Visualizing explicit and implicit relations of complex information spaces In this work, we describe how EdgeMaps provide a new method for integrating the visualization of explicit and implicit data relations. Explicit relations are specific connections between entities already present in a given data set, while implicit relations are derived from multidimensional data based on similarity measures. Many data sets include both types of relations, which are often difficult to represent together in information visualizations. Node-link diagrams typically focus on explicit data connections while not incorporating implicit similarities between entities. Multidimensional scaling considers similarities between items; however, explicit links between nodes are not displayed. In contrast, EdgeMaps visualize both explicit and implicit relations by combining graph drawing and spatialization techniques. We have applied this technique to three case studies (philosophers, painters, and musicians) and explored how integrated visualizations of explicit and implicit relations reveal novel patterns and relationships. An important goal of information visualization is to reveal different types of relationships within abstract data. Through interaction, the viewer is able to find and understand connections between bits of information. Relations can be explicitly present in a data set as links that specifically connect information items or implicitly by inferring relations based on similarity of attributes. For both types of relationships -explicit and implicit -several visualization techniques have been proposed and refined over recent years. Two of the most popular techniques for visualizing relations are node-link diagrams (NLD) and multidimensional scaling (MDS). On the one hand, NLD techniques are usually applied to explicit relations or connections that are visualized as edges between nodes representing, for example, online communities, computer networks, or linked web pages. On the other hand, MDS is typically used for implicit relations between documents or other types of multidimensional data. MDS spatializes attribute similarities between items by placing similar items in close proximity to each other and less similar items further apart.. Although NLD and MDS techniques are widely studied and increasingly deployed, they both have significant limitations with regard to readability and interpretability of the resulting visualization. Layout algorithms for NLD visualizations are typically optimized for reducing edge crossings, with the side effect that node positions are not utilized as meaningful visual variables. Furthermore, as the number of edges increases, it becomes hard to distinguish directionality, if present, and identify high-degree nodes. The resulting visualization of an MDS algorithm, on the other hand, lacks a guiding structure to put elements into context with each other. It is often difficult to understand the meaning of the positional proximity of elements. We argue that the limitations of both techniques could be attributed to the fact that they are constrained to either explicit or implicit relations, yet many data sets feature both types of relationships.. In this paper, we explore how both explicit and implicit relations can be visualized as EdgeMaps, integrated views that combine graph drawing and spatialization. EdgeMaps integrate NLD and MDS techniques utilizing both visual linkage and proximity for the representation of complex -explicit and implicit -relations between items. The intent behind this approach is to make effective use of visual variables that have been underutilized in NLD and MDS techniques.. As case studies for this paper, we have chosen data sets of philosophers, painters, and musicians from the Freebase data community. While there are many biographical records associated with these prominent personalities of philosophy, art, and music, a particularly interesting aspect is the existence of influence connections between people, which are a type of explicit relations. On the other hand, birth dates, interests, movements, and genres are attributes that indicate implicit relations between philosophers, painters, and musicians. We chose these dimensions because they provide a compelling case for the visualization of explicit and implicit relationships and allow us to explore complex data relationships. Visualizing influences between musicians or philosophers as edges may indicate who had more impact, yet it is not possible with these links alone to see the extent of the impact. By encoding meaningful data relations into both position and edges, it becomes possible, for example, to explore the influence of musicians across genres or of philosophers over time (see Figures 1 and 2) .. The remainder of the paper is structured as follows. First, we provide an overview of prior work, after which we explain our design goals and the data sets we use as case studies. We then introduce the visual representations provided with EdgeMaps ('Visualizing explicit and implicit relations' section) and describe the web-based interface design ('Creating a web-based visualization interface' section). Using the case studies, we illustrate new ways for exploring complex relations ('Revealing complex relationships' section). We then discuss the limitations and open questions of this work ('Discussion' section) and conclude the paper. As information spaces grow in size and complexity, there is a growing need for visual representations that help us make better sense of diverse data relations and patterns. With this work, we have approached this challenge by making the following contributions:. . A novel information visualization technique that combines implicit relations (topical and temporal similarity) with explicit relations (influences). . A detailed discussion of the design considerations concerning visual representations and interaction techniques of the EdgeMaps visualization. . The implementation of a web-based system incorporating basic use patterns on the Web such as browser's history, bookmarks, and link sharing. . An application to three case studies exploring data about personalities from philosophy, art, and music examining the types of novel insights and uses.. The EdgeMaps technique represents implicit relations as the underlying layouts for node-link diagrams in which nodes stand for people and edges stand for the explicit influence connections between them. By constraining the selection to one node at a time, it is possible to visually distinguish between incoming and outgoing edges. Novel visual patterns resembling the aesthetics of fireworks and waves not only look more appealing, they also allow for a closer examination of influence differences. In contrast to the notorious yarn-ball effect of dense graph visualizations, we have suggested that an interactive pivotal exploration along edges between nodes may better allow viewers to grasp network structure than complicated overviews. While much more work is necessary to help us better explore and understand complex information spaces, we see EdgeMaps as a promising step towards this effort. The design and implementation of EdgeMaps constitute a first step towards integrating explicit and implicit data relations. While the idea of integrating graph drawing and spatialization techniques is promising, we discuss several limitations and challenges that Figure 16 . In the painters' timeline view, there is a slightly higher concentration of blue and purple tones on the right. Searching for terms indicating artistic movements confirms the temporal development of impressionist and abstract art. suggest opportunities for more research on the visualization of complex data sets featuring diverse relations. As visualizing relationships is at the heart of information visualization, our work builds upon many previous contributions in the field, with particular regard to the use of visual variables, graph drawing methods, and casual visualization.. While not part of his visual information-seeking mantra ('Overview first, zoom and filter, then detailson-demand'), Shneiderman 1 notes the challenge of being able to explore relationships between information items. He stresses the importance of interaction for relating data entries; however, equally if not more important are the appropriate visual representations of different types of relations. To think about representing relationships visually, it is worth considering the visual variables that are at our disposal. In Semiology of Graphics, Bertin 2 distinguishes between eight visual variables: size, value, texture, colour, orientation, shape, and the two dimensions for the position on the plane. MDS renderings use planar position as the primary visual variable, while NLDs typically rearrange position in order to minimize edge crossings. Stone 3 makes the case that colour can make visualizations more effective and beautiful when used well. She shows how colour can be used for labelling and quantifying data. It would be interesting to explore the use of colour for conveying similarity between items as a degree of association in Bertin's terms.. There has been extensive research on drawing and interacting with NLDs, 4 often aiming at reducing edge crossings, which is one of several geometrical and graph-theoretical metrics for graph aesthetics. 5 Recent additions to this research include EdgeLens, a technique for interactively exploring overlapping edges, 6 and EdgeBundles, a method for combining edges with similar paths. 7 Another problem of large graphs is occlusion, especially when arrowheads of directed edges impair the perception of the actual nodes. A study of directed graphs examined a range of visual cues for directionality and their effect on determining direct and two-step connections. 8 While these contributions can significantly improve the readability of large NLDs, we argue that contextual attributes of graph elements need to be more acknowledged. This perspective is supported in earlier work on computer network visualization, where edge and node attributes (e.g. flow, capacity, utilization) of regional and international Internet links were regarded to be more important than the network topology. 9 As part of a social network visualization, it was shown how the visual representation of number of friends, gender, and community structure enriches the NLD and allows for interactive filtering. 10 While conventional NLD techniques focus almost entirely on explicit relations, MDS can be seen as a complementary approach focusing on proximity as a visual representation of implicit relations or similarity. MDS has been used for document visualizations with the goal of visually conveying 'thematic patterns and relationships' of text collections. 11 While the idea of spatializing document collections based on their similarities or differences is promising, the resulting galaxies and themescapes still appear abstract and difficult to interpret. An approach to making MDS more interactive focused on steering the algorithm, but did not look at using interactivity to make the MDS view more meaningful and accessible. 12 Besides linkage and similarity, another important relation is based on the temporal dimension and references between temporally structured items. Considering that time is generally seen as a linear dimension, the challenge is to visualize relations between items that are mapped onto a linear axis. Arc diagrams show cross-references along a linear axis by adding visual semicircles to linear views of documents, music pieces, and DNA sequences. 13 In work that explored the use of arcs to visualize email threads, it was shown how the combination of arcs displayed above and below the main axis improved readability.. 14 Several contributions to information visualization have looked at enriching and combining techniques for visualizing different types of relations. For example, a visual document hierarchy was accompanied with arcs representing cross-references between different sections. 15 Furthermore, NLDs were made more readable by assigning nodes into multiple regions and allowing for interactive edge filtering. 16 A related approach places graph nodes on a multivariate grid allowing for new forms of exploration. 17 Another technique provides a three-dimensional juxtaposition of different visualizations on panes linking corresponding nodes using edges between the panes. 18 All these techniques underline that there is a need for integrating explicit and implicit relations and enabling their interactive exploration; however, there is a tendency to emphasize one over another.. A related area within information visualization focuses on social, casual, and artistic aspects of visualization. For example, Many Eyes is an online community that allows web users to upload their data sets, create and customize visualizations, and discuss these with other community members. 19 Many Eyes is one example among many web-based visualization projects that make visualizations more readily available within the web browser, which has become a major trend in visualization research and practice. 20 The development that visualization is becoming part of everyday activities, moving beyond professional, specialized domains, is also described as casual information visualization, implying novel design challenges and audiences. 21 One example of this development is the increasing use of visualization as a medium for artistic expression, 22 which also aims at creating beauty and triggering curiosity besides supporting data analysis and sense making. Against the backdrop of casual information practices with growing information spaces, considerations of aesthetics and curiosity also enter the domain of information seeking. 23

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 B 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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


Grasp quality measures: review and performance The correct grasp of objects is a key aspect for the right fulfillment of a given task. Obtaining a good grasp requires algorithms to automatically determine proper contact points on the object as well as proper hand configurations, especially when dexterous manipulation is desired, and the quantification of a good grasp requires the definition of suitable grasp quality measures. This article reviews the quality measures proposed in the literature to evaluate grasp quality. The quality measures are classified into two groups according to the main aspect they evaluate: location of contact points on the object and hand configuration. The approaches that combine different measures from the two previous groups to obtain a global quality measure are also reviewed, as well as some measures related to human hand studies and grasp performance. Several examples are presented to illustrate and compare the performance of the reviewed measures. This paper has presented several grasp quality measures (summarized in Table 2 ) applicable to the synthesis and evaluation of fingertip grasps. The quality measures have been classified into two large groups: measures associated with the location of contact points on the object boundary, and measures associated with the hand configuration. Most quality measures in the literature are associated with the location of contact points, so this first large group was divided into three subgroups. The first one contains measures based on algebraic properties of G, which have limited practical application as they do not consider any restriction on the forces applied at the contact points. The second subgroup considers the measures based on geometric relations of grasp, oriented toward the improvement of grasps in the presence of inertial forces and the synthesis of independent contact regions. They are specially used to provide robustness to the grasp. The third subgroup contains measures that consider limitations on the finger forces, and includes one of the most used criterion in grasp synthesis, i.e. the largest ball and its variations.The second large group of quality measures includes criteria defined to obtain appropriate hand configurations for the grasp. A proper grasp should be optimal with respect to both groups of quality measures, and with this purpose different global quality indexes have been proposed to simultaneously quantify the grasp with respect to both groups.. Although some studies compare the optimal grasps obtained according to different criteria for different objects in 2-dimensional (Bone and Du 2001; Morales et al. 2002; Borst et al. 2004 ) and 3-dimensional grasps (Miller and Allen 1999) , the selection of the best criterion in each real case is not always trivial. Besides, even knowing the criterion to be applied, the complexity of real cases often makes the computational cost of any grasp optimization really high. In order to provide an idea of the behavior of each quality measure, Sects. 3.4 and 4.2 present application examples on simple cases that allow the intuitive interpretation of the measure. In fact, it is not possible to provide a general recommendation for the use of any grasp quality measure, as the quality value depends on several aspects of the grasp. In general, quality measures may consider: (a) locations of the contact points on the object, (b) directions of the forces applied at the contact points, (c) magnitudes of the applied forces at the contact points, and (d) gripper configuration. The consideration of these elements may provide a better idea on the most convenient quality measure for a particular task.. Most of the presented grasp analysis is based on quasistatic considerations. Dynamic manipulability was originally proposed for serial manipulators (Yoshikawa 1985a (Yoshikawa , 2000 , and was formulated for cooperative robots as the ratio between an input torque and the resultant acceleration of the grasped object . The concept has been recently extended to the field of multifingered grasping (Yokokohji et al. 2009 ).. The commercial availability of hands with integrated tactile sensors and fingertip sensors that can be adapted to specific hands (Silva et al. 2013; Yousef et al. 2011) , also provides a new field of application for the presented quality measures, traditionally associated to grasp planning stages. In fact, a fingertip sensor could provide information on the magnitude of the contact force and its point of application, which can be used to estimate the direction of the force being applied on the object. This information is exploited for locally optimizing some quality index by adjusting the grasp force or even the contact location, such that the overall grasp stability during real executions is increased (Dang and Allen 2013; Laaksonen et al. 2012; Bekiroglu et al. 2011) .. Some studies have analyzed the change of grasp quality with the location of contacts and the variation of the friction coefficient (Zheng and Qian 2004) , and even with the number of contacts (Rosell et al. 2010) . It has been suggested that, without other considerations, grasp quality increases slightly for more than a given number of contact points. A large number of contact points is typical in power grasps, but the applicability of quality measures for power grasps has hardly been tackled. One way to quantify the robustness of a power grasp is by considering the minimum virtual work rate required to move the object along a virtual displacement (Zhang et al. 1994) . Another metric was proposed to minimize the distance between the object and predefined contact points on the hand, which was used to plan a pregrasp shape that is later used for online grasp planning (Ciocarlie and Allen 2009) . Although in theory most of the above measures can be applied to grasps with any number of contact points , the explicit consideration of the limited forces that some parts of the hand can apply on the object allows the definition of contact robustness, i.e. how far a contact is from violating contact constraints, which is different from grasp robustness, i.e. how far the grasp is from overcoming the object immobilization constraint .. Most of the measures presented in this survey were developed for fingertip grasps using fully actuated multifingered hands. The application of the measures to underactuated hands, in particular the measures related to gripper configuration (Sect. 4), requires the development of new theoretical tools. For instance, if finger joints are modeled as elastic elements, the instantaneous kinematics of the hand and object can be predicted by considering a quasi-static equilibrium when the hand is perturbed (Quenouelle and Gosselin 2009; Odhner and Dollar 2011) . Such mapping allows the application of the presented manipulability measures. The theoretical framework of parallel robots has been recently proposed as a tool for studying fingertip grasps and dexterous manipulation for underactuated hands (Borras and Dollar 2013) .. The adaptation of classical manipulability indices (condition number, singular values) to parallel robots has been studied and they do not seem to be consistent for analyzing such robots (Merlet 2006) ; the adaptation of grasp quality measures for underactuated hands is currently an open area of research (Malvezzi and Prattichizzo 2013) .. The grasp quality measures reported in this survey do not consider the effect of compliance. For analyzing compliant grasps a grasp stiffness matrix K is required; the grasp is stable if the stiffness matrix is positive definite (Howard and Kumar 1996) . A measure of grasp stability is based on the eigenvalue decomposition of the generalized matrix M −1 K , with M a metric that allows that twists and wrenches lie on the same vector space (Bruyninckx et al. 1998 ). However, this measure depends on the choice of the metric M. A frame-invariant quality measure can also be developed based on the computation of principal rotational and translational stiffnesses for a grasp with stiffness matrix K (Lin et al. 2000) .. When dealing with whole-hand grasps, in general it is not possible to generate forces in all directions. Thus, the concepts of active and passive force closure arise: an external wrench can be counterbalanced if there exist strictly active or passive internal forces (Bicchi and Pratichizzo 2000) . Note that in this way, the condition for active force closure is stricter than for pure force closure. A grasp optimization for this case can, for instance, minimize the joint efforts . Also, when considering hand and contact compliance, specific solutions to the force distribution problem ω = G f can be obtained (Bicchi 1994) . The implications of compliance in the grasp analysis is receiving a renewed interest due to the evolution of underactuated robotic hands (Prattichizzo et al. 2012 ).. There are still more open research problems related to the quality measures. First, it is worth mentioning the need for efficient algorithms (both in terms of computational complexity and computational cost) to generate optimal grasps according to different quality criteria. A second aspect is the automatic determination of the relevant quality measures for the problem at hand, either to select the most appropriate one or the most convenient combination. Even when there are already some measures that try to consider the goal of the grasp (i.e. the task to be performed), this is also an aspect that requires further research and more practical proposals. In any case, continuous advances in the development of dexterous grasping devices will require the definition and formalization of new quality measures as well as optimal procedures to apply them.

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 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 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 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 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 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 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 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 O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O


On-board analysis of uncalibrated data for a spacecraft at mars Analyzing data on-board a spacecraft as it is collected enables several advanced spacecraft capabilities, such as prioritizing observations to make the best use of limited bandwidth and reacting to dynamic events as they happen. In this paper, we describe how we addressed the unique challenges associated with on-board mining of data as it is collected: uncalibrated data, noisy observations, and severe limitations on computational and memory resources. The goal of this effort, which falls into the emerging application area of spacecraft-based data mining, was to study three specific science phenomena on Mars. Following previous work that used a linear support vector machine (SVM) on-board the Earth Observing 1 (EO-1) spacecraft, we developed three data mining techniques for use on-board the Mars Odyssey spacecraft. These methods range from simple thresholding to state-of-the-art reduced-set SVM technology. We tested these algorithms on archived data in a flight software testbed. We also describe a significant, serendipitous science discovery of this data mining effort: the confirmation of a water ice annulus around the north polar cap of Mars. We conclude with a discussion on lessons learned in developing algorithms for use on-board a spacecraft. There are a number of resource-constrained environment application domains in which data mining is desirable. Examples include embedded mobile devices, sensor webs, and on-board settings such as spacecraft or unpiloted air vehicles. Typically, these environments have limited CPU and RAM resources. In many cases, the data available is uncalibrated. An emerging paradigm in this category, addressed in this paper, is the mining of scientific data on-board a spacecraft. A primary purpose of scientific planetary spacecraft is to collect measurements of physical values that provide information to gain an understanding of the world (e.g. space environment, planetary surface or atmosphere, etc.) Historically, data is collected by pre-specifying when and where to acquire measurements. Collected data is transmitted to the ground, calibrated, and then analyzed by domain experts such as scientists. There is no opportunity to adjust what is acquired or transmitted based on the content of the data.. Recently, we posited that significantly more science could be accomplished by a mission or spacecraft by analyzing data on-board. We demonstrated the principles through the use of a linear support vector machine (SVM) on-board the Earth orbiting EO-1 spacecraft [3, 4] . There are three major reasons that on-board science data mining is desirable. First, it can enable detection and rapid reaction to dynamic events. Second, on-board data analysis can aid in prioritizing the data that is collected. Finally, that analysis can produce additional science products (e.g., data summaries or dynamic event detections) that consume little bandwidth but provide key insights. We focus on the latter two cases, which both enable more effective use of limited bandwidth.. A common property of remote missions is that the spacecraft or instrument is capable of collecting more data than can be accommodated by the downlink volume available. In this circumstance, an opportunity exists to collect additional data and select only the most interesting for transmission. Success of such an operational mode relies on being able to identify, on-board, data that is more interesting than what would be collected with the traditional method of preselecting all imaging targets. This requires a specification of what constitutes "interesting" data and an encoding of that specifiation into an algorithm that can operate in the computational environment of the spacecraft on the data in the form it is available (i.e., uncalibrated, noisy).. In this paper, we present three data mining techniques for use on-board the Mars Odyssey spacecraft, ranging from simple thresholding to state-of-the-art reduced-set SVM technology. Each of these algorithms has been thoroughly tested on archived data in a flight software testbed. We describe the algorithms and test results, including a significant, serendipitous scientific finding that resulted from the data mining effort: the confirmation of a water ice annulus around the north polar cap of Mars. We also present lessons learned in developing successful on-board science data analysis applications. There are a number of benefits to mining scientific data on-board a spacecraft including data prioritization, summarization, and reaction to dynamic events. This is an emerging paradigm and presents a significant change from the traditional ways of operating a spacecraft. Successful on-board data mining must meet the accuracy requirements provided by scientists while operating within the constrained on-board computing environment. We have presented three such algorithms for use on-board the Mars Odyssey spacecraft. These algorithms have all met the science requirements and processing requirements and are in the process of being integrated into the Odyssey flight software for future use on-board the spacecraft.. In addition to developing the algorithms themselves, we have also conducted a careful empirical study to assess the resource requirements and to determine whether they are realistic given the anticipated spacecraft computing environment. We have demonstrated that each algorithm falls well within the CPU and memory constraints. Finally, we have contributed a discussion of the lessons learned when working in this application area that can serve to guide future efforts to enhance the analysis capabilities of spacecraft. Processing The algorithms were profiled for execution time and memory consumption on a Linux workstation (Workstation in Table 2 ) and on the PPC750 testbed (Testbed in Table 2 ). The Workstation machine was configured with a 1.793 GHz AMD Opteron Processor with 8 GB RAM, and the Testbed machine with a 150 MHz PPC750 with 128 MB of RAM. For the purposes of testing, time required for file I/O was not counted. We report execution speed for the thermal anomaly and polar cap detector algorithm in terms of the number of pixels per second that can be processed. We report the number of framelets per second for the aerosol opacity estimation algorithm. We tested both the full SVM and the reduced-set SVM on the Testbed, but only the full SVM on the Workstation. We considered running the reduced-set SVM on the Workstation unnecessary since the processing time is strictly linearly related to the number of support vectors. In Table 2 , the performance of reduced-set SVM on the Workstation was estimated from the full SVM results.. The Mars Odyssey spacecraft has a RAD6000 processor running at 20 MHz. On-board analysis methods would only be allowed to use about 20% of the processor, and up to 40MB of the heap memory. The THEMIS instrument collects data at the rate of about 9600 pixels per second. The algorithms would be expected to run during and after data acquisition to determine if the collected data contains an event of interest and should therefore be stored for later transmission to Earth. Although the PPC750 Testbed is similar to the spacecraft, its processor is of a more recent generation and is approximately 10 times faster than Mars Odyssey; given the 20% processor allocation, the Testbed is about 50 times faster. Therefore, we also show estimated processing speeds for each algorithm in a Spacecraft setting ( Table 2 ). Our profiling results show that the algorithms can easily keep up with the output of the instrument even given the limitations of on-board processing power.

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


Load balancing via random local search in closed and open systems In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Jointhe-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner.We first analyze the natural Random Local Search (RLS) strategy. Under this strategy, after sampling a new server randomly, clients only switch to it if their service rate is improved. In closed systems, where the client population is fixed, we derive tight estimates of the time it takes under RLS strategy to balance the load across servers. We then study open systems where clients arrive according to a random process and leave the system upon service completion.In this scenario, we analyze how client migrations within the system interact with the system dynamics induced by client arrivals and departures. We compare the load-aware RLS strategy to a load-oblivious strategy in which clients just randomly switch server without accounting for the server loads. Surprisingly, we show that both load-oblivious and load-aware strategies stabilize the system whenever this is at all possible. We further demonstrate, using large-system asymptotics, that the average client sojourn time under the load-oblivious strategy is not considerably reduced when clients apply smarter load-aware strategies. Load balancing is a key component of today's communication networks and computer systems in which resources are distributed over a wide area or across a large number of systems and have to be shared by a large number of users. Load balancing enables efficient resource utilization and thereby tends to improve the quality of service perceived by users. Traditionally, load balancing has been achieved by applying smart routing policies: when a new demand arrives, it is routed towards a particular resource depending on the current loads of the various resources, see [14] and references therein. In contrast, we are interested in systems where a new task is initially assigned to a resource chosen at random irrespective of the current resource loads, but where tasks can be re-assigned, i.e., migrate from one resource to another.. Our primary motivation stems from the increasing popularity of Dynamic Spectrum Access (DSA) techniques [1] as a potential mechanism for broadband access in future wireless systems. A common implementation platform for DSA is the use of reprogrammable Software-Defined-Radios (SDRs). These new radios are frequency-agile or flexible, and have the ability to rapidly jump from one frequency band to another in order to explore and exploit large parts of the spectrum. A central question in DSA is how multiple users may fairly and efficiently share spectrum in a distributed manner. Typically, the service rate of a user on a given frequency band is inversely proportional to the number of users transmitting on this band, i.e., to the load of the band. As new users entering the system have no way of determining the load on each frequency band, they have to initially select a band randomly. Should a user receive a quite poor quality of service on a given band, she may resample a new band at random and decide to switch to it. The overall system performance then strongly depends on the distributed resampling and switching strategy implemented by each user.. Though our primary motivation is DSA, our methods and results could provide insight into a number of other applications. One such pertains to wireline networks, where there has recently been interest in multipath routing [15] . Here, users may use several path to download files, and have to select the appropriate path or the set of paths. Another application is in transport networks, where one might wish to understand how Wardrop equilibria, which correspond to the equalization of journey times across alternative routes, are achieved or approximated by network users acting on limited information. Our results could also shed insight on how quickly such equilibria can be re-established following major disruptions or other changes to the network. Finally, note that distributed load resampling can also be thought of as a game between selfish users. In fact, it is an instance of a congestion game (see e.g. [18] ), and our results shed light on the time to reach a Nash equilibrium in such a game, but it also helps understanding the outcome of the game with a dynamic population of players.. We consider a generic system consisting of multiple servers (in DSA, frequency bands) employing the Processor Sharing (PS) service discipline, shared by clients who have to initially pick a server at random, and may later resample servers and migrate during their service. We restrict our attention to two natural distributed resampling and migration strategies, the Random Local Search (RLS) and Random Load-Oblivious (RLO) strategies. When implementing the RLS algorithm, a user resamples a new randomly chosen server at the instants of a Poisson process, and migrates to this new server if its load is smaller than that of the initial server. In contrast, under the RLO algorithm, a user hops between servers according to a random Markovian jump process irrespective of the loads of the visited servers.. We investigate both closed systems with fixed population of clients, and open systems with a population whose dynamics are governed by client arrivals and the completions of their services. In closed systems, we are interested in characterizing the time that it takes under the RLS algorithm to balance all server loads (note that here the RLO algorithm does not balance loads except in an average sense -so we do not study this algorithm in closed systems). In open systems, users arrive at the various servers according to independent stochastic processes of fixed intensities, and leave upon service completion. In this scenario, client migrations within the system interact in a complicated manner with the system dynamics induced by client arrivals and departures. We aim at characterizing system stability under the RLS and RLO strategies, as well as at deriving estimates of user sojourn times. Our contributions are as follows:. • Closed systems. We show that, starting from an arbitrary allocation of users to servers, the time τ it takes to achieve perfect balance of server loads scales at most as log(m)`m 2 n + log(m)´, where m and n denotes the number of servers and users, respectively. This considerably improves over the existing bounds that stated that τ scales at most as m 2 (see e.g. [12] ). We also investigate the time τ to reach an approximate -balance (a system reaches an approximate -balance if there exists p such that the number of users associated to any server lies between (1 − )p and (1 + )p). Achieving such balance is much faster than reaching a perfect balance, and we show that τ scales at most as log(m)/ .. • Open systems. We demonstrate that both RLS and RLO strategies achieve the largest stability region possible, i.e., that the system is stable under these two algorithms provided that. μi, where λi denotes the initial user arrival rate at server i and μi is the service rate of this server. The result is not surprising for RLS, but less intuitive for RLO since, under this algorithm, users take no account of server loads when migrating. For both RLS and RLO strategies, we derive approximate estimates of the average user sojourn time using large-system asymptotics. The estimates are shown to be exact when the number of servers grows large, but turn out to be quite accurate for systems of limited sizes as well. Our first numerical results suggest that again, surprisingly, the average client sojourn time under the load-oblivious RLO strategy is not considerably reduced when clients apply smarter load-aware RLS strategy. To our knowledge, this paper is the first to analyze the performance of RLS and RLO algorithms in open systems.. The paper is organized as follows. In the next section, we describe our model and notation. Sections 3 and 4 are devoted to the analysis of closed and open systems, respectively. We give the related work in Section 5, and provide concluding remarks in Section 6. In this paper, we have analyzed the performance of distributed load balancing schemes where clients independently decide to resample and change server to improve their service rate. We considered two natural random resampling and migration strategies: A load oblivious strategy RLO where clients randomly move from one server to another without accounting for the actual server loads, and a load-dependent selfish strategy RLS where clients randomly resample servers and migrate only if their rate is improved.. In closed systems where the population of clients is fixed, we have provided a new tight bound on the time to balance server loads under RLS strategy. This time can be interpreted as the time to reach a Nash Equilibrium in this selfish routing game. Our bound considerably improves the bounds available in the literature. But it holds only in the case of homogenous systems where servers have identical service rates. It seems challenging and interesting to figure out how to apply our methodology to obtain bounds on the time to balance the system in the case of heterogenous systems. It might also be interesting to investigate the time it takes to balance the system in scenarios where client migrations are limited, in the sense that from a given server, clients can migrate to a restricted subset of servers (as for example specified via a graph).. In open systems where clients arrive at the various servers at different rates, we provided a first analysis of the system dynamics. These dynamics are complicated as the client arrival and departure processes interact with the client migration processes. We have shown that both RLO and RLS load balancing strategies are able to stabilize the system whenever this is at all possible. It may appear somehow surprising that a completely distributed and load-oblivious algorithm such as RLO can achieve maximum stability. Using large-system asymptotics, we also provided approximate estimates of the mean client sojourn time. The results show that again, surprisingly, the load-oblivious RLO strategy does not yield significant performance losses compared to the load-dependent RLS strategy. These findings are valid for exponential service requirements, and it would be interesting to know whether they remain valid for other service requirement statistics.. An interesting extension of the present work (especially relevant when considering spectrum sharing issues) is to analyze the case where clients may use resources from several servers simultaneously. There are some preliminary results in this direction in [15] , but neither the time to reach equilibrium or the population dynamics are studied. There have been many studies on distributed, selfish load balancing algorithms and routing games in closed systems, see e.g. [16] and references therein. Refer to [18] for a quite exhaustive survey. Much of the work in this area has concentrated on finding the fastest sequence of moves that would balance the system, also called Nashification [11] . One class of algorithms is the elementary step system, first described in [19] in which a sequence of best response moves are performed by the clients. Of course this requires that the clients know the status of all the other servers. In [4, 5] the authors study closed systems with limited information about the servers' status. They consider a synchronous system where at each step, each server samples a new server randomly and if the load of the sampled server is smaller, then a client moves with probability (Nc −Nn)/Nc, where Nc is the load on the current server and Nn is the load of the sampled server. It is shown that the expected time to balance the system is O(log log m + n 4 ). A modification of this load balancing algorithm is studied in [5] , and it is shown that the expected time to balance the system is O(log m + n log n). In [12] , the author considers clients dynamics identical to those considered in this paper and uses the potential function introduced in [10] to quantify the time to achieve system balance. It is shown that the expected time to reach a balance scales at most as O(m 2 ). We provide significant improvements on this bound.. In open systems, the client moves interact in a complicated manner with the client arrival and departure processes. There is very little work trying to understand this interaction. None of the existing work deals with a system similar to that studied here. For instance, [2] analyzes the interaction in a game-theoretical framework, where arrivals are adverserial, and where a central controller moves clients with the aim of stabilizing the system. The performance of the classical work stealing load-balancing scheme has also been studied, see e.g. [3] and references therein. Of course there is an abundant literature on the performance of classical load-balancing schemes in open systems where clients are assigned to a given server for the entire duration of their service, see e.g. the analysis of the supermarket model in [13, 17] . To our knowledge, the present paper provides the first analysis of natural distributed resampling and migration strategies in open systems.

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


Analysis of Composite Dynamics of Two Bifurcating Neurons This paper presents pulse-coupled two bifurcating neurons. The single neuron is represented by a spike position map and the coupled neurons can be represented by a composition of the spike position maps. Using the composite map, we can analyze basic bifurcation phenomena and can find some interesting phenomena that are caused by the pulse-coupling and are impossible in the single neuron. Presenting a simple test circuit, typical phenomena are confirmed experimentally. The bifurcating neuron has been studied as a simple (artificial) neuron model having interesting phenomena [1] - [6] . The neuron has a periodic base signal and repeats integrateand-fire behavior. Depending on the shape of the base signal the neuron can output rich periodic and chaotic spike-trains. Deriving a one-dimensional spike position map we have investigated the rich spike-trains and related bifurcations [2] .. In this paper we present a pulse-coupled system of two bifurcating neurons (ab. PCBN) and analyze the basic bifurcation phenomena. The pulse-coupling is based on interaction of firings and the dynamics can be integrated into the composite map of the spike position maps of the two single neurons. Using the composite map, we clarify that the PCBN have interesting phenomena including a co-dimension-two bifurcation and some bifurcations to coexistence state of various attractors. Such phenomena are impossible in the single neuron. Presenting a simple test circuit, we can confirm typical phenomena experimentally. Preliminary results along these lines can be found in a conference paper [4] .. The motivations for studying the PCBN include the following two points. First, our simple pulse-coupling method is fundamental to construct pulse-coupled (artificial) neural networks. The networks can exhibit various spatiotemporal phenomena that have been utilized for applications including dynamic associative memory, image segmentation and spike-based communications [3] , [6] - [11] . It should be noted that the pulse-coupling method is different from smooth coupling method [12] and has not been established so far. Development of simple pulse-coupling method itself is an ongoing topic [3] , [6] . Second, analysis of composite dynamics of plural maps is a fundamental problem: it is interesting to explore how rich phenomena can be caused by the composition. Also the composite maps relates deeply to time-variant systems and their applications [13] - [17] . It should be noted that this paper firstly proposes an analysis method of PCBNs by means of a composite map. The method may be developed into an analysis tool for pulsecoupled networks. We have studied the pulse-coupled bifurcating neurons that have a variety of spike-train dynamics. The dynamics can be integrated into the composite map and basic bifurcation phenomena are analyzed. It is clarified that some interesting phenomena are impossible in the single neuron. Presenting a simple test circuit, typical phenomena have been confirmed experimentally. Future problems include analysis of rich bifurcation phenomena and development pulse-coupled artificial neural networks with engineering applications.

O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O


Predictive Ensemble Pruning by Expectation Propagation Abstract-An ensemble is a group of learners that work together as a committee to solve a problem. The existing ensemble learning algorithms often generate unnecessarily large ensembles, which consume extra computational resource and may degrade the generalization performance. Ensemble pruning algorithms aim to find a good subset of ensemble members to constitute a small ensemble, which saves the computational resource and performs as well as, or better than, the unpruned ensemble. This paper introduces a probabilistic ensemble pruning algorithm by choosing a set of "sparse" combination weights, most of which are zeros, to prune the ensemble. In order to obtain the set of sparse combination weights and satisfy the nonnegative constraint of the combination weights, a left-truncated, nonnegative, Gaussian prior is adopted over every combination weight. Expectation propagation (EP) algorithm is employed to approximate the posterior estimation of the weight vector. The leave-one-out (LOO) error can be obtained as a by-product in the training of EP without extra computation and is a good indication for the generalization error. Therefore, the LOO error is used together with the Bayesian evidence for model selection in this algorithm. An empirical study on several regression and classification benchmark data sets shows that our algorithm utilizes far less component learners but performs as well as, or better than, the unpruned ensemble. Our results are very competitive compared with other ensemble pruning algorithms. E NSEMBLE of multiple learning machines, i.e., a group of learners that work together as a committee, has attracted a lot of research interest because it is a good approach to improve the generalization ability [1] . Because of their simplicity and effectiveness, ensembles have become a hot topic in machine learning. This technique originates from Hansen and Salamon's work [1] , which shows that the generalization ability of a neural network can be significantly improved through ensembling a number of neural networks. Ensembles have already been successfully applied to many areas and there have been many ensemble learning algorithms in the literature, such as Bagging [2] , Boosting [3] , Arcing [4] , random forests [5] , rotation forests [6] , COPEN (pairwise COnstraints Projection-based ENsemble) [7] , negative correlation learning, and evolutionary computation-based algorithms [8] , [9] .. However, the existing ensemble learning algorithms often generate unnecessarily large ensembles. These large ensembles are memory demanding. Obtaining a prediction for a fresh data point can be done expensively in large ensembles. Although these extra costs may seem to be negligible when dealing with small data sets, they may become serious when the ensemble method is applied to a large-scale data set.. In addition, it is not always true that the larger the size of an ensemble, the better it is. Some theoretical and empirical evidences have shown that small ensembles can be better than large ensembles [2] , [10] , [11] . For example, the boosting ensembles, Adaboosting [3] and Arcing [4] , pay more attention to those training samples that are misclassified by former learning machines in the training of next machines and finally reduce the training error to zero. In this way, Boosting ensembles are prone to overfitting the noise in the training set [12] . In these circumstances, it is necessary to prune some overfitting individuals to achieve good generalization.. In the last decades, several ensemble pruning algorithms have been proposed, such as Kappa pruning [13] and concurrency pruning [14] . However, these algorithms all resort to greedy search, which is without either theoretical or empirical quality guarantees.. Yao and Liu [10] first adopted a global optimization approach, genetic algorithm (GA), to weigh the ensemble members by constraining the weighs to be positive. Zhou et al. [11] later also proved that small ensembles can be better than large ensembles. A similar genetic algorithm approach can be found in [15] . However, these GA-based algorithms try to obtain the optimal combination weights by minimizing the training error and, in this way, these algorithms become sensitive to noise.. Motivated by the above reasons, we modeled the ensemble pruning as a probabilistic model with truncated Gaussian prior for both regression and classification problems [16] . The Expectation-Maximization (EM) algorithm is used to infer the combination weights, and our algorithm shows good performance in both generalization error and pruned ensemble size. However, the EM algorithm is sensitive to the initialization and it does not guarantee to obtain optimal solutions due to converging to local maxima.. In order to resolve the unstable issue of EM, this paper extends our previous work and proposes a probabilistic ensemble pruning algorithm based on expectation propagation (EP). The algorithm treats ensemble pruning as a weight-based optimization, aiming to improve the generalization performance of the ensemble by tuning the weight of each ensemble member. By introducing a sparsenessinducing prior for each combination weight, many of the posteriors of weights are sharply distributed around zero, leading to pruning unimportant learning machines. As negative combination weights are unreliable and not intuitive [17] , [18] , [19] , we follow this constraint and employ a left-truncated prior to prevent negative values in the combination weights.. By incorporating the truncated prior, the normalization integral in Bayesian inference becomes intractable. This paper uses expectation propagation to approximate the posterior of weights. EP [20] is a deterministic algorithm for approximating Bayesian inference that extends assumed density filtering (ADF) to incorporate iterative refinement of the approximations. As the leave-one-out (LOO) error can be obtained as a by-product in the training of EP without extra computation, the LOO error is used together with Bayesian evidence for model selection.. An empirical study on several regression and classification benchmark data sets shows that our algorithm utilizes far less component learners yet performs as well as, or better than, the unpruned ensemble. The results are very competitive compared with other existing ensemble pruning algorithms.. The original contribution of this paper over the previous paper [16] is the use of Expectation Propagation instead of Expectation-Maximization to overcome stability problem of EM (sensitivity to initialization and convergence to local maxima), and a comprehensive empirical study. The benefit of obtaining an LOO estimate in the training of EP is an additional advantage of this approach.. Ensemble pruning algorithms can improve accuracy significantly as shown by the theoretical and empirical studies in this paper. A smaller ensemble will also reduce test (application) time after the ensemble is trained and pruned. However, such benefits come with the cost of a longer training time. There is a trade-off between training and application times when considering ensemble pruning. When an application has a very large training set, ensemble pruning can be computationally expensive or even prohibitive. For applications that are characterized by relatively small training sets but large test ones, e.g., in the field of transductive learning, ensemble pruning algorithms are highly appropriate as smaller ensembles pruned by an ensemble pruning algorithm can improve the accuracy and reduce the application time in the test stage. In this paper, we provide our approach on a poker hand problem characterized by a relatively small training set and a large test set.. The rest of this paper is organized as follows. After the background introduction in Section 2, Section 3 presents the EP pruning algorithm for regression and classification problems, respectively, followed by experimental results and analysis in Section 4. Finally, Section 5 concludes the paper and presents some future work.. There are many symbols used in this paper. Fig. 1 reports the meaning of these notations. We use lowercase letters for vectors and uppercase for matrices. Scalar quantities will be typed in normal. Given that large ensemble may not always be better than small ensemble [10] , [11] and large ensemble consumes much more computational resources, this paper propose a probabilistic ensemble pruning algorithm in order to get a set of sparse combination weights to prune an ensemble.. As the previous research implies that negative combination weights in the ensemble may degrade the performance, we introduce a left-truncated, nonnegative, Gaussian prior over every combination weight in this probabilistic model to prevent negative weights. However, after incorporating the truncated Gaussian prior, the normalization integral becomes intractable and expectation propagation has been used to approximate the posterior calculation. As the LOO error can be obtained as a by-product in EP training without extra computation, the LOO error is used together with Bayesian evidence for ensemble pruning.. An empirical study on several regression/classification benchmark data sets shows that our algorithm utilizes far less component learners but performs as well as, or better than, the unpruned ensemble. The results are very competitive compared with ARD pruning and some other heuristic algorithms.. EP pruning offers a way to estimate the combination weights and prune the ensemble with the following compelling advantages: 1) good generalization ability. Although our algorithm employs only a few of the ensemble members, they perform as well as, or better than, The results are averaged over 10 runs. 5. In the five cards, there is no one pair, two pairs, three of a kind, straight (five cards, sequentially ranked with no gaps), flush (five cards with the same suit), full house (pair plus different rank three of a kind), four of a kind (four equal ranks within five cards), straight flush (straight plus flush), or royal flush (Ace, King, Queen, Jack, Ten plus flush). the unpruned ensemble; 2) the highly spare model is obtained by the sparseness-inducing prior and behaves optimally compact; and 3) no parameters to tune.. Currently, most of the ensemble pruning algorithms, including the proposed algorithm in this paper, carry out postpruning, i.e., pruning after all learners are generated, which is offline pruning. Since the EP pruning algorithm operates sequentially by adding one learner, deleting one learner or reestimating the hyperparameter , which acts like an "online" pruning algorithm, it is possible to generalize the EP pruning algorithm to a prepruning scenario to reduce the computational complexity. This will be our future work. Other further work for this study is to generalize the pruning algorithm to multiclass problems. The goal of ensemble pruning is to reduce the size of ensemble without compromising its performance. The pruning algorithms can be classified into two categories, selection-based and weight-based pruning algorithms. In the following, we review the two kinds of strategies, respectively.

O 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 B 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Tantalum carbide and nitride diffusion barriers for Cu metallisation The reactions in the Si/TaC/Cu and Si/Ta 2 N/Cu metallisation systems were investigated by x-ray diffraction, Rutherford backscattering, scanning electron microscope and the transmission electron microscopy. The results were then combined with the assessed ternary SiTa-C, Ta-C-Cu, Si-Ta-N and Ta-N-Cu phase diagrams. It was found that both barriers ultimately failed due to diffusion of Cu through the barrier and accompanied formation of Cu 3 Si at temperatures higher than 725 °C. However, in the TaC barriers the formation of amorphous TaO x layer with significant amounts of C took place at the TaC/Cu interface already at 600 °C. Similar behaviour at "low" temperatures was also noted in the Ta 2 N barriers. Interest in copper for conduction lines and structures has been wide, since it offers many advantages over the currently used Al based materials. Unfortunately, the interaction between Si and Cu is strong and detrimental to the electrical performance of Si even at temperatures below 200 °C [1] [2] [3] . Thus, it is necessary to implement a barrier layer between Si and Cu. Refractory metals such as tantalum are frequently suggested to be used as barrier layers in Cu metallised IC's. However, according to our investigations thin elemental Ta barrier layers may not posses sufficient stability when in contact with Si and Cu [4] . In order to improve the performance of the barrier layers it is essential to understand the underlying mechanisms leading to the failure. This can be achieved by using a combined thermodynamic and kinetic approach. By utilising this method it was found that the use of binary tantalum compounds like tantalum nitride and tantalum carbide could improve the performance of the barrier layers. The phase relations in the Si/TaC/Cu and Si/Ta 2 N/Cu metallisation systems are examined with the help of the calculated ternary phase diagrams. The information extracted from these diagrams are coupled with the experimental results obtained to reveal the mechanism(s) leading to the failure.

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


A Logical Framework for Modeling and Reasoning about Semantic Web Services Contract In this paper, we incorporate concrete domain and action theory into a very expressive Description Logic (DL), called ALCQO. Notably, this extension can significantly augment the expressive power for modeling and reasoning about dynamic aspects of services contracting. Meanwhile, the original nature and advantages of classical DLs are also preserved to the extent possible. A key aspect in Web services behavior (described by services choreography) is contracting them to (i) make all parties compatible, (ii) guarantee expected QoS parameters, and (iii) ensure every participating service to terminate in a correct state. It is generally accepted that semantic Web services (SWS) should be based on a formalism with a well-defined model-theoretic semantics, particularly, on some sort of logics [2] . Given that DLs are usually considered as the underpinning of many W3C standard languages, it is quite natural and promising to resort to a variant of DLs to model a semantic Web services contract (SWSc). Our present work extends the classical DLs with concrete domain and action theory, which makes it feasible to integrate planning and process modeling into DLs yet still retain decidable reasoning ability. We restrict the underpinning of our framework to a comparatively simple yet quite expressive Description Logic, viz., ALCQO. Meanwhile, we have incorporated concrete domain and action theory into ALCQO, so as to equip it with the abilities to describe, coordinate, and trace the dynamic behaviors of involved parties.. In future, we will try to work out the tight complexity bounds of action reasoning, and implement some practical algorithms.

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


Sub-structural niching in estimation of distribution algorithms We propose a sub-structural niching method that fully exploits the problem decomposition capability of linkagelearning methods such as the estimation distribution algorithms and concentrate on maintaining diversity at the sub-structural level. The proposed method consists of three key components: (1) Problem decomposition and sub-structure identification, (2) sub-structure fitness estimation, and (3) sub-structural niche preservation. The substructural niching method is compared to restricted tournament selection (RTS)-a niching method used in hierarchical Bayesian optimization algorithm-with special emphasis on sustained preservation of multiple global solutions of a class of boundedly-difficult, additively-separable multimodal problems. The results show that sub-structural niching successfully maintains multiple global optima over large number of generations and does so with significantly less population than RTS. Additionally, the market share of each of the niche is much closer to the expected level in sub-structural niching when compared to RTS. One of the daunting challenges in the field of genetic and evolutionary computation is the systematic and principled design of scalable genetic algorithms (GAs) and significant progress has been made along these lines. A design decomposition theory has been proposed and several competent GAs-GAs that solve hard problems quickly, reliably, and accurately-have been developed [8] . One such class of competent GAs is the estimation distribution algorithms (EDAs) [29, 21] . EDAs replace the traditional variation operators of GAs with probabilistic model building of promising solutions that identifies key sub-structures (or building blocks) of the underlying search problem, and sampling the model to generate new candidate solutions. EDAs have successfully solved problems of bounded difficulty at a single level or at multiple hierarchical levels requiring only polynomial (oftentimes sub-quadratic) number of function evaluations [28, 27, 31] .. One of the important components required by EDAs for successfully solving multimodal, hierarchical, dynamic, and multiobjective optimization problems is an efficient niching method. The niching mechanism has to stably maintain a diverse population throughout the search, thereby allowing EDAs to (1) identify multiple optima reliably when solving multimodal and multiobjective problems, (2) identify the global optimum by deciding successfully between substructures when all the hierarchical interactions are revealed, and (3) rapidly identify global solutions as and when changes occur in non-stationary problems. Such a niching method not only needs to adaptively identify and conform to all the niches and niche-distance distributions, but also need to maintain them effectively over the duration of the search.. Traditional niching methods usually maintain diversity at the level of individuals and are not often adaptive to the niche size and distribution. Additionally, they also do not exploit the underlying working mechanism of EDAs and other linkage-learning algorithms. That is, the traditional nichers often use distance information based on the entire individual and do not often directly respect or exploit problem decomposition. Therefore, in this paper we propose a niching method that respects problem decomposition, and utilizes the sub-structure identification capability of EDAs, and maintains diversity at sub-structure level in a stable manner. Such a niching method is not only advantageous for maintaining multiple niches, but also effective for hierarchical [27] , and dynamic [3, 1] problem optimizations where sub-structure niche preservation is what actually required.. The proposed method consists of three components: (1) Sub-structure identification, where we use the probabilistic model built by EDAs, specifically, extended compact GA [16] , (2) sub-structure fitness estimation, where we use the fitness-estimation procedure proposed by Sastry et al [34] , and (3) sub-structure niche preservation, where different mechanisms can be envisioned, and suitability of each is based on the purpose and objective of niching. The key idea of the sub-structure niche preservation mechanism is to preserve highly-fit sub-structures in desired proportions in the population in a stable manner over the duration of the search.. The sub-structural niching mechanism is compared with restricted tournament selection [17] -a nicher used in hierarchical Bayesian optimization algorithm (hBOA)-on a class of boundedly-difficult additively-separable multimodal problems. Specifically, we compare (1) the stability of maintaining multiple niches over a large number of generations, (2) the capability of allocating market share to different niches at the desired level, and (3) the population size required to consistently maintain all the global optima.. The paper is organized as follows. The next section provides a brief introduction to the extended compact genetic algorithm, followed by a detailed description of the proposed sub-structural niching mechanism. The performance of the proposed method is compared to that of RTS in section 4, followed by key conclusions of the paper. In this paper we proposed a sub-structural niching mechanism, which, in contrast to traditional niching mechanisms, exploits the problem decomposition capability of estimation distribution algorithms and stably maintains diversity at the sub-structure, or building-block level rather than at individual level. The sub-structural niching mechanism consists of three components: (1) Sub-structure identification, where we use the probabilistic model built by EDAs, specifically, extended compact GA [16] , (2) sub-structure fitness estimation, where we use the fitness-estimation procedure proposed by Sastry et al [34] , and (3) sub-structure niche preservation, where different mechanisms are can be envisioned, each suitable based on the purpose and objective of using the niching method. Regardless of how it is done, the key idea of the sub-structure niche preservation mechanism is to preserve highly-fit sub-structures in desired proportions in the population in a stable manner over the duration of the search.. We also tested performance of the sub-structural niching mechanism on a class of boundedly-difficult additively separable multimodal problems and compared it with those of restricted tournament selection (RTS)-a niching method used in hierarchical Bayesian optimization algorithm. The results show that not only is the sub-structural niching mechanism able to stably preserve multiple global optima over large number of generations, but does so with a high probability requiring significantly less population size than RTS. The results indicate that sub-structural niching can be particularly effective with hierarchical and dynamic problem optimization.

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