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- 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.

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- 1. Mathematical models for the determination ofarchaeological potentialNevio Dubbini*, Gabriele Gattiglia** * Department of Mathematics, University of Pisa**Department of Archaeological Sciences, University of Pisa
- 2. PISA Mathematical models for the determination of archaeological potential 2 di 23
- 3. OBJECTIVES Geology Archaeology Mathematics Predictive Map of Archaeological Potential Archaeological Map Geomorphological Map Mathematical model Open digital archaeological archive Open Data Cooperation Transparency Mathematical models for the determination of archaeological potential 3 di 23
- 4. SAMPLEAREA Mathematical models for the determination of archaeological potential 4 di 23
- 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 Mathematical models for the determination of archaeological potential 5 di 23
- 6. DATA MODELSECONDARY DATA•obtained dataPRIMARY DATA•Historicalcartography data•Archaeologicaldata•Urban data•Geographical/geomorphologicaldata Mathematical models for the determination of archaeological potential 6 di 23
- 7. PROBLEMS • Need to work with heterogeneous data; • Need to standardize heterogeneous dataSOLUTIONS ….. the archaeo-logical data model Mathematical models for the determination of archaeological potential 7 di 23
- 8. ARCHAEO LOGICALDATA MODEL Map of Archaeological Potential Archaeological Map Archaeological intervention Phase Preliminary report Sub-group Context quantification Mathematical models for the determination of archaeological potential 8 di 23
- 9. INTERVENTIONS Described by: •PolygonsCONTEXT 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. Mathematical models for the determination of archaeological potential 9 di 23
- 10. ARCHAEOLOGICAL • represents the possibilities that a more or less significantPOTENTIAL 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 Mathematical models for the determination of archaeological potential 10 di 10
- 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 Mathematical models for the determination of archaeological potential 11 di 23
- 12. WHY A MATHEMATICAL MODEL?• Mathematical models can be applied to otherurban centres in order to facilitate land usedecisions generality• Mathematical models help in predictions• Mathematics may have an impact onarchaeological practice and territorial planning Mathematical models for the determination of archaeological potential 12 di 23
- 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?Mathematical models for the determination of archaeological potential 13 di 23
- 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 isvery easy to implement• Drawbacks - provide on/off results - simply juxtapose a number of easy rules Mathematical models for the determination of archaeological potential 14 di 23
- 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 potentialMathematical models for the determination of archaeological potential 15 di 23
- 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 Mathematical models for the determination of archaeological potential 16 di 23
- 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 Mathematical models for the determination of archaeological potential 17 di 23
- 18. PAGE RANK INTUITIVELYA page that points to other pages distributes itsimportance in equal parts to those pages w1 w2 w2 1 / 2w1 w3 w 1 / 2 w 3 1 Mathematical models for the determination of archaeological potential 18 di 23
- 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 Mathematical models for the determination of archaeological potential 19 di 23
- 20. PAGE RANK FOR ARCHAEOLOGICAL POTENTIAL II• The matrix controlling the transfer of importance isconstructed on the basis of a categorization ofarchaeological finds• The categories characterise the geometry of thedistribution of importance• Geological information is used to excludecertain cells from the computation of potential Mathematical models for the determination of archaeological potential 20 di 23
- 21. A SIMULATIONN = 100 cells, “finds” in cells• 15, importance 3, gives importance 1/6 to cells3,4,5,6,7,8• 37, importance 1.5, gives importance1/8 to cells 45,47,49,51,53,55,57,59• 39, importance 1.7, gives importance 1/8 to cells46,48,50,52,54,56,58,61• 68, importance 2, gives importance1/5 to cells 13,14,15,16,25 Mathematical models for the determination of archaeological potential 21 di 23
- 22. A SIMULATION Page rank has the possibility of distributingthe importance of a cell to other cellsMathematical models for the determination of archaeological potential 22 di 23
- 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! Mathematical models for the determination of archaeological potential 23 di 23

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