In this study, we explore the combined effects of layout and motion on viewers' perceptions of social network graphs. We ask viewers to interpret the overall network and we ask domain specific questions about managing change within a departmental team to understand how network display influences viewers' overall perception of the network. We find that motion has a positive effect on viewers' perceptions of change in status from formal to informal networks. We also find no main effect for hierarchical versus spatially central layout on viewers' accuracy. There is a significant interaction effect of motion and hierarchical layout. Finally, we find that when viewers are asked to make interpretations of the overall graph, they bring their own pre-existing graphical vocabulary that may influence their interpretation.
Visualizations can be powerful tools for exploring network data and communicating their properties. However, relatively little work has been done to verify that the observer's perception of a network is the one that is intended by the creator of the visualization. As with any means of communication, to gauge its effectiveness we must consider the communication process in its entirety. Communication is a process that depends as much upon how the receiver decodes information as it does on the encoding practices of the sender. Visualization strategies must take into account how viewers are likely to decode the information presented to them as well as addressing the quality and quantity of information encoded within a network graph. This paper presents a study whose purpose is to more fully understand how viewers perceive information presented in graphical representations of complex social network data.
There are two sides to the question of whether an observer's perception of a network matches what was intended. The designer of the visualization usually intends to convey one or more properties of the network data, and one can ask whether these properties are apparent to the observer. However, observers may also make many other inferences from the visualization that were not explicitly intended by its creator. This is because observers bring a rich vocabulary of graphical idioms and conventions to the table when they interpret the visualization. These additional inferences may result in an incorrect interpretation of the data, as we show by example in the study we present.
Advances in the field of network visualization have allowed more people to create ever more sophisticated visual displays of network data. Freeman (2000) traces the history of visual display of network data. As in the general field of data display, the display of network data presents many options and opportunities for communicating information about social structure. Individuals who wish to use network visualizations to communicate information about organizations and even to change those organizations have a range of options to choose from, including motion, 3-dimensional layouts, and user interaction. Some people have questioned the use of ever more complex graphical displays, most notably, Tufte (1990), who encourages the use of as little ink as possible when rendering graphs. On the other hand, Levy et al. (1996) found that users prefer the less parsimonious 3-dimension display to 2-dimensions when they are showing graphs to others and when they believe that it is important to remember the information that is presented. In this case, the extra level of complexity introduced when moving from two to three dimensions might make a display more memorable.
Another important factor to consider is whether it makes the underlying message more or less clear. When generating graphical displays of social network data, users must be aware that complexity is also more likely to introduce unintended information. This is not to say that more sophisticated displays should always be avoided. For example, we show in this paper that the use of motion indeed gives observers a clearer picture of whose prominence varies the most between the authority and advice network. Rather, when users take advantage of sophisticated network representations, they should be aware of the multifaceted information that is likely to be communicated.
One means to address the multi-faceted information that can be conveyed by a graph is to build information directly into the graph layout to highlight particular features of the displayed network. While building intended consequences directly into the layout with clear visual indicators is a good idea, it does not in itself control unintended consequences, which should be balanced with the other considerations of visual display. A second approach is to draw the graph in a way that maximizes positive general features of graph drawing aesthetics. Davidson and Harel (1989) define these features as: nodes that are not too close to each other, edges that are not too long, nodes that do not go through edges. One common approach for maximizing these characteristics of a graph is using simulated annealing with an "energy function" that includes the graph attributes described by Davidson and Harel (1989).
Ultimately, good visual displays are those that "tell the truth about the data" (Tufte, 1983) but often social network data reveal more than one truth. The question of what viewers perceive when viewing graphical representations of data can be explored at several different levels. At the most basic graph-theoretic level one might test viewers' perceptions of graph properties. For example, Ware & Franck (1996) test viewers' ability to perceive whether or not a path of length two existed between two highlighted node. At the social network level McGrath, Blythe and Krackhardt (1995) explore viewers' perceptions of individual node's "prominence" in graphs. Considerably less analysis has been done exploring how viewers make sense of the overall network and apply that understanding in a real world context. In this study, we ask viewers to interpret the overall network and we ask domain specific questions about managing change within a departmental team to understand how network display influences viewers' overall perception of the network.
The effectiveness of network representations can also be assessed at several different levels. Accuracy (Ware & Franck, 1996), response time (McGrath et al., 2000) and viewers' preferences (Levy et al., 1996) are all factors of the display that can be taken into account. In this paper, we report of both viewers' accuracy in perceiving change in status from formal to informal relationships and viewers' interpretation of how social structure data informs their perceptions of managing of organizational change.
There are three facets to our study, which we describe in more detail below. First, we consider network displays that have been created to communicate a particular aspect of the data, such as the status of the entities represented as nodes. (Another set of displays would include those that are used to explore data without an a priori sense of which network features might emerge.) Previous researchers ( Brandes et al., 2001, Krempel & Plumper ,2003) have designed visualizations that specifically to convey information with visual cues, such as node characteristics and location. Second, we explore whether an observer's inference about the real-world context to be conveyed is more accurate using visualizations designed to convey a specific social network property than it is using a visualization that adheres to generally agreed upon graph drawing aesthetics but with no particular property of the network data highlighted. We explore whether the introduction of motion to the visualization can make the observer more likely to perceive the information that was intended. Third, we describe anecdotal experiences of how certain choices in the layout of the graph can lead the observer to unintended inferences. Our specific hypotheses relate to the effectiveness of motion as a mechanism for communicating change, the impact of layout on both viewers' interpretation of individual actor's status and the overall network influence on managing change, and the interaction between motion and layout on viewers' perceptions of social network properties of the graph.
In this study, we consider the effect of motion to highlight change across structural relationships, graph layout to communicate structural characteristics of power within the organization, and congruence of node positioning between the first and second network layouts. Freeman (2000) demonstrated how animation could be used to display differences in graphs, for example individuals' impressions and interactions. Clearly, animation has the potential to be a powerful tool for communicating network properties. We expect that motion will highlight change that occurs between different networks. The change might be a result of change in time or change in relations. At the same time, Qin and Simon (1995) suggest that movie-type pictures may in fact obscure rather than highlight the underlying phenomenon. Their work on viewers' perceptions of physical phenomenon suggests that animated displays may be confusing to viewers. In fact, viewers may miss the underlying process while watching the animation, or in fact, viewers may be misled by their perceptions of the change process that they view. Unlike the physical examples presented by Qin and Simon (1995), the social network example is always based in representation. While wheels and pulleys can actually be viewed in "real life" as well as displayed in a stylized form for communication, social networks can only be seen in their representation, graphical or otherwise. The change that occurs in social networks is not bound by physical properties of motion. For this study, we consider motion between two social network graphs in which each node moves in a direct line from their spatial position in the first graph to their spatial position in the second graph. We test the following hypothesis:
H1: Motion is more effective than still before and after representations for highlighting change across network relationships.
Viewers' perceptions of the information presented in a sociogram are influenced by the layout of the graph. Any given network structure can be displayed in different ways to highlight different features of the graph. Experimental research (McGrath et al, 1997) found that viewers may perceive nodes placed in the center of the graph as more prominent than those placed at the periphery. Recently, Brandes et al. (2001) suggested a layout that uses a type of spatial hierarchy layout to position "actors at vertical positions that exactly represent their status score, and by determining horizontal positions algorithmically in such a way that the overall visualization is readable" (Brandes, 2001 p. 9). Brandes et al. (2001) present a prescriptive model of layout that uses vertical positioning to convey information about status. McGrath et al. (1997) use an empirical test of viewers' perception to determine the influence of layout on perception of prominence. They find that actors that are positioned in the center of the graph are viewed as more prominent than those positioned at the periphery. We are still left with the question of how different layout styles might affect the way viewers interpret information in social network graphs. In this research we compare how a sociogram drawn with actors placed highest to lowest vertically based on their status score with a sociogram that is drawn with the most prominent actor at the center and follows general graph drawing principles to position the other actors. We refer to the first layout as spatial hierarchy and the second as spatial centrality. We test the hypothesis that:
H2: Spatial hierarchy is more effective than spatial centrality for highlighting actors' power.
In addition to the independent effects of motion and layout on viewers' interpretations of changes in graphs, motion might have a particularly strong influence on the accuracy of viewers' perceptions about changes in graphs when the second graph matches layout orientation with the first. Specifically, in this paper, we consider two layouts for the informal network. With Hypothesis 2, we predict that the layout proposed by Brandes et al. (2001) which positions nodes on a vertical axis depending on the node's Katz status score will be more effective for communicating actors' power than the layout strategy described in McGrath et al. (1997) in which prominent nodes are positioned centrally in the graph. In this case, the first network is a formal authority network in which nodes are arranged in a standard organization chart form, which also uses the vertical axis to denote status in the organization. Here we predict that when the first and second graph use consistent layout orientations, in this case using the vertical placement to represent status, then motion will be particularly effective in communicating change.
H3: The accuracy of the spatial hierarchy layout for indicating actors' status will be enhanced by motion when the first and second graphs use the same meaning for vertical axis.
Many explorations of social network representations consider the way viewers perceive particular aspect of the multifaceted information that is present in a social network representation. Most of the research that we have discussed evaluates viewers' perceptions of particular aspects of the graph. At the same time, it is valuable to consider viewer's overall perception of the network. Good graphical representations should not, therefore, lose the forest for the trees. Here, we attempt to understand how the representation of the graph (specifically layout as motion was held constant across the two auditing teams for each group of viewers) might impact viewers' overall impression of the network by asking viewers to compare the two networks. By reviewing viewers' qualitative interpretations of the two different auditing teams we can begin to understand how graph representation impacts their overall impression of the graph.
One particularly relevant application of social network visualization is the use of social network visualizations to help manage organizations. Social network analysis has been used to understand the influence of formal and informal networks of relationships within organizations (Krackhardt, 1993). Krackhardt (1996) suggests that understanding the social networks that exist within an organization will help a new manager to, "diagnose and successfully introduce organizational changes." More recently, organization researchers have encouraged more proactive use of social network analysis and the presentation of network diagrams as a means of understanding the relationships that exist in organizations and intervening to influence those relationships (Cross et al., 2002).
Simply reviewing these diagrams with managers usually results in myriad recommendations, as people immersed in the patterns of relationships define and resolve issues affecting group performance." (Cross et al., p.39)
For this experiment, we present participants with a change management case that is described by Krackhardt (1996) as the Halifax auditing team case. This case presents the story of an auditing team that is undergoing a change in the auditing procedure. Background about the organization was presented to participants.
The exercise was conducted with four groups of upper-division undergraduate business students totaling 133 students participating in a core management class. Before beginning the visualization exercise, students were asked to read an article introducing social network analysis as a managerial tool (Krackhardt and Hanson, 1993), and they participated in a classroom discussion of management and social network analysis that included a discussion of the importance of understanding the informal relationships that exist within and support the mission of the organization becomes vital. We also noted that skilled managers must be able to understand the role of both formal relationships and informal relationship in the performance of organizations. We discussed the observation that organization restructuring usually focuses on formal relationships, however, the impact of restructuring affects both the formal and informal structure organizations. We discussed the fact that if managers understand who wields power in informal networks and how coalitions function, they can work with informal networks to facilitate change and improve performance. Finally we observe that mapping advice networks shows the most influential players in the day-to-day operations of a company.
Data on the formal organization structure and the informal advice structure were presented to the participants. In the original case, one member of the secretarial staff, Nancy, is identified as a key actor for change through analysis of the informal advice relationships and observation. For this study, we manipulated the way this data was presented in two ways: by using two different layouts for the informal advice network, and using motion from the formal to the informal versus showing before and after representations of the formal and informal network.
In order to compare viewers' perceptions of the overall network based on the layout of the informal network, we added a fictionalized "second" team that was the same network with the name labels changed. Participants saw the same layout for the formal network and they saw the informal layout that they did not see for the first team. We did not combine motion and before and after representations for any single session. Rather we varied motion and before and after by participant groups. We were careful to vary the order of presentation of the informal layouts so that both hierarchy and spatial centrality were viewed first a similar number of times (for both the motion and before and after case). Because there was a good possibility of the first exercise influencing participants' responses to the second presentation of the formal and informal data, we do not include the second team in the analysis of motion and layout on accuracy. We only include participants' responses comparing the first and second team on their impression of successful organizational change. The study design is summarized in Table 1. Figure 1 shows the layout that we used to display the formal authority network as well as the two different layouts that we used to display the informal advice network. In the formal organization layout and both informal layouts, the shape of nodes indicates the team member's formal organization roles: a diamond for the top manager, Manuel; ovals for the middle managers, Stuart, Charles, and Donna; rectangles for the auditors, Wynn, Carol, Harold, Fred, Sharon, and Bob; and no shape for the administrative assistants, Kathy, Nancy, Susan, and Tanya. The shapes remain constant between representations of the formal and informal networks.
To test our hypothesis about the effectiveness of motion, we used motion to represent change from the formal to the informal networks for 72 of the 133 participants. In the cases using motion we mapped each node's location on the formal organization chart to its new location in the informal network presented in the spatial hierarchy or spatial centrality layout. A node moved from its location in the first to the second through a straight line which allows viewers to trace how node location changes between the two networks. In the no motion condition, viewers are presented first with the formal organization chart, then the presentation changes directly to the informal advice network.
To compare the spatial hierarchy and spatial centrality layouts we used different criteria for positioning nodes. For the spatial hierarchy layout, the vertical positioning of nodes depended upon their Katz Status score. Horizontal positioning was determined to maximize graph drawing aesthetics. For the spatial centrality layout, we position the most central actors in the center of the drawing. Viewers may read status information based upon the direction of the arrows attached to nodes. Figure 1 shows the different conditions viewed by participants. Next to the caption for each of the lower two figures is a link to show an animation of the smooth transition between that figure and the formal authority network. See this version of the paper to try java applets that show both the image and the smooth transition.
Participants answered several questions about the auditing team. First participants identified the four most powerful people in the formal network, then the four most powerful people in the informal network. Next, they were asked to indicate on a scale from 1 = "greatly decreased" to 5 = "greatly increased" how network members' power changed from the formal to the informal networks. (It is important to note that participants were not presented with information about Katz Status scores, nor were they directly asked about status, rather, they answered questions about "power".) Finally, viewers were asked, "Based on all of the information available to you, who do you believe are the key agents for change? Who should top management spend its efforts with for promoting the changes in the auditing system?" Next, we presented a second team and told the participants that this team had the same formal structure but a different informal structure. In fact, the second team was the same as the first team with the names relabeled. The second informal network was displayed using the layout for the informal network that was not used for the first auditing team. After participants viewed both auditing teams and answered questions about each, we asked them to predict which would be "more likely to successfully implement a change in the auditing procedure." They wrote short answers explaining their responses. One of the authors generated 10 categories that summarized all viewers' responses. Three graduate research assistants were trained to review all verbatim responses and categorize responses. Only responses agreed upon by at least two of the three raters were included in the analysis. In the following section we report the results of participants responses in this exercise.
Consistent with Brandes et al.'s (2001) work, we use Katz's (1953) Status measure for both the formal and informal networks to define status. Status is an important concept in management theory. The Katz Status measure is similar to Bonaicich's eigenvalue measure of status. Podolny (1994) uses Bonacich's eigenvalue measure of status to describe the status that derives from investment banking relationships. Here we consider change in status occurs when different relationships are considered. We use the difference between each actor's Katz Status measure in the formal and informal network to define the change in status from formal to informal network. Table 2 shows the Katz Status scores and how they change for the auditing team's formal and informal networks. Manuel, Charles, and Stuart clearly lose power in the shift from formal to informal relationships while Nancy and Donna clearly gain power.
To determine how well participants perceived the change in status from the formal authority to informal advice network, we calculated and overall accuracy score for each participant by combining the accuracy of their assessments of the change in status from the formal to informal network for each member of the auditing team. A response of "3" indicated that viewers saw no change in an actor's power from the authority to the advice network. Responses less than 3 indicated that viewers thought an actor lost power and responses greater than 3 indicated that viewers thought that the actor gained power from the authority to the advice network. Since the spatial hierarchy layout was partially determined by Katz's Status measure scores, we expected that when viewers saw the advice layout presented as a spatial hierarchy, they would be more likely to answer correctly in accordance with the Katz Status scores. Table 3 shows the average overall accuracy of viewers' perceptions of the change in power from the formal network to the informal network for both layouts, with and without motion..
In fact, when we compare the main effects and interaction effects for layout and motion, we find statistically significant effects for only motion and the interaction of layout and motion. Surprisingly, the hierarchy layout alone does not result in a statistically significant increase in viewers' accuracy of perception of change from the formal to informal network. Figure 2 displays the differences in effect between centrality and hierarchy for the motion and no motion conditions.
In particular, for cases using motion, viewers who saw the spatial hierarchy layout were more likely to recognize that Manuel and Charles lost power. Viewers in both the spatial centrality and spatial hierarchy case saw that Nancy gained power between the authority and advice networks. Interestingly, in neither the spatial centrality nor spatial hierarchy case did many people (47% and 50% respectively) see that Donna gained power. This suggests that for assessing change in status the hierarchical layout as proposed by Brandes et al. (2001) does perform more effectively than the spatial centrality layout.
Finally, we explored viewers' overall impressions of the structure of formal and informal relationships by asking them a domain specific question related to managing change. We asked each viewer the following question, "Given all that you have learned about (the two auditing teams) which team do you think will be more likely to successfully implement a change in the auditing procedure? Why?" Table 4 summarized viewers' responses.
We found that when viewers chose the auditing teams whose informal advice network was presented as a spatial hierarchy they were more likely to report reasons that are consistent with traditional descriptions of a hierarchical organization. They were more likely to recognize the key role of Nancy or Manuel in the change process. Also, they were more likely to report consistency between the formal to the informal network. For example:
"I think that Hierarchy's group would definitely be more successful in implementing some changes. Hierarchy's group has many different authority figures, but there is still one central figure to oversee everything. There is an excellent flow of input in Hierarchy's group so that by the time ideas are finalized they should be perfect."
"Hierarchy's team is much simpler in its connections and many people would not be getting the same information from different people. Due to the simplicity of Hierarchy's team, change would occur at a much faster rate."
"I think Hierarchy's team would be better able to implement change because their informal advice structure is simpler and more spread out. In Centrality's team they have a lot of people going to Nancy for advice, which may cause her to be overwhelmed. In Hierarchy's team the advice links are more spread out. Nancy does give out a lot of advice but also receives help. Where Nancy from Centrality's team does not. Hierarchy's team can succeed because everybody is working together in a more efficient manner."
On the other hand, when viewers chose the team whose informal network was presented using a spatial centrality layout, they were more likely to describe the auditing team in ways that are consistent with the description of an organic structure. They describe more communication or more connections throughout the network and more change from the formal authority hierarchy to informal relationships. For example, they reported:
"Centrality's group because it did not seem as hierarchical. Also, everyone had contact with one another. It seems to me that Centrality's group would have an easier time because it is more informal. It was not as easy to designate a person to implement change the best for Hierarchy's group. There needs to be more equality and evenness like Centrality's group."
"It seemed like Centrality's team talked to more people and the people towards the bottom had more say and more responsibilities than Hierarchy thus Centrality's team could probably get the job done better."
"Centrality's team would be more likely to implement a change successfully because they communicate more with each other. The boss is not the only one. Even the people who are not in charge given advice and contribute to the company. This team seems more open to change because of that. They seem like they work together more and do not just depend on one head boss."
Display elements such as layout and the use of motion clearly can have a significant effect on the viewer's perceptions of a network. In this study we have demonstrated that an automatic layout that maps a particular node-based network property into an easily discernible graphical property can improve the accuracy of the viewer's perception of the network property, especially when motion is used. Here we chose the Katz status property and mapped it to the vertical dimension of the node. It is interesting to note the interplay between the roles of the different display elements in effective communication: in this case, the advantage of the direct-mapping layout over the generic aesthetic layout was statistically significant only when motion was used between the common formal layout and the advice layout. Presumably, motion helps the viewer in aligning the nodes in the two layouts.
It is unlikely that there is 'one right way' to draw a graph. The most important network features to be communicated should be considered when designing the layout and rendering. However, one must also take into account the secondary messages that will inevitably be sent with any particular choice of drawing, since viewers bring a rich context to the interpretation of graphical information. In our study, when viewers chose the spatial hierarchy layout as likely to be more successful with change, they often reported that the spatial hierarchy was more efficient, using less communication, and they were more likely to see both Manuel and Nancy as key players. This is consistent with a standard perception of organizational hierarchy. Especially since the first network they saw was a formal hierarchy, they seem to have mapped the spatial hierarchy layout to their overall impressions about the characteristics of an organizational hierarchy. On the other hand, when viewers chose the spatial centrality layout as the team likely to be successful with change, they were more likely to report that the team had more communication and connection, and more change from formal to informal. Again, in this case, their perceptions of the team are more consistent with perceptions of an organic structure.
Mapping status to the vertical dimension of the graph layout has an unwanted side-effect of making the network appear inherently hierarchical, which may outweigh its benefits. One question is whether there are other direct mappings of status into a simple graphical feature that might avoid such side-effects. An interesting follow-up study might investigate a mapping of Katz status into distance from the center of the graph, where nodes are constrained to lie on concentric circles whose radii increase as status decreases, but are otherwise laid out according to general aesthetic principles. This layout may counteract the unintended inference of hierarchy. However, we note that such direct mappings necessarily remove one degree of freedom for computing node layout, with a corresponding increase in unintended graphical inferences. This can limit a viewer's ability to explore other properties of the network. For example, the spatial hierarchy layout violates the general principle of making lines have roughly the same length, which in this domain will lead to people generally being placed close to those others with whom they have an advice relationship.
Our study validated our main hypotheses about the use of layout and motion together to visually communicate a particular property of network data. We also found evidence of unintended communications that must be considered in designing a presentation of a graph. Although we are able to make some recommendations about the design of a presentation, it is clear that there is much still to be learned in this fascinating area.
| Group | First Viewing | Model of Change | Second viewing |
| 1 (n=40) | Informal=Spatial centrality | No Motion | Informal=Spatial hierarchy |
| 2 (n=30) | Informal= Spatial hierarchy | Motion | Informal= Spatial centrality |
| 3 (n=32) | Informal= Spatial centrality | Motion | Informal= Spatial hierarchy |
| 4 (n=31) | Informal= Spatial hierarchy | No Motion | Informal= Spatial centrality |
| Name | Formal | Informal | Difference | |
| Manuel | Lost | 1 | 0.57 | -0.43 |
| Charles | Lost | 0.37 | 0.17 | -0.2 |
| Stuart | Lost | 0.37 | 0.19 | -0.18 |
| Donna | Gained | 0.5 | 0.66 | 0.16 |
| Wynn | Same | 0 | 0 | 0 |
| Carol | Same | 0 | 0 | 0 |
| Harold | Same | 0 | 0 | 0 |
| Fred | Gained | 0 | 0.02 | 0.02 |
| Sharon | Gained | 0 | 0.02 | 0.02 |
| Bob | Same | 0 | 0 | 0 |
| Kathy | Gained | 0 | 0.08 | 0.08 |
| Nancy | Gained | 0 | 1 | 1 |
| Susan | Same | 0 | 0 | 0 |
| Tanya | Gained | 0 | 0.08 | 0.08 |
| Spatial Hierarchy | Spatial Centrality | Both Layouts | |
| Motion |
.75 (.20) n=30 |
.61 (.14) n=32 |
.68 (.18) n=62 |
| No Motion |
.50 (.24) n=31 |
.58 (.25) n=40 |
.54 (.24) n=71 |
| With and Without Motion |
.62 (.24) n=61 |
.59 (.21) n=72 |
.61 (.23) n=133 |
| Df | SS | F | P | |
|
Motion (0/1) |
1 | .56 | 12.65 | .0005 |
|
Layout (Hierarchy/Centrality |
1 | .03 | .74 | .39 |
| Motion*Layout | 1 | .37 | 8.32 | .005 |
| Total | Centrality | Hierarchy | ||
| Number of times layout is viewed second | 58 | 57 | ||
| Groups are same/equal | 13 | N/A | N/A | |
| Group is more connected | 43 | 27 | 16 | |
| Group is less connected | 2 | 0 | 2 | |
| More communication | 18 | 16 | 2 | ** |
| Less communication | 0 | 0 | 0 | |
| Claire/Nancy plays key role | 13 | 4 | 9 | * |
| Carl/Manuel plays key role | 6 | 0 | 6 | ** |
| Carl/Manuel has more power | 5 | 3 | 2 | |
| Carl/Manuel has less power | 1 | 0 | 1 | |
| More Change from formal to informal | 18 | 14 | 4 | * |
| Less Change from formal to informal | 11 | 5 | 6 |
Chi Square p<.1, * p<.05, ** p<.01, ***p<.001
1 College of Business Administration, Loyola Marymount University, Los Angeles California, USA. email: cmcgrath@lmu.edu
2 Information Sciences Institute, University of Southern California, Los Angeles California, USA. email: blythe@isi.edu