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

3 di 23 Mathematical models for the determination of archaeological potential

OBJECTIVES

Predictive Map of Archaeological

Potential

Archaeological Map

Geomorphological Map

Mathematical model Open digital archaeological archive

Open Data

Cooperation

Transparency

Geology

Archaeology

Mathematics

4 di 23 Mathematical models for the determination of archaeological potential

SAMPLE

AREA

5 di 23 Mathematical models for the determination of archaeological potential

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

6 di 23 Mathematical models for the determination of archaeological potential

DATA MODEL

•Urban data

•Historical

cartography data

•Geographical/

geomorphological

data

•Archaeological

data

PRIMARY DATA

•obtained data

SECONDARY DATA

7 di 23 Mathematical models for the determination of archaeological potential

• Need to work with heterogeneous data;

• Need to standardize heterogeneous data

PROBLEMS

….. the archaeo-logical data model SOLUTIONS

8 di 23 Mathematical models for the determination of archaeological potential

ARCHAEO LOGICAL

DATA MODEL

Context quantification

Sub-group

Phase

Preliminary

report

Archaeological

intervention

Archaeological Map

Map of Archaeological

Potential

9 di 23 Mathematical models for the determination of archaeological potential

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

10 di 10 Mathematical models for the determination of archaeological potential

• 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

11 di 23 Mathematical models for the determination of archaeological potential

• 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

12 di 23

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

13 di 23

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

14 di 23

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

15 di 23

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

16 di 23

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

17 di 23

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

18 di 23

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

19 di 23

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

20 di 23

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

21 di 23

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

22 di 23

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

23 di 23 Mathematical models for the determination of archaeological potential

• 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