mathematical models for the determination of archaeological potential
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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 di 23 Mathematical models for the determination of archaeological potential
PISA
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OBJECTIVES
Predictive Map of Archaeological
Potential
Archaeological Map
Geomorphological Map
Mathematical model Open digital archaeological archive
Open Data
Cooperation
Transparency
Geology
Archaeology
Mathematics
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SAMPLE
AREA
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TIMELINE
07/2011
starting up
10/2011 data entry
04/2012
Archaeological Map
webgis
04/2013 Map of
Archaeological
Potential webgis
2 years project
July 2011- June 2013
Diachrony
Completeness
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DATA MODEL
•Urban data
•Historical
cartography data
•Geographical/
geomorphological
data
•Archaeological
data
PRIMARY DATA
•obtained data
SECONDARY DATA
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• Need to work with heterogeneous data;
• Need to standardize heterogeneous data
PROBLEMS
….. the archaeo-logical data model SOLUTIONS
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ARCHAEO LOGICAL
DATA MODEL
Context quantification
Sub-group
Phase
Preliminary
report
Archaeological
intervention
Archaeological Map
Map of Archaeological
Potential
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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.
Described by:
•Polygons
INTERVENTIONS
CONTEXT
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• represents the possibilities that a more or less significant
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
ARCHAEOLOGICAL
POTENTIAL
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• 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
PARAMETERS
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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
Mathematical models for the determination of archaeological potential
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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?
Mathematical models for the determination of archaeological potential
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MAP ALGEBRA
• Simple features are combined into rules such as
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
)()1()01( Asoilmksourcefromancedistslope
Mathematical models for the determination of archaeological potential
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REGRESSION BASED METHODS
• Linear regressions produce equations of the
following type:
- 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
,11 kk xbxbay
Mathematical models for the determination of archaeological potential
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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
Mathematical models for the determination of archaeological potential
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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
Mathematical models for the determination of archaeological potential
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PAGE RANK INTUITIVELY
A page that points to other pages distributes its
importance in equal parts to those pages
13
312
21
2/1
2/1
ww
www
ww
Mathematical models for the determination of archaeological potential
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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
Mathematical models for the determination of archaeological potential
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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
Mathematical models for the determination of archaeological potential
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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
Mathematical models for the determination of archaeological potential
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A SIMULATION
Page rank has the possibility of distributing
the importance of a cell to other cells
Mathematical models for the determination of archaeological potential
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• 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!
REFERENCES
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