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The Journal of Space SyntaxThe Journal of Space SyntaxThe Journal of Space SyntaxThe Journal of Space SyntaxThe Journal of Space Syntax

The Journal of Space Syntax

ISSN: 2044-7507

Year: 2010. Volume: 1, Issue: 1

Online Publication Date: 14 July 2010

http://www.journalofspacesyntax.org/

Solutions for visibility-accessibility and signage problems via layered-graphs

Nicholas Sheep Dalton1 and Ruth Conroy Dalton2

1 The Open University2 Bartlett School of Graduate Studies, University College London

Pages: 164-176



Journal of Space Syntax, Volume 1, Issue 1, Pages 164-176, 2010

Solutions for visibility-accessibility and signage problems via lay-

ered-graphs

Nicholas Sheep Dalton1 and Ruth Conroy Dalton2

1 The Open University2 Bartlett School of Graduate Studies, University College London

Abstract

One of the rare representational problems encountered in space syntax analysis arises during the

construction of axial representations of architectural configurations and is the so called 'visibility-

accessibility problem'. This describes a situation where it is possible to see a space but not to be able

to directly move towards it. This condition arises in a number of cases, for example, in an office

containing half-height partitions or glass walls, in an urban street where safety barriers prevent indis-

criminate pedestrian movement or in an atrium-building that permits direct views to the second story

but does not facilitate direct access to those same spaces. This paper introduces a new spatial repre-

sentation called the multi-layered network that is intended to serve as a more generalized representa-

tion of topological spaces than previous representations. Evidence is presented to substantiate aspects

of the proposed representation based on an extension of current topological representations and asso-

ciated computational methods. A software implementation of the multi-layered network is demon-

strated along with examples from a sample of hitherto 'problematic' cases. Finally, it is argued that

this new multi-layered representation could equally be used as the underlying mechanism for a spatial

representation that might be able to accommodate signage-information, for example, and so, by ex-

tension, could establish testable conditions with the potential to measure the effect of signage 'catch-

ment areas' and signage placement in a building.

Keywords: space syntax, representation, visibility-accessiblty, graph, integration, navigation, signage

1. Introduction

Space syntax (Hillier and Hanson, 1984; Hillier, et al., 1993; Hillier, 1996, 1999) has proven to be a

powerful predictor of movement at the urban level and capable of providing insight into patterns of

usability at the building level. One problem discovered when mapping buildings is how to construct

a representation of a building where elements of that building can be seen but are not directly acces-

sible. One example of this is in a building with an atrium: a large, open, multilevel space in a building

allowing one to look up and observe spaces on subsequent floors, without affording direct access to

them (for example, by a directly visible staircase, escalator or lift/elevator; see Doxa, 2003; and

Parvin, 2008). While it could be argued that these kinds of spaces are rare and can be handled by

adhoc methodological means, it is the contention of this paper that these problems provide an impetusto reinterpret the representations used by space syntax theory.

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The visibility-accessibly problem is present in a variety of ways and a variety of scales in

buildings and urban contexts. Take, for example, an open plan office with numerous, half-height

partitions or many desks impeding direct movement: a situation mentioned in a number of spatial

studies of office buildings (Serrato, 1999; Bakke and Yttri, 2003; Kostakos, 2007; Sailer, et al., 2007).

Here, an isovist generated at a standing-eye-height (Benedikt, 1979; Davis and Benedikt, 1979) pro-

vides complete visible access to surrounding spaces but the physical blockage of the half-height

partitions or desks gives rise to impeded accessibly. The space of an open plan office can therefore be

held to be simultaneously trivial (merely a single, open space) and complex (requiring the planning of

multiple, sinuous paths through a labyrinth of partitions and/or desks).1

Modern office buildings can also present analytic difficulties through the use of glass-walled

partitions (Figure 1), giving greater light, reducing noise but creating situations where an occupant

can see a destination but will be forced to take a more circuitous route to reach it. Again, this gives

rise to the operational question of how to map these spaces. A second, common type of glass barrier

is the traditional museum display cabinet, such as those found in the Natural History Museum of

Cambridge (UK). As with glass cubicles, the cabinets interrupt free movement but afford some visual

clues (from one side of the cabinet through to the other) to the understanding of the wider spatial

layout. Related to both half-height cubicles and museum display cases are the sales areas of many

department stores. In such environments it is frequently possible to see across to the far side of the

store whilst the direct route is blocked by a complex array of display racks, of varying heights, forc-

ing the visitor to take more indirect routes through the space (and hence being exposed to a greater

number of goods for sale).

These visibility-accessibility problems are not confined to the building scale, at the urban

level one example is provided by the use of pedestrian rails or barriers common in many urban cen-

tres such as Oxford Circus or Piccadilly Circus in London (UK) intended to separate pedestrian and

vehicular traffic (Major and Penn, 2008; Suvanajata, 2003). With the barriers in place, traversing the

urban-space necessitates planning a route around the barriers, yet the destination remains clearly

visible at all times.

One question that these space types, presented above, pose is, 'is this space simple or com-

plex?'. In the half-height partition situation, if considered from the lower view-point (of a child or

wheelchair-user for example) the space is unquestionably complex. From the perspective of a fully-

grown and able-bodied adult, the space appears simpler but is clearly still more complex than a

completely open space. If a space syntax analysis of such a space were to be performed, the decision

about which view-point should be used would be regarded primarily as an operational one. The deci-

sion would be made either intuitively or mediated by the experience and professionalism of the re-

searcher. The space would then be mapped either as a single space or as a complex labyrinth (or even

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mapped twice in both ways). In each case, the analysis would be adequate but not entirely satisfac-

tory. Intuition suggests that the space is neither irrevocably complex nor a trivial single space but, in

fact, somewhere in between these two extremes.

A second, similar and connected problem is that of the effect of signage in a building or

quasi-urban environment like the Barbican Centre (a mixed-use residential and arts centre) in Lon-

don. Most signs serve to indicate the distal presence and initial heading of a room, space or group of

spaces (such as a department). The effect of a sign is to reduce the conceptual and topological dis-

tance from one space (of a situated observer) to many others, creating an effect somewhat similar to

a 'hyperlink'. Currently, there is no clear mechanism in space syntax analysis to accommodate the

effect of signage in a complex building. Like 'programme' and other factors influencing movement

patterns in a building, signage is just one of the assumed reasons why the correlation between space

and observed movement rarely exceeds a 'threshold' correlation coefficient of approximately 0.7 to

0.8 r-squared.

The axial map is a transformation of geometric space into a graph (or network) representa-

tion; there is no facility to alter this objective spatial description to permit signage to be taken into

account. Yet the effects of signage are neither random nor unbiased: signs are situated in one location

and point to, or link to, another location. Signs exist to make space more navigable or even 'intelli-

gible' in the Hillierian sense (Hillier, 1996), something that, at the urban level, is normally attributed

solely to space. Signs are deliberate attempts to alter how the space in a building is experienced but,

unlike space, they tend to eliminate irrelevant information creating pseudo-spatial asymmetries. For example a building-user may observe a sign indicating the direction to a toilet but are unlikely to find

one indicating the direction of the air-conditioning plant or the cleaners' cupboard. Signs are also uni-

directional, for example, a visitor may regularly encounter signs indicating the way to the toilets but

it is rare to have one saying for example 'this way back to, the restaurant'.

Signage is one of the ways in which occupants of or visitors to large complex buildings can

overcome the deficiencies of poor configuration or simply accommodate the complexities of large

buildings. Given that signage is frequently used in a remedial way (small building such as domestic

dwellings tend not to need signs indicating the 'Kitchen', or 'Living Room') to overcome what are

essentially spatial problems, we have, as yet, no representational mechanisms to understand the spa-

tial context of signs. Crucial to the integration of the use of signage into a representation such as space

syntax is an interpretation of the effect that a sign has on conceptual complexity. Imagine, for ex-

ample, standing in a typical hospital such as described by Peponis (Peponis, et al., 1990). One might

ask directions to a specific ward/room and be given the instructions, 'go down here turn left then

simply follow the yellow line down main corridor'. In space syntax analysis the concept of a change

of direction being synonymous with a step change in depth is common but following 'the main corri-

dor' might actually involve several changes of direction, especially if these did not include decision

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points, which would no longer need to be considered in direction-giving. In effect, the existence of

the corridor-route conceptually 'straightens' the path, linguistically, but by a degree which is undeter-

mined.

These and other similar phenomena can be reduced down to a consideration of the visibility

and accessibility of space. Given that there are a number of phenomena which appear to reduce the

topological depth from one space to another is there a single representation which can represent the

problems presented? Pervious work such as Doxa (2001) has focused on an isovist Visibility Graph

approach, this paper contents that an axial approach which could be extended to the convex or the

isovist representations of space could be a more elegant solution.

We can begin by looking at a simple hypothetical building the kind one might experience

from (figure 1). In the hypothetical building the space exists with a courtyard (centre to the left

fraction of figure 2) looked down upon by a gallery from either side of the first story space. When one

arrives it is possible to see up and observe movement on the first story. From the point of view of the

upper floors they are poorly constituted. From the ground it is clearly obvious that it is possible to

find some currently hidden route up to the first story. It is also possible to interpret the space as open

for communication. The visitor on the ground is potentially free to converse with others at the first

story. The ability to potentially be observed and interact with others is a component of a social space

and yet in representational terms the two spaces have a large accessibility distance between them. In

representational terms the atrium would operate the same as if the first floor were underground some-

thing which appears counter intuitive.

Figure 2 introduces a basic axial floor plan of a simple notional two story building with an

entrance at the bottom leading into a courtyard. A staircase that is not directly visible from the en-

trance space (moving from the back of the courtyard space) leads up to the second story space. In this

configuration the central entrance space becomes the most integrated space of the building.

Figure 1 A complex office example, containing an atrium space, mezzanines and glass walls creating a

visible link from public to private and secured areas.

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Traditional space syntax could take one of two approaches to solve this problem. Firstly it

can assume that the effect of inter-visibility without accessibility is small on the overall movement

economy of the building. In this manner the accessibility axial map can be used. Given the number of

architects who have designed spaces where you can see but not access directly, it would be counter-

intuitive to dismiss these kinds of designs as irrelevant on the use of space out of hand. Should we

then model 'visibility' space? This would mean effectively making each space that was visible also

accessible; clearly this stands against intuition as well.

2. The Proposal

The proposal of this paper is that the established representations of space syntax can be extended and

adapted to accommodate these situations. The underlying representation in space syntax is the graph

or network. Mathematically the graph (G) is represented by a set of nodes (N) and a set of edges (E)connecting nodes (see figure 3).

G = (N, E)

It is the suggestion of this paper that a more suitable representation is the 'layered-graph'. A

layered graph (M) can be considered as a set of nodes (N) and a set of a set of edges (E1, E2 etc)

Figure 2 a map of total depth of the axial

map of a notional building showing the

courtyard as the most integrated space.

A B

C

D

EF

G

HFigure 3. A graph representation of a building

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M = (N ,{ E1, E2, E3…})

This differs from a hypergraph (Harary 1994) where edges can link more than one node. The

layered-graph can be considered simply to be a graph formed of layers. That is, nodes are present on

more than one 'layer' but the edges between nodes may differ from layer to layer. A path can be

formed through the edges in one layer but paths cannot be constructed through edges in more than

one layer. As is common in space syntax, edges are typically two way (undirected) and edges may or

may not be weighted. For simplicity of explanation in this paper, edges are not weighted as is typical

in angular analysis but the results presented here are equally applicable or adaptable to weighted,

angular graphs. Figure 4 shows such a layered-graph.

In the case of the visibility-accessibility problem, as described in the introduction, the asso-

ciated graph can be represented as two distinct edge sets: the edge set of the inter-visible spaces (EV)

and the edge set of any mutually accessible spaces (EA). Note that the accessible edge set, EA, is the

one with which space syntax researchers are typically familiar. Note also that EA is also typically a

subset of EV and that EV is a superset of EA. Namely, that we can usually see all locations that are

immediately accessible to us.

Figure 5. Visibility and

accessibility integration

Figure 4. Layered-graph with two'layers' (edge sets)

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Figure 5 shows an axial map representation of a courtyard-building containing a second

storey (to the right) which forms an atrium at the lower floors. At the top is a 'superlink' representing

a staircase between the ground and first floors. The two cyan-coloured links represent the visibility-

relationship between the ground-floor entrance-space and an upper level passageway. In this case, the

integration values have been computed as if the visibility link were a full spatial link: as if a staircase,

for example, linked the courtyard to the upper floors. It can be observed that such visibility links

cause the integration core to shift towards this conceptual 'staircase' (the dotted, super link). This

causes the upper floors to be more integrated than might be expected. All calculations and subsequent

visualisations were performed using Webmap@home version 0.91.1 (Dalton 2005).

The primary benefit of the layered-graph representation is that we can consider simulta-

neously two graphs/networks. First, the accessibility graph (N, EA), which must define the lower

bound of the integration structure of the graph. Clearly, it is unreasonable to assume that the integra-

tion values of the upper floor will decrease if it is visible (linked in (N, EV)). We can naturally expect

that if the upper floor is directly visible, the degree of its relative segregation might decrease or, at

worst, remain the same. Second, the visibility graph (N, EV) defines the upper limit of the integration

values. Namely, if it were treated as an accessibility graph, (one could almost imagine a visitor float-

ing magically upwards, along the 'visibility axis' towards the upper floor) then the upper floor could

never be more integrated than if it were directly connected in some physical manner.

Restating these intuitions in space syntax terms: if the step depth from the central, lower

atrium space to one of the upper levels is calculated, then the depth to the upper level space should lie between the shortest, 'accessibility' geodetic depth (9 steps in the accessibility network, in this ex-

ample) and the shortest, 'visibility' geodetic depth (3 steps in the visibility network). Thus it should be

possible to formulate a function, f, which will take into account the effect of the impact of spatial

inter-visibility on standard accessibility graphs:

f(Dea

( i,j ), Dev

(i,j))

Where Dea( i,j ) is the geodetic distance between node 'I' and node 'J' and Dev

(i,j) is the

shortest geodetic distance for the accessibility layer/graph and Dev

(i,j)) is the equivalent distance in

the visibility-layer. It might be surmised that the simplest function to measure the reduction in segre-

gation caused by the effect of spatial inter-visibility is to interpolate the new depth between the first

and second cases (accessibility and visibility). The simplest means to do this is to use a linear interpo-

lation formula:

Dhg(I,j) = Dea

( I,j ) * !!!!! + Dev

(i,j)* (1-!!!!!)

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Where ! is a constant factor taking a value between 1 and 0. In the above example, given a

! -factor of 0.5, it could be established that the layered-graph depth is ( (9*0.5)+ (6*0.5)) = 7.5. This

! =0.5 example demonstrates a situation where accessibility and visibility contribute equally to the

overall depth of spaces. Clearly this factor can be used only for positively (i.e. not negatively) weighted

graphs and can be generalised, if necessary, for a greater number of layers/edge sets (one layer for

accessibility, one for visibility and one for signage, for example).

Given the definition of layered-graph, geodetic distance provided above, a familiar J- graph

representation (all shortest paths to node 'A') can be constructed and, from this, the total and average

depths can be computed in the same manner as for non-layered J-graphs.

Figure 6 provides a visual explanation of this process: each part of the figure shows a J-graph with a origin-node, A, of the graph presented in figure 3. In this figure, the accessibility connec-

tions are shown as black lines and the visibility connections are shown as dotted, red lines. The

leftmost part (a) of figure 6 shows the typical J-graph as defined in the Social Logic of Space (Hillier

and Hanson, 1984). The rightmost part of figure 6 (c) shows the visibility J-graph, where every

visibility-link is considered to be a single step in the J-graph. It can be seen that, in this case, space H

is now at the same depth as spaces B and D due to its visible connection to space G.

The middle diagram of figure 6 (b) presents the new, hybrid J-graph showing the effect of

applying the depth formula as outlined above. In this case, the ! -factor is 0.5. By examining space-

G, for example, it can be seen that it is now situated between depth 4 (its 'accessibility' level) and

depth 1 (its 'visibility' level). The formula calculates a new depth, of 3, for space-G in the hybrid J-

graph. In the pure visibility case (c), space-H has a depth equal to spaces D and B which is counter-

intuitive. In contrast, in the hybrid J-graph, space-H still occupies the most distant location from A,

which is aligned with our intuition.

If the axial map first presented in figure 2 is processed in the hybrid-manner described above

(merging both accessibility and visibility links), the result is that the total depth values for the upper

floors are lowered, as originally hypothesized. The presence of the visibility links reduce the degree

Figure 6. a J-graph from space-A from figure 3 for a) accessibility b) hybrid accessibility/visibility c) visibility

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of segregation of the upper level. The ! -factor of 0.5 is just a example intended to demonstrate the

influence of the visibility links on the resultant patterns of integration. By examining figure 7, it can

be seen that the integration core of the building moves away from the courtyard entrance, yet it

remains more integrated than in the visibility-only case. The upper floor becomes more integrated but

not as integrated as in the pure visibility case in figure 5. Overall, the integration pattern shifts so that

the upper and lower spaces become equally accessible (in this example, it is assumed that the lower

floors do not have windows overlooking the ground floor) and the back plane becomes the most

integrated part of the building.

Table 1 shows the values of total depth computed for each node in the visibility (EV), the

accessibility (EA) graphs. The third column contains the values which have been computed using thenew values of depth for the layered-graph method with a !-factor of 0.5. As to be expected, the

visibility depths are always lower than the accessibility ones (making a space visible lowers its con-

ceptual distance from everywhere else). From this case it can be see that it is possible to interpolate

between the visibility and accessibility total depths and, by implication, it should also be possible to

interpolate between the global integration (radius infinity) values. While this could be used as an

approximation, in many cases, this could mask any benefits of this approach. First, the interpolation

between integration values would break down in the case of using some non-global depths (for ex-

ample radius 3) as the value would shift due to the change in connectivity. Second, the interpolation

of global values also fails when asymmetric values are used, these would occur in the case of signage

(A points to B which does not point back to A) and may also appear in the case of visible upper levels.

For example, it could be thought that looking down on a lower level might be more likely than

looking up; in this case a different !"factor could be applied depending upon the direction of gaze. As

such the layered-graph computation has certain advantages and hence was the method programmed

into the webmap@home software.

Figure 7. the hybrid axial line

representation, calculated using

a !!!!!-factor of 0.5

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Setting the !-factor

The value of the !-factor now becomes the necessary parameter to understanding the impact of vis-

ibility on the spatial structure of the building. Given the simple definition of the !-factor presented

here, it might be possible to derive a value for the !-factor through experimental means. By experi-

menting with a range of !-factor values it could be possible to determine what !-factor might best

improve the correlation with observed movement for a particular building or building typology. A

more detailed experiment could consist of the introduction of a temporary visibility-barrier into an

already studied spatial system and then examine its effect on movement rates of new visitors (and

hence those not familiar with the layout) to the space.

One final observation is that when !-factor =1.0, this is equivalent to the visibility-is-equiva-

lent -to-accessibility map and when !-factor = 0.0 this corresponds to the accessibility-only map (i.e.

the current space syntax value). It is the suggestion of this paper that !-factor values would be ap-

proximately equal for specific visual contexts or situations. For example, in the case presented in the

introduction, of the half-height partitions in an office building, it might be expected that a !-factor

value of, for example 0.82, might emerge as the best correlate (across all offices with half-height

partitions), while an atrium-building might be best represented by a !-factor value 0.7. Further em-

Table 1 values for accessibility total depth (column 2) and visibility total depth (column 3) for all nodes in

figure 7 and, in column 4, the total depth for !!!!!-factor = 0.5

AXIAL line # Accessibility Visibility VisibiltyTD0.5

1 72 38 55

2 57 38 47.5

3 70 51 60.5

4 87 68 77.5

5 70 51 60.5

6 87 68 77.5

7 87 68 77.5

8 87 68 77.5

9 89 55 72

10 78 46 62

11 65 52 58.5

12 78 46 62

13 95 63 79

14 95 63 79

15 95 63 79

16 95 63 79

17 56 50 53

18 57 57 57

19 60 58 59

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pirical and observational work will need to be completed and, to this end, the software which has

been developed to perform the accessibility-visibility calculations, for axial line analysis, is to be

made freely available.

Extensions

Given the layered-graph mechanism, it might be fruitful to explore the utility of this representation to

other problems. Consider, once again, figure 7 and, this time, imagine that the axial line graph repre-

sents a non-atrium building: the cyan-coloured links, instead of representing an inter-visibility condi-

tion between two spaces, represent two different signs indicating the presence and the initial direction

of travel of two spatially remote and physically unconnected spaces. Again, the core hypothesis of

this paper is that the mere existence of a sign certainly cannot make the target location appear to be

any further away compared to its actual 'accessibility-distance' and certainly can not cause it to appear

any closer than if it were little more than a single change of direction away, must still hold true.

Observe also that, in this case, the sign-as-link is one way (it is a directed graph) insomuch as a sign

may indicate the presence of a destination from an origin, but once that destination has been reached

the same sign cannot be re-utilised to return to the origin (although, in rare situations, a second sign

might serve this purpose). The effect of signage is as if a building has been artfully constructed using

numerous one-way mirrors, providing brief glimpses to spatially remote locations. The layered-graph,

as a description of a building's signage system, could also be used to form simple experiments. If

pedestrian, mean flow-rates at regular 'gates' within a building could be observed both with and

without the effect of signage, then it might be possible to calculate the !-factor value which is neces-

sary to calibrate the signage-link model. Clearly it is simpler to alter a buildings' signage (to someextent) than it would be to modify the inter-visibility of spaces within a building and so form a viable

empirical test of the layered-graph representation.

Layered-graph and intelligibility

It has become apparent, that one effect of signage is to reduce the overall segregation (or raise the

mean integration) of a complex building. Another effect that might be anticipated of a layered-graph

representing signage-links is that it might raise the apparent intelligibility of a sufficiently complex

building (since the intelligibility of small systems will always be high, this effect must be confined to

systems in excess of approximately fifty spaces). This hypothesis could be tested via the basic obser-

vation that the intelligibility of the layered-graph of a well signed building should be reasonably

expected to be higher than that of the accessibility-only graph. This leads to one theoretical problem:

since the calculation of intelligibility depends upon a correlate of the measure of a node's connectiv-

ity, what precisely is connectivity in the context of a layered-graph? Each and every node has two, or

more, edge sets leading from it so the degree of a node (its connectivity), instead of a single integer

value, is transformed into an ordered list of degrees drawn from each edge set. That is to say, for each

layer there is a different connectivity/degree. It would be reasonable to assume that one definition of

connectivity, in the context of a layered-graph, would be to apply the !-factor to the degree/connec-

tivity value. So for a node, N, with two Edge sets, EA and EV,

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K(N) = k(N,EA) * ! !

! ! ! + (1-!!!!!) * k(N,EV)

Where K(N) is the degree/connectivity of node, N, and k(N, E) is the degree of edge set E for

node N, given this equation for K, an approximation of intelligibility can be duly created.

3. Conclusions

This paper has introduced the concept of a layered-graph and shown how it can be used in space

syntax to represent a wide range of real-world situations including a solution to the visibility-accessi-

bly problem and, potentially, signage in buildings. This layered-graph approach appears to be a fur-

ther generalisation of the current space syntax representations. For example, when the more general

case of accessibility being directly equivalent to visibility, then the layered-graph is reduced to the

simpler graph typical of space syntax methods. While this paper has not incorporated either the effect

of angular analyses or other graph-weightings, the concept of the layered-graph is not antithetical to

these representational methods. It is evident that the layered-graph approach can be used to represent

a number of different problematic cases found in real world buildings and even urban environments.

As such, it seems reasonable to warrant further research and testing in this area.

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Contact Details:

Nicholas Sheep Dalton [email protected]

The Departments of Mathematics and Statistics, and Computing,

The Open University,Walton Hall, Milton Keynes,Buckinghamshire.MK7 6AAUnited Kingdom

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