scenario while our work extends to a multipath routing network where the network traffic can be steered. Third and most importantly, Lee et al. [24] , [25] require that the current system state is fully observable at the decision maker. To achieve this, the authors assume a centralized mechanism which knows all the channel states of all the links over the network. However, our work differs from [24] , [25] significantly in that we do not require that the current system's state is known, which is of great practical interest since in multihop cognitive wireless mesh networks, the decision makers, i.e., the edge routers in our scenario, cannot be aware of the appearance of all primary users in the whole network as a priori. Moreover, our schemes enjoy a decentralized implementation, in contrast to centralized mechanisms in [24] , [25] by utilizing the feedback signals and local information only. In our previous work of [26] , we proposed a routing optimization scheme to combat with the randomness of instantaneous traffic in noncognitive wireless mesh networks. With respect to [26] , this paper differs in the following ways: First, in the wireless mesh networks considered in [26] , the capacity of each wireless link is assumed to be fixed, i.e., time invariant. However, in cognitive wireless mesh networks, due to the unpredictable appearance of primary users, the bandwidth of each wireless link is random. Second, in [26] , the QoS requirement is not considered. Nevertheless, in this paper, we particularly address the QoS concern of each user, e.g., the expected accumulated delay on the paths cannot exceed a user-specific delay tolerance, as will be elaborated in Section 4. Third and most importantly, the analysis in [26] was based upon the assumption that all the users have convex utility functions. In this paper, we extend the techniques to address the scenarios with nonconvex utility functions. We will discuss the aforementioned issues further in the following sections.

O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Topology vs generalized rough sets This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j a r relations and pre-order relations, respectively. Some known results regarding connections between generalized rough sets and topology are reviewed. And some new perspectives about these connections are shown. In past several years, rough set theory (see [15] , or [25] ) has developed significantly due to its wide applications. Various generalized rough set models have been established and their properties or structures have been investigated intensively (see [36, 37] , or [35, [20] [21] [22] [23] 11] ).. An interesting and natural research topic in rough set theory is to study rough set theory via topology. Indeed, Polkowski [25] pointed: ''topological aspects of rough set theory were recognized early in the framework of topology of partitions". Skowron [29] and Wiweger [34] separately discussed this topic for classical rough set theory in 1988. Polkowski [24] constructed and characterized topological spaces from rough sets based on information systems. Pawlak [15] and Polkowski [25] summarized related work respectively. Kortelainen [8] considered relationships between modified sets, topological spaces and rough sets based on a pre-order (also see [5] ). Lin [12] continued to discuss this topic, and established a connection between fuzzy rough sets and topology. Furthermore, using topology and neighborhood systems Lin [13] established a model for granular computing. Some authors discussed relationships between generalized rough sets and topology from different viewpoints. Skowron et al. [30, 31] generalized the classical approximation spaces to tolerance approximation spaces, and discussed the problems of attribute reduction in these spaces. Other papers on this topic we refer to [1, 10, 7, 14, 3, 21] . In addition, connections between fuzzy rough set theory and fuzzy topology were also investigated (see [26, 32, 11] ).. However, there are some problems still remain to be solved. For example, the relations between various generalized rough sets and topology need to be cleared. In the literatures, topologies with different forms are proposed corresponding to the same class of relation based rough sets. For example, reflexive relation based rough set model (see [7, 3] ). Are these topologies the same topology? In this paper, we investigate systematically relations between several classes of generalized rough sets and topology. These generalized rough sets are induced by inverse serial relations, reflexive relations, similarity 0888-613X/$ -see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.ijar.2010.07.010 The following table gives a summary of relations between generalized rough sets and topology (where R* is the largest pre-order relation included in R).. In the above table the abbreviations ISR, SR, POR and ER stand for inverse serial relation, similarity relation, pre-order relation and equivalent relation respectively, and Int and Cl stand for the interior and closure operators of the corresponding topological spaces respectively.. Topology is a powerful mathematical tool to many applied areas such as computer science (see [28] ), fuzzy set theory (see [5] ) and rough set theory (see [25] ). In this paper we gave a detailed discussion of relation between rough set theory and topology. First, in the relation based rough set theory, we proved the uniqueness of binary relation determined by the socalled algebraic method. Then, we mainly considered three classes of rough set theories induced by inverse serial binary relations, reflexive relations and pre-order relations respectively, and investigated connections between these rough set theories and topology. We used the fact that the inverse serial relation based rough set theory is the most basic theory to induce a topology to show a mistake existing in a related literature. Another basic fact is that different relation based generalized rough set models induce different topological spaces. We proved that two interesting topologies corresponding to reflexive relation based rough set model given recently by the literatures are different, and gave a condition under which the both are the same topology. Furthermore we showed that for the pre-order relation based rough set theory three known topologies coincide. Some correspondences between generalized rough sets and topology are shown. There are still some interesting problems which need be further discussed. For example, how to find the concrete form of topology induced by inverse serial relations is a good topic to investigate. There are some problems about fuzzy rough set theory and fuzzy topology (see [26] ). The powerful topological tool can be applied to make more thorough studies on generalized rough set theory. Naturally, Similar to Skowron et al. [30] we should discussed the problem of attribute reduction in more general approximation spaces.

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


Stability in terms of two measures of dynamic system on time scales By using a notion of upper quasi-monotone nondecreasing, this paper presents a new comparison principle which connects the solutions of two higher-dimensional dynamic systems on time scales. Then the stability criteria of a solution of a dynamic system in terms of two measures are obtained. Finally, two examples are provided to illustrate our results. It is well known that dynamic systems on time scales is emerging as an important area of investigation since it demonstrates the interplay of the two different theories, namely, the theories of continuous and discrete dynamic systems [1] [2] [3] . The investigation of stability analysis of nonlinear systems has produced a vast body of important results, for example, Lyapunov stability, partial stability, eventual stability, practical stability, and so on [4] [5] [6] . The notion which unifies and includes those several known concepts of stability in a simple set up, is the stability in terms of two measures [7] .. In the investigation of dynamic systems, the comparison principle is important to discuss the stability of solutions [8, 9] , and has been applied in dynamic systems on an arbitrary time scale. In the difference system, some stability criteria are obtained via quasi-difference inequality with the notion of upper quasi-monotone nondecreasing [10] . In this paper, the definition of upper quasi-monotone nondecreasing is extended to time scales and gives examples to illustrate the difference with quasi-monotone nondecreasing. On the basis of this study, this paper is developing a new comparison principle which connects the solutions of two higher-dimensions of such equations on time scales [1] . By using the vector Lyapunov functions together with the new comparison principle, criteria of stability for dynamic systems in terms of two measures, are obtained on time scales. In the end of the paper, two examples are provided to illustrate our results.

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Applying forces to elastic network models of large biomolecules using a haptic feedback device Abstract Elastic network models of biomolecules have proved to be relatively good at predicting global conformational changes particularly in large systems. Software that facilitates rapid and intuitive exploration of conformational change in elastic network models of large biomolecules in response to externally applied forces would therefore be of considerable use, particularly if the forces mimic those that arise in the interaction with a functional ligand. We have developed software that enables a user to apply forces to individual atoms of an elastic network model of a biomolecule through a haptic feedback device or a mouse. With a haptic feedback device the user feels the response to the applied force whilst seeing the biomolecule deform on the screen. Prior to the interactive session normal mode analysis is performed, or pre-calculated normal mode eigenvalues and eigenvectors are loaded. For large molecules this allows the memory and number of calculations to be reduced by employing the idea of the important subspace, a relatively small space of the first M lowest frequency normal mode eigenvectors within which a large proportion of the total fluctuation occurs. Using this approach it was possible to study GroEL on a standard PC as even though only 2.3% of the total number of eigenvectors could be used, they accounted for 50% of the total fluctuation. User testing has shown that the haptic version allows for much more rapid and intuitive exploration of the molecule than the mouse version. Biomolecules undergo conformational change in response to the binding of their natural ligands and one of the aims of biomolecular modelling is to understand and predict these functional motions. One simple, but successful model employed for this task is the Elastic Network Model (ENM) introduced into protein research by Tirion [1] . This is a coarse-grained model where a subset of atoms are connected to each other with elastic bonds. The dynamical behaviour of an ENM can be determined by normal mode analysis. Originally, normal mode analysis of biomolecules used the same accurate force-fields that are employed for Molecular Dynamics (MD) simulation and required considerable computational effort, but ENM normal mode analysis has largely taken over due to its relative ease of implementation, its lighter computational load, and due to the fact that results are comparable to results of accurate force-field normal mode analysis [1] . The lighter computational load occurs because usually a subset of atoms is used (for proteins normally the C a atoms, for DNA and RNA the P atoms) and energy minimization is not carried out. As a consequence ENM normal mode analysis has been performed on a large number of biomolecules some of which are of considerable size [2] [3] [4] [5] [6] [7] . Given the assumptions that are inherent in normal mode analysis, the small difference between the results from these two methods is probably of little consequence. Indeed, comparisons between movements in the low frequency modes of ENMs with functional movements derived from pairs of X-ray structures [8] suggest the same level of correspondence seen in similar studies using accurate force-field normal mode analysis. The binding of a ligand to a biomolecule gives rise to specific forces that induce the conformational change [9] [10] [11] , and a pertinent question is whether these forces applied to a harmonic model of the biomolecule would produce a movement that corresponds well to the experimentally determined functional movement. Ikeguchi et al. [10] have already performed such an analysis on harmonic models derived from MD simulations using quasi-harmonic analysis and also to an ENM. Their results are very encouraging. For an ENM of F1-ATPase the movement in the b E subunit correlated well (correlation coefficient of 0.84) with the experimentally determined functional movement. External forces have also been applied to ENMs of proteins to determine residues that play a key role in eliciting a known functional movement [12] and to understand the response of proteins to forces such as those that might arise in atomic force microscopy [13] . Therefore, a tool that allows a user to explore the response of an ENM of a biomolecule to applied forces would be of considerable value.. In this paper we describe the implementation and testing of such a tool. We have developed two versions, one where an atom is selected and then a force is applied using a mouse, and the other where a haptic feedback device is used to select and apply forces to atoms. The application of haptics in molecular simulation has quite a long history with the first such project, GROPE1, starting in 1967 at the University of North Carolina [14] . More recent applications using personal computers allow the user to feel interaction forces between a probe molecule and the biomolecule [15] [16] [17] [18] [19] [20] . These applications assume that both the protein and the ligand are completely rigid. A method for including molecular flexibility based on minimizing the potential energy of a protein-ligand system has also been described [21] , but with this system problems would arise from the delay in calculating the global response of large molecules to changes in position of the ligand.''Interactive Molecular Dynamics'' includes molecular flexibility by allowing the user to apply forces through a haptic device during an MD simulation [22] . A drawback with this approach, however, is that the user will react to events that occur on a very short timescale. This is avoided in an ENM, although it is known that some key aspects of dynamical behaviour of biomolecules at physiological temperature are not well described by the harmonic model. Bolopion et al. [23] have recently developed a tool that allows the user to interact with a molecular simulation based on quasi-statics [24] , via a haptic feedback device. They give details on the coupling between the haptic device and the molecular simulation.. In this work we use ENMs and make use of the concept of the important subspace [25] [26] [27] in normal mode analysis which is related to the concept of the essential subspace as determined by performing a principal component analysis of MD trajectories [28] [29] [30] [31] [32] . The important subspace, is a space of the first M lowest frequency normal mode eigenvectors within which a large proportion of the total fluctuation occurs, and is used here in order to make it possible to use the software on standard computers even with very large biomolecules. Elastic Network Models have proved useful for understanding the large-scale motions that occur in biomolecules. One particular application is to apply forces to specific regions of the molecule and to see its response. This can be done either to mimic forces that may arise in the interaction with a ligand or as part of an investigation to understand the mechanical properties of a molecule. ENMs are of particular use in the investigation of the properties of large biomolecules rather than small ones [2] . There are two reasons for this. The first reason is that small molecules do not have domains and their functional movements involve protein side chains or loops which are badly modelled by an ENM. The second reason is that the simulation of very large systems is computationally expensive using more accurate methods such as MD. The advantage of using an ENM is that it separates the computationally expensive calculation of the eigenvalues and eigenvectors from the calculations required during the interactive session enabling it to run on standard computers. Haptic interaction during a standard MD simulation, however, would require access to a powerful supercomputer for large molecules. In the development of the system, it has been clear that unless it were able to deal with large systems it would be of limited usefulness. Despite the separation of the calculation of the eigenvalues and eigenvectors from the calculations required in the interactive session it is apparent that for large systems such as GroEL the basic calculation (as given in Eq. 9) would require too much memory for an average PC. In order to deal with this we have utilized the concept of the important subspace from normal mode analysis. This has allowed us to develop the software to deal with large systems with a quantifiable approximation. The approximation allows us to reduce the memory required for large systems and involves the effective removal of the higher frequency modes which are not thought to be related to global functional movements. If memory reduction is necessary the same approximation can be used to speed up the calculation. Speed is particularly important for the haptic application due to the sensitivity of the human sense of touch.. Existing systems, such as the one by Bolopian et al. [23] , strongly couple the haptic device to the molecular simulation in a continuous control loop with scaling factors for the force and position information. In these systems transparency and stability can present difficulties. In our approach the force is calculated based on the magnitude and direction of a vector the user creates by manipulating the haptic device. Only this force vector needs to be scaled down to the molecular level for it to be used in the ENM. The resulting conformation is displayed but no information is fed back to the haptic device, other than a force based on the original force vector the user created. In this sense our approach presents a linear pipeline to the force application and simulation process where the haptic device provides an intuitive interface for inputting forces in three dimensions and for comparing their effect on the flexibility of the biomolecule. For example, the user may apply a force close to f hapmax in one direction and see little change to the structure whilst applying the same force in another direction could cause significant conformational change. Use of the important subspace means that an update rate of 1000Hz can be achieved, even for large biomolecules. This rapid rate means that as the user varies the force the molecule's structure is perceived to update instantly. This approach avoids stability issues which might result when simulating dynamics as it simply calculates the response of the molecule in static equilibrium.. As an example of possible usage consider the famous allosteric enzyme aspartate transcarbamylase. The binding of the regulatory molecule cytosine triphosphate (CTP) to the regulatory dimers influences catalysis by causing the two catalytic trimers to counter rotate. This mechanical coupling between the regulatory dimers and the catalytic trimers can be clearly seen using the software. Applying forces at the region where CTP binds causes the expected counter rotation of the catalytic trimers.. Although we have developed two versions, one for haptic devices, the other for a mouse, it is clear from user Table 1 . The results are based on a PC capable of 11 million operations per CPU cycle and 2 GB of available memory testing that the haptic version is by far the most convenient. Our testing showed that even on a very small biomolecule the haptic version allowed for much more rapid and intuitive exploration than the mouse version. Initially a PDB file is read to determine the atomic coordinates. If the structure was solved using NMR then only ''Model 1'' coordinates are used. The nodes of the ENM are C a atoms, for protein, and P atoms for DNA or RNA. The default value for R c is 11Å, however, this may be adjusted by the user. Normal mode analysis is performed to calculate the eigenvalues and eigenvectors, which can be saved to avoid recalculation in future sessions. Matrix Y, shown in Eq. 2, can now be computed and also saved. However, for large biomolecules there may be insufficient memory or it may take a signficant amount of time to compute, requiring Method 2 to be used. The software may also read the eigenvalues and eigenvectors computed by other ENM normal mode analysis software, providing the input file contains eigenvalues followed by eigenvectors sorted in ascending order. Furthermore, output from the ENM webserver, ElNemo [35] may be used. ElNemo provides up to 25 modes in the form of PDB files containing displaced coordinates and a list of eigenvalues that can be used in Method 2, if the original PDB file is also loaded. B-factors and T exp are required to calculate c and s atom , as shown in Eqs. 5 and 8. If no B-factor information is available, as for structures solved by NMR, then c can no longer be determined using Eq. 5 and it is set equal to 1.0. In addition, the B-factors used in Eq. 8 are also all set to 1.0. If T exp is unspecified it will be set to 300 K as a default value. These default values for the B-factors and T exp are also used when only a subset of normal mode eigenvalues and eigenvectors are loaded.. When Method 2 is used M is calculated as the minimum of two values, M M and M T , where M M is restricted by the available memory and M T is restricted by the processor speed. These values are determined before loading any eigenvalues and eigenvectors. M M is calculated in two ways depending on whether Methods 1 and 2 are used together in the same session or whether only Method 2 is used. If Method 1 is used then the amount of memory required to store Y is computed and the remaining available memory determines M M . If Method 2 is used exclusively then the total amount of selectable modes, M M , is computed based on the entire amount of available memory. M T is calculated based on the total amount of time taken to evaluate Eq. 10. An estimate could be made based on the number of double precision floating point operations allowed within 60 ms, which ensures interactive performance. However, a more accurate value for M T is determined by timing the entire calculation. To compute the maximum value for M T such that Eq. 10 can be computed within 60 ms a binary search is carried out. A flow chart describing the calculation of M is shown in Fig. 1 . During the session the user may select individual modes or subsets of the available modes.. Use of the software poses two main issues; how to navigate the large biomolecular structures and how to apply desired forces to the atoms. Two types of input devices are considered in the software implementation, either full mouse control or enhanced haptic control with optional mouse commands.

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


Local linear regression with adaptive orthogonal fitting for the wind power application Short-term forecasting of wind generation requires a model of the function for the conversion of meteorological variables (mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary. Local linear regression is an appealing nonparametric approach for power curve estimation, for which the model coefficients can be tracked with recursive Least Squares (LS) methods. This may lead to an inaccurate estimate of the true power curve, owing to the assumption that a noise component is present on the response variable axis only. Therefore, this assumption is relaxed here, by describing a local linear regression with orthogonal fit. Local linear coefficients are defined as those which minimize a weighted Total Least Squares (TLS) criterion. An adaptive estimation method is introduced in order to accommodate nonstationarity. This has the additional benefit of lowering the computational costs of updating local coefficients every time new observations become available. The estimation method is based on tracking the left-most eigenvector of the augmented covariance matrix. A robustification of the estimation method is also proposed. Simulations on semi-artificial datasets (for which the true power curve is available) underline the properties of the proposed regression and related estimation methods. An important result is the significantly higher ability of local polynomial regression with orthogonal fit to accurately approximate the target regression, even though it may hardly be visible when calculating error criteria against corrupted data. Wind power is a renewable energy that now represents a significant part of the electricity generation mix in a number of European countries. This phenomenon is not only limited to Europe, as the installation of important wind power capacities is also being discussed and planned in rapidly developing countries such as China, India or Brazil. However, large scale integration of wind generation causes difficulties in the management of a power system, owing to its variability and limited predictability. An additional challenge is to conciliate this integration with the on-going deregulation of the European electricity markets. Increasing the value of wind generation through improving the performance of prediction systems is one of the priorities in wind energy research for the coming years (Thor and Weis-Taylor 2002) . A status report on wind power forecasting has been published in (Giebel et al. 2003 ).. Short-term predictions of wind power production at a given site, say up to 48-72 hours ahead, are commonly produced by using as input predictions of relevant meteorological variables, provided by a meteorological office. Relevant meteorological variables obviously include wind speed, but also wind direction, air density or temperature. Forecasts of meteorological variables are converted to power forecasts by passing them through the so-called wind farm power curve. From a statistical point of view, the challenge here is to estimate this conversion function, which is nonlinear and bounded, in addition to being nonstationary due to e.g. changes in the site environment, seasonality or climate change.. Local polynomial regression is an appealing nonparametric approach to modeling a wind farm power curve, for which the model coefficients can be adaptively estimated with recursive Least Squares (LS) methods, see e.g. (Nielsen et al. 2002 , Sanchez 2006 ). An assumption when applying LS estimation methods is that a noise component is present in the response variable only, i.e. the power output in our case. However, it appears unlikely that the forecasts of meteorological variables used as input do not have an error component. Recently, Pinson et al. (2007) showed that the application of local polynomial regression with LS fit may yield somewhat inaccurate estimate of the true conversion function, even though it may still be appropriate for point prediction purposes where error measures are calculated against noisy response data (Jonsson 1994) . Our aim here is to describe a method that provides better estimates of the true conversion function, by relaxing the assumption that the noise component is only on the response variable. This work is motivated by the current research efforts on wind power ensemble forecasting (Giebel 2005 , and references therein). More particularly, Nielsen et al. (2006) concluded that a better understanding of the ability of various estimators to approximate the true regression function that defines a wind farm power curve is needed to improve ensemble predictions of wind generation.. Our approach has been developed with local linear regression as a basis, in order to obtain a nonparametric estimate of the nonlinear power curve. Howver, in contrast to classical LS estimation, the coefficients of the local linear models are then orthogonally fitted by using a Total Least Squares (TLS) criterion. Developments towards the fitting of a linear model with a TLS criterion can be traced back to the works by Golub and Van Loan (1980) . This is used here in a nonparametric regression framework to fit local linear models. The aim of this approach is hence similar to that of principal curves, as introduced by Hastie and Stuetzle (1989) and subsequently discussed by Tibshirani (1992) , Verbeek et al. (2002) , and Einbeck et al. (2005) , among others: it is to locally minimize the distance between observations and the estimated nonparametric regression function. In order to accommodate nonstationarity, an adaptive estimation method is introduced which, for each local linear model, is based on tracking the left-most eigenvector of the augmented covariance matrix. Adaptivity in time is ensured by exponential forgetting of past observations. Since in practice noise distributions may be skewed and heavy-tailed in addition to not being Gaussian, a robust version of the estimation method is presented for estimates that would be less affected by such noise characteristics.. The paper is structured as follows. The proposed local linear regression with orthogonal fitting is defined in Section 2. The issue of adaptive estimation of the local model coefficients for this regression is then addressed in Section 3. In Section 4, the proposal for robustification of the previously introduced estimation method is described. The properties of the regression and estimation methods are demonstrated in Section 5. Simulations are based on semi-artificial data. They are primarily produced by passing real-world wind speed data through a modelled power curve in order to obtain noise-free power data. Both wind speed and power data are then corrupted to generate realistic datasets of wind speed forecasts and corresponding power measurements. The use of such datasets will allow us to demonstrate that the proposed method is better able to approximate the target regression when noise is present in both wind speed and power variables, since the target regression is indeed available. Concluding remarks in Section 6 end the paper. Local linear regression is an appealing approach to modeling the conversion of wind to power, for which the local models are commonly fitted with an LS criterion. Doing so is actually equivalent to making the assumption that a noise component is present in the response variable only. This assumption is not realistic for the wind power forecasting application, when the wind-to-power conversion function is estimated with meteorological forecasts as explanatory variables. Therefore, even if a power curve estimated with LS fit may be considered optimal in a minimum-MSE sense (with the MSE calculated against the noisy data), it does not provide an accurate estimate of the true underlying conversion function. This drawback of the LS-fitting approach has been clearly illustrated in the present paper.. In order to relax the assumption of the noise component being on the response variable only, the definition of local linear regression with orthogonal fitting has been introduced. This follows the concept of self-consistency, and has an aim similar to that of principal curves, though it is restricted to a nonparametric regression framework: it is to locally minimize the Euclidean distance between the observations and the estimated regression curve. In practice, the estimates of the local model coefficients are defined as those that minimize a TLS criterion. In order to accommodate long-term variations of the local model coefficients, an adaptive estimation method based on tracking of the left-most eigenvector of the augmented covariance matrix P + n has been described. The interest of such a method is that it eliminates the need to compute a singular value decomposition every time a new observation is available, which significantly decreases computational costs. In addition, only the augmented covariance matrix P + n needs to be updated and stored at each time-step. Note that it will be possible in the future to consider other recursive schemes to update P + n . More particularly, one may control the information content used to update P + n in the direction of its largest eigenvalue, e.g. with selective forgetting methods (Parkum et al. 1992 ).. The ability of local linear regression with adaptive orthogonal fitting to better estimate the true conversion function of wind to power has been shown from simulations on a semi-artificial dataset, i.e. for which both the true regression model and realistic simulated data were available. When calculating error criteria against the true regression model, the improvement achieved when applying the proposed regression and estimation methods is indeed significant. However, it has been clearly explained that such improvement is difficult to appraise when evaluating estimated regressions against corrupted data. This ability of better approximation of the underlying conversion process is a desirable feature for application to ensemble prediction of wind power. Future works will concentrate on evaluating the benefits of using the proposed regression method for this purpose. In the former case, the distance to be minimized is measured along the y-axis (dashed line), while for the latter, this distance is that between the observation p i and its orthogonal projection p ⊥ i on the curve (dash-dotted line). The fitting point p is represented by a square while the data points are represented by circles. For both types of fitting, the location ofp on the u-axis is user-defined, while its position on the y-axis results from the fitting approach employed. n , that is, from local linear regression whose coefficients are either fitted with an LS or a TLS criterion. One can visually appraise the greater ability of the former estimation method to yield a better estimate of the target regression.

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


Beyond the visuals: tactile augmentation and sensory enhancement in an arthroscopy simulator Abstract This paper considers tactile augmentation, the addition of a physical object within a virtual environment (VE) to provide haptic feedback. The resulting mixed reality environment is limited in terms of the ease with which changes can be made to the haptic properties of objects within it. Therefore sensory enhancements or illusions that make use of visual cues to alter the perceived hardness of a physical object allowing variation in haptic properties are considered. Experimental work demonstrates that a single physical surface can be made to 'feel' both softer and harder than it is in reality by the accompanying visual information presented. The strong impact visual cues have on the overall perception of object hardness, indicates haptic accuracy may not be essential for a realistic virtual experience. The experimental results are related specifically to the development of a VE for surgical training; however, the conclusions drawn are broadly applicable to the simulation of touch and the understanding of haptic perception within VEs. This paper explores tactile augmentation as a means of generating a sense of touch within a virtual environment (VE) given the challenges of accurately simulating the haptic properties of virtual materials.. Tactile augmentation involves the addition of physical objects into a VE. It is cheaper and simpler than incorporating a haptic device, and more realistic than a purely visual environment. However, the incorporation of a real object limits the potential variability of the haptic environment. Therefore the potential of using visual cues to allow alteration of the physical object is demonstrated.. It is argued that the interrelated nature of our sensory systems and the dominance of the visual sensory channel (Welch and Warren 1986) can be used to support simulation design. The utilization of visual cues to create a 'sensory illusion or enhancement' and alter the haptic experience by making a surface 'feel' harder or softer than it is in reality is explored. This is significant given the relative ease of producing high fidelity visual cues compared to accurate haptic feedback.. Sensory enhancements are demonstrated as a means to create haptic variability and improve the realism offered by tactile augmentation. The research informs the design of the Sheffield Knee Arthroscopy Training System (SKATS), a virtual reality (VR) simulator for training knee surgery skills. Fig. 1 ) is a VE for training basic skills associated with knee arthroscopy (keyhole surgery of the joint) (McCarthy 2000) . The aim of this paper has been to consider the use of tactile augmentation and sensory enhancements in VR design. SKATS is undergoing iterative development to provide visual and physical resistance to movement of surgical tools in response to training requirements and user acceptance criteria. The challenges of developing a suitable haptic device for surgery simulation have been discussed. The SKATS system with tactile augmentation enhances the VE whilst offering a means to collect and validate user requirements. Hence, this acts as a stepping-stone to inform the development of an innovative haptic feedback device to be implemented in a later version, aimed at training a wider skills base including diagnostic tasks.. This work has offered benefits in terms of the technical development of SKATS. A technique has been developed to align and calibrate the real and virtual model. Furthermore a means to deform a material, such as cartilage, effectively in the VE has been demonstrated. It is recommended that alternative means of varying the visual appearance of hardness such as lighting and textural effects and other more complex paradigms should be investigated for achieving sensory illusions.. The demonstrated combinatorial nature of haptic perception and susceptibility to sensory enhancements could be exploited more broadly in simulator design to improve the viability of tactile augmentation and overcome the challenges of developing accurate haptic feedback. This phenomenon is likely to be valuable to VR research where it is easier to produce high fidelity visual cues than effective haptic feedback devices. However the necessary fidelity of haptic training systems for many applications (including surgery), are not yet known. Whether a mechanical device or a physical structure generates the feel of a surface, a greater understanding is required to ensure functional fidelity and skill transfer. The experiment produced two main findings. Firstly, participants were influenced in their perception of hardness by the presentation of visual information. Secondly, the success of the enhancement varied based on the discrepancy between the visual and haptic information. These findings are discussed further in the following sections. In describing the results, responses were termed as correct or incorrect. A correct response was defined as the participant conforming to the visual enhancement. That is, the response was correct in terms of the visual appearance of the pad, not the haptic properties (which would have resulted in the response 'the same' for each trial).. The mean number of correct responses and the type of incorrect responses across participants for each condition are provided in Table 2 . Figure 3 illustrates the percentage of responses overall. There were more correct than incorrect responses indicating that the participants were influenced by the visual enhancements. The application of the Binomial test supported this conclusion (P \ 0.01). The mean values in Table 2 show that more correct responses were given when there was a greater disparity between the visual and haptic cues (i.e. in conditions 1 and 5). There were fewest correct responses when simulating a hard surface in condition 2. This suggests that an illusion of a softer surface can be created more easily than a harder surface with less proportional change of the visual environment.. A two way ANOVA was used to analyze the effect of the two independent variables; condition (the level of visual deformation) and plate position. Application of the Mauchly statistic gave a P value for plate of 0.358 and of condition of 0.368 indicating no heterogeneity of covariance indicating appropriate use of the F test.. The analysis indicated a main effect of condition [F (4, 76) = 14.99; P \ 0.01]. Therefore it can be concluded that the amount of visual deformation had an effect on the response to the visual stimuli and the effectiveness of the enhancement. As Fig. 4 suggests there were more correct responses for conditions 1, 4 and 5.. Further analysis of the incorrect responses (see Fig. 4 ) suggested that when an incorrect response was given in a soft condition, the plate was more often identified as being the same rather than harder than the control. Post hoc analysis using the Binomial test supported this statistically for conditions 4 (P \ 0.01) and 5 (P \ 0.01). In condition 3, the plate was more often identified as being softer, than correctly identified as being the same, or incorrectly as harder (P \ 0.01). In condition 1 and 2 there was less difference in the type of incorrect response given. Figure 5 illustrates the correct responses by pad position on the plate. The two way ANOVA indicated a main effect of plate position [F (4, 76) = 4.194; P \ 0.01)]. A post hoc Bonferroni comparison revealed the difference to lie between the responses given for pad 3 compared to pad 2 (P \ 0.05) and pad 5 (P \ 0.05). An interaction between pad position and condition [F (4,304) = 2.728, P \ 0.01] was also indicated.

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


Towards open science: The myExperiment approach By making research content more reusable, and providing a social infrastructure which facilitates sharing, the human aspects of the scholarly knowledge cycle may be accelerated and 'time-to-discovery' reduced. We propose that the key to this is the sharing of methods and processes. We present myExperiment, a social web site for discovering, sharing and curating Scientific Workflows and experiment plans, and describe how myExperiment facilitates the management and sharing of research workflows, supports a social model for content curation tailored to the researcher and community, and supports Open Science by exposing content and functionality to the users' tools and applications. Based on this we introduce the notion of the Research Object -the work objects that are built, transformed and published in the course of scientific experiments -and suggest that by encapsulating methods with results we can achieve research that is more reusable and repeatable and hence rapid and robust. To accelerate the time to discovery of new research results we must look at the human component of the discovery cycle. Scientific advance relies on social processes in which scientists share hypotheses, insights and results, and the data and methods that support these. Traditionally, scholarly discourse and dissemination have focused on peer reviewed journal articles, mediated by the scholarly publishing process and gatherings such as conferences where researchers exchange knowledge in more informal ways. The Web is now widely used as a distributed platform for the dissemination of an increasingly diverse range of digital research materials: we are witnessing evolving practice in scholarly publishing [1] and communities supported by research portals and repositories. Significantly, there are also now tens of thousands of publicly available web services across business and science [2] . In this evolving landscape we observe an expansion in the kinds of scientific commodities being published, for example:. • Primary and secondary data sets, along with standard metadata sufficient to support their interpretation and re-use, although tying together published results with the "supplementary data" upon which they are based has unsolved issues to do with persistence [3] .. • Algorithms, software tools, scripts and procedures, through community services like OpenWetWare [4] , which provides an exchange for techniques in biological sciences, and the nanoHUB gateway [5] which hosts user-contributed resources in the nanotechnology domain.

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Structure and parameter estimation for cell systems biology models In this work we present a new methodology for structure and parameter estimation in cell systems biology modelling. Our modelling framework is based on P systems, an unconventional computational paradigm that abstracts from the structure and functioning of the living cell. The process of designing models, consisting of both the optimisation of the modular structure and of the stochastic kinetic parameters, is performed using a memetic algorithm. Specifically, we use a nested evolutionary algorithm where the first layer evolves rule structures while the inner layer, implemented also as a genetic algorithm (GA), fine tunes the parameters of the model. Our approach consists of an incremental methodology. Starting from very simple P system modules specifying basic molecular interactions, more complicated modules are produced to model more complex molecular systems. These newly found modules are in turn added to the library of available P systems modules so as to be used subsequently to develop more intricate and circuitous cellular models. The effectiveness of the algorithm was tested on three case studies, namely, molecular complexation, enzymatic reactions and autoregulation in transcriptional networks. Living cells represent complex biomolecular systems with fully interrelated processes. In order to understand, manipulate or control cellular systems to produce a desirable output, integrate partial knowledge, and to predict their behaviour, the development of good models is crucial. A new integrative and interdisciplinary field, systems biology, is emerging to study the dynamics of cellular systems as a whole. Systems biology has been presented recently in textbooks and article collections [1, 11, 16] . Systems biology is closely related to the also young and growing research field of synthetic biology [3] . The final goal when modelling a cellular system is to obtain the necessary understanding to be able to control its functioning. A deeper knowledge of the organisation and functioning of cellular processes will allow us to engineer our own cellular systems exhibiting a desired behaviour or producing a prefixed output.. The macroscopic continuous and deterministic approach based on ordinary differential equations (ODEs) constitutes the most used methodology in cellular modelling within systems and synthetic biology. Although ODEs have been successfully applied in different systems there are two key assumptions in this approach, namely continuity and determinism that are not always fulfilled. There are many systems where the number of particles of the reacting species are low and the reactions involved are slow. In these systems the previous assumptions are invalid and mesoscopic, discrete and stochastic approaches are instead more suitable [16] . In this paper we will use a new approach, P systems, which integrates this last type of modelling into a computational framework. P systems represent an unconventional computational paradigm [13] that abstracts from the structure and functioning of the living cell. A P system consists of a cell-like membrane structure, with compartments containing multisets of objects which evolve according to given rules. These rules are applied according to an extension of Gillespie's well known Stochastic Simulation Algorithm (SSA) [4] to the multicompartmental structure of P system models [12] .. The design of models in systems and synthetic biology is real world problem solving. Therefore, it is a hard process prone to failure where one has to reconsider many times the choice of the model parameters and structure made at different points. The use of computational automated tools can provide the means to optimise both the kinetic parameters and the network topology or rule structure. Nevertheless, the use of computer simulation has been mainly focused on the computation of the corresponding dynamics for a given model parameters and structure. In contrast to this classical approach we have developed a methodology based on evolutionary algorithms (EA) that optimises both the kinetic parameters and structure of our models with respect to a given desirable behaviour.. Evolutionary algorithms (EAs) [2] has been developed for solving computation problems in many fields. The approach mimics the process of biological evolution and the mechanisms of natural selection and genetic variation. Suitable codings are used to represent possible solutions to a problem, and the search is guided by using some genetic operators and the principle of survival of the fittest. Due to their merits of self-organization, self-learning, intrinsic parallelism and generality, EAs have been successfully applied to economic prediction, optimum control, engineering and scientific computations [5] . In this paper, we propose a memetic algorithm [8] to approach the automatic design of cell systems biology models. Its main idea is to use a nested evolutionary algorithm where the first layer evolves model structures while the inner layer, implemented as a genetic algorithm (GA) [10] , acts as a local search for the parameters of the model. The paper is organised as follows. The next section introduces the modelling methodology and the evolutionary computation methods used in this work. In Section 3 the case studies and the experimental design are presented. Results are discussed in Section 4. Finally, some conclusions and future work are given in Section 5. A memetic algorithm has been designed to automatically develop and optimise both the modular structure and parameters of cellular models based on stochastic P systems. Specifically, we use a nested evolutionary algorithm where the first layer evolves model structures while the inner layer implemented as a GA, acts as a local search for the parameters of the model.. The effectiveness of the algorithm was tested by three case studies with incremental model complexity, namely, molecular complexation, enzymatic reactions and autoregulation in transcriptional networks. The experimental results demonstrate that for each case our algorithm was able to find a rule structure and stochastic kinetic constants which reproduce very accurately the target time series. More interestingly, in the case of autoregulation in transcriptional networks our algorithm was able to find more than one equally plausible model (hypothesis). This shows the suitability of our algorithm to find a set of possible designs of cellular systems. Furthermore one of these possible designs could be chosen to be actually engineered in the lab according to its implementation feasibility. This links our research with the emerging field of synthetic biology. Finally, the comparing results for the case of enzymatic reactions by using the elementary library and by adding the newly found module shows the obvious advantage of using the latter approach. This points out the great potential to automatically design more complex and circuitous cellular models in the future by using our algorithm.. Future research lines include the automatic design of more complex regulatory transcriptional networks and the study of eukaryotic cellular systems with relevant compartmentalised structure by using and extending our algorithm. In this work we use three relatively simple cellular systems as a proof of concept of the feasibility of our methodology.

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