The Department of Archaeological Science of the University of Pisa is undertaking the MAPPA project, which is a research project in which archaeologists, geologists, mathematicians will study predictive modelling tools applied to the archaeological potential of an urban area. The project main objectives are: - Enhancing the development in archaeological research by fostering collaboration among different sectors and by developing a common langua¬ge. - Creating a model that may be applied to all urban centres in order to facilitate land use decisions. Within this con¬text, we propose predictive mathe¬matical models, which will have an impact on archaeological he-ritage protection, territorial planning and historical knowledge. - Making raw data from archaeological in¬vestigations available. The project proposes that after acknowledging au¬thorship of the data, the latter shall be made publicly available and easy to consult. Based on the discussions between the mathematical, archaeological and geological teams, an analogy arose between the criteria used for attri¬buting archaeological potential and those used for assigning importance to web pages by search en¬gines. Indeed, the key issue of the archaeological interpretation process, from an abstract viewpoint, is the identification of the relations that exist among finds, both in spatial terms and in functional terms. In other words, the presen¬ce of a particular find near another that has already been discovered could strengthen or weaken the pro¬bability that they will form a more complex structu¬re, and so strengthen or weaken the archaeological potential of the area itself. This is exactly the crite¬ria upon which page ranking algorithms are based, whereby each web page attributes importance to the web pages it points to (via a link) and, in turn, recei¬ves importance from the web pages it receives a link from. In order to adapt a page rank model to the determi¬nation of archaeological potential, variants need to be created: - A three-dimensional grid will model the subsurface of the urban area. A single cell plays the role of a web page, and its importance will be the archaeological potential; - The information available for a cell will be used in a relative manner to build the elements of the matrix that, like in page rank models, assigns the transfer of importance among cells, and in an abso¬lute manner, providing the absolute value of the archaeological potential; - The matrix controlling the transfer of importance will be constructed on the basis of categories used for classifying the archaeological finds. The categories characterise the geometry of the distribution of importance; - Geological information will be used in a binary manner, allowing to exclude certain cells from the calculation of archaeological potential.

1. Mathematical models for the determination of
archaeological potential
Nevio Dubbini*, Gabriele Gattiglia**
* Department of Mathematics, University of Pisa
**Department of Archaeological Sciences, University of Pisa

2. PISA
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3. OBJECTIVES
Geology
Archaeology
Mathematics
Predictive Map of Archaeological
Potential
Archaeological Map
Geomorphological Map
Mathematical model
Open digital archaeological archive
Open Data
Cooperation
Transparency
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4. SAMPLE
AREA
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5. TIMELINE 2 years project
July 2011- June 2013
10/2011 data entry
07/2011
04/2012 04/2013 Map of
starting up
Archaeological Map Archaeological
webgis Potential webgis
Diachrony
Completeness
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6. DATA MODEL
SECONDARY DATA
•obtained data
PRIMARY DATA
•Historical
cartography data
•Archaeological
data
•Urban data
•Geographical/
geomorphological
data
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7. PROBLEMS • Need to work with heterogeneous data;
• Need to standardize heterogeneous data
SOLUTIONS ….. the archaeo-logical data model
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8. ARCHAEO LOGICAL
DATA MODEL
Map of Archaeological
Potential
Archaeological Map
Archaeological
intervention
Phase
Preliminary
report
Sub-group
Context quantification
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9. INTERVENTIONS Described by:
•Polygons
CONTEXT stratigraphic data are described
by:
•Polygons for deposit and cut
•lines are used to denote the
characteristics of contexts
Each feature is drawn according
to its exact location and
dimension.
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10. ARCHAEOLOGICAL • represents the possibilities that a more or less significant
POTENTIAL archaeological stratification is preserved
• is calculated by analyzing and studying a series of historical,
archaeological and paleo-environmental data retrieved from
various sources, with a degree of approximation that may
vary according to the quantity and quality of the data
provided and their spatial and contextual relationships
• is a factor independent on any other following intervention
that is carried out, which must be regarded as a contingent
risk factor
• the map of archaeological potential is a predictive model
and, as such, is knowingly created as a decision-making tool
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11. PARAMETERS
• type of settlement
• density of settlement
• multi-layering of deposits
• removable or non-removable nature of
archaeological deposit
• degree of preservation of the deposit
• depth of the deposit
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12. WHY A MATHEMATICAL MODEL?
• Mathematical models can be applied to other
urban centres in order to facilitate land use
decisions  generality
• Mathematical models help in predictions
• Mathematics may have an impact on
archaeological practice and territorial planning
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13. MODELS IN LITERATURE
• Map Algebra (Cumming 1997)
A predictive model for generating a decision
rule to predict archaeological potential
• Regression (Wheatley, 2002)
For questions that map-algebra approach
cannot answer, like
- How can a predictor influence
the model?
- How can continuous quantities
be predicted?
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14. MAP ALGEBRA
• Simple features are combined into rules such as
(slope  10)  (distance from source  1 k m)  (soil  A)
to predict the presence of archaeological sites. It is
very easy to implement
• Drawbacks
- provide on/off results
- simply juxtapose a number of
easy rules
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15. REGRESSION BASED METHODS
• Linear regressions produce equations of the
following type:
y  a  b1 x1    bk xk ,
- y is the variable to be predicted (e.g. the
archaeological potential)
- x ’s are the inputs
• Drawback: does not take into account the
great complexity in determining archaeological
potential
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16. HOW TO CONSTRUCT A MODEL?
From an abstract viewpoint
• A key issue is the identification of the relations
among finds
• Relations both in spatial terms and in
functional terms
• These relations could strengthen or weaken the
probability of the presence of a more complex
structure  strengthen or weaken the
archaeological potential of the area itself
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17. PAGE RANK MODELS
• Analogy between the criteria for attributing
archaeological potential and criteria for
assigning importance to web pages by search
engines
• In page rank algorithms web pages
- attribute importance to
the web pages they point to (via a link)
- receive importance from the web
pages they receive a link from
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18. PAGE RANK INTUITIVELY
A page that points to other pages distributes its
importance in equal parts to those pages
w1  w2

w2  1 / 2w1  w3
w  1 / 2 w
 3 1
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19. PAGE RANK FOR
ARCHAEOLOGICAL POTENTIAL I
• A 3-d grid models the subsurface. A single cell
plays the role of a web page
• The information of each cell is used in a
- relative manner, to form the
matrix that assigns the transfer
of importance among cells
- absolute manner, providing the
value of the archaeological
potential
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20. PAGE RANK FOR
ARCHAEOLOGICAL POTENTIAL II
• The matrix controlling the transfer of importance is
constructed on the basis of a categorization of
archaeological finds
• The categories characterise the geometry of the
distribution of importance
• Geological information is used to exclude
certain cells from the computation of potential
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21. A SIMULATION
N = 100 cells, “finds” in cells
• 15, importance 3, gives importance 1/6 to cells
3,4,5,6,7,8
• 37, importance 1.5, gives importance
1/8 to cells 45,47,49,51,53,55,57,59
• 39, importance 1.7, gives importance 1/8 to cells
46,48,50,52,54,56,58,61
• 68, importance 2, gives importance
1/5 to cells 13,14,15,16,25
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22. A SIMULATION
 Page rank has the possibility of distributing
the importance of a cell to other cells
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23. REFERENCES • Anichini F., Bini M., Fabiani F., Gattiglia G., Giacomelli S.,
Gualandi M.L., Pappalardo M., Sarti G. 2011, Definition of the
parameters of the Archaeological Potential of an urban area, in
MapPapers, I, pp.47-49
• Bini D., Dubbini N., Steffè S. 2011,Mathematical models for the
determination of archaeological potential, in MapPapers, I, pp.77-
85
follow us
www.mappaproject.org
@mappaproject
nevio.dubbini@for.unipi.it
g.gattiglia@arch.unipi.it
@g_gattiglia
THANK YOU!
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