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Theory and practice of cost functions
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... In Figure 2, two cost components are combined, the isotropic penalties are multiplied by slope costs. Alternative approaches for combining costs are published by Herzog (2013a;2014). In other LCP studies, different isotropic cost factors depending on the terrain (e.g. for walking on grassland, sand, or snow) might be more appropriate (De Gruchy et al. 2017;Groenhuijzen and Verhagen 2015;Herzog 2014;Rogers et al. 2015). ...
... The slope values can be computed directly from the DEM (Herzog 2013b). Slope is the most popular cost component in archaeological LCP publications (Herzog 2014), different cost functions are available (Herzog 2013a) for estimating the costs required for ascending (positive slope values) or descending gradients (negative slope values) in terms of time, the energy consumption, or some other figure. Some issues with DEMs and slope computations are discussed in Herzog (2013b). ...
... Most of the slope-dependent cost functions are anisotropic, i.e. the costs for descending a gentle gradient are less than that of climbing a gentle slope (Herzog 2013a). But in many situations paths are used in both directions. ...
Network research has recently been adopted as one of the tools of the trade in archaeology, used to study a wide range of topics: interactions between island communities, movements through urban spaces, visibility in past landscapes, material culture similarity, exchange, and much more. This Oxford Handbook is the first authoritative reference work for archaeological network research, featuring current topical trends and covering the archaeological application of network methods and theories. This is elaborately demonstrated through substantive topics and case studies drawn from a breadth of periods and cultures in world archaeology. It highlights and further develops the unique contributions made by archaeological research to network science, especially concerning the development of spatial and material culture network methods, and approaches to studying long-term network change. This is the go-to resource for students and scholars wishing to explore how network science can be applied in archaeology through an up-to-date overview of the field.
... A common method for explaining known past routes is the use of least-cost path (LCP) analysis (e.g. Fonte et al., 2017;Güimil-Fariña & Parcero-Oubiña, 2015;Herzog, 2013Herzog, , 2022Lewis, 2021). LCP analysis is predicated on the assumption that humans-whether modern or past-use all available information to economise their behaviour when traversing the landscape (Surface-Evans & White, 2012;Zipf, 1949). ...
... LCP analysis is predicated on the assumption that humans-whether modern or past-use all available information to economise their behaviour when traversing the landscape (Surface-Evans & White, 2012;Zipf, 1949). In this approach, a slope-based cost function that expresses the cost of traversing a specific slope gradient when walking, with cost often measured in timetaken or energy expended, is used to calculate an LCP between a specified origin and destination (Herzog, 2013). When the path of the calculated LCP and the tobe-explained known past route is deemed to be sufficiently similar, 1 it is suggested that the resulting LCP, and the hypothesis that its underlying cost function aims to represent, reflects the decision-making processes used by past people when creating the known past route. ...
... Whilst the comparison of multiple LCPs derived using different slope-based cost functions estimating the cost of movement when walking has been used to assess which single cost function, and by extension hypothesis, best explains the known past route (e.g. Güimil-Fariña & Parcero-Oubiña, 2015;Herzog, 2013Herzog, , 2020Herzog, , 2022; see also Field et al., 2019 for a reconstructive example; but see Campbell et al., 2019 who argues against the notion of a single maximal cost function), this approach misrepresents what cost functions are, their relationship to the hypotheses that they aim to represent, and their role in explanation. For example, Güimil-Fariña and Parcero-Oubiña (2015) compared four cost functions, despite three of these aiming 1 Similarity here is subjectively chosen by the analyst. ...
Explaining material traces of movement as proxies for past movement is fundamental for understanding the processes behind why people in the past traversed the landscape in the way that they did. For this, least-cost path analysis and the use of slope-based cost functions for estimating the cost of movement when walking have become commonplace. Despite their prevalence, current approaches misrepresent what these cost functions are, their relationship to the hypotheses that they aim to represent, and their role in explanation. As a result, least-cost paths calculated using single cost functions are liable to spurious results with limited power for explaining known past routes, and by extension the decision-making processes of past people. Using the ideas of multiple model idealisation and robustness analysis, and applied via a tactical simulation, this study demonstrates that similar least-cost paths can be produced from slope-based cost functions representing both the same hypothesis and different hypotheses, suggesting that least-cost path results are robust but underdetermined under the tested environmental settings. The results from this tactical simulation are applied for the explanation of a Roman road in Sardinia. Using probabilistic least-cost paths as an approach for incorporating multiple cost functions representing the same hypothesis and error in the digital elevation model, it is shown that both model outcomes representing the minimisation of time and energy are unable to explain the placement of the Roman road. Rather, it is suggested that the Roman road was influenced by pre-existing routes and settlements.
In this chapter, the authors introduce the theme of computational/digital methods in the realm of sensory archaeologies. To this purpose, the concept of sensoriality and its relevance for the archaeological discourse is rediscussed. Key concepts such as perception of material culture help us in better defining possible modalities through which archaeologists can benefit from the use of formal methods to answer questions related to the relationship between ancient space and its original inhabitants. In this context, recent advances in the field of computational methods can now provide a significant contribution to the development of ‘digitally mediated’ sensory archaeologies.
Network research has recently been adopted as one of the tools of the trade in archaeology, used to study a wide range of topics: interactions between island communities, movements through urban spaces, visibility in past landscapes, material culture similarity, exchange, and much more. This Oxford Handbook is the first authoritative reference work for archaeological network research, featuring current topical trends and covering the archaeological application of network methods and theories. This is elaborately demonstrated through substantive topics and case studies drawn from a breadth of periods and cultures in world archaeology. It highlights and further develops the unique contributions made by archaeological research to network science, especially concerning the development of spatial and material culture network methods, and approaches to studying long-term network change. This is the go-to resource for students and scholars wishing to explore how network science can be applied in archaeology through an up-to-date overview of the field.
This paper investigates how the spatial resolution of slope data affects the modelling of recreational trails in mountainous areas. It measures the impact of spatial resolution on a) the estimation of cost functions that link walking speeds and slope, and b) the modelling of moving times and mapping of routes using these functions. Cost functions that build on a mountain hike GPS record and slope data derived from a Digital Elevation Model (DEM) at varying resolutions are estimated and their ability to predict accurate moving times is evaluated. The cost functions are supplemented with recently published cost functions to map the quickest routes between the hike start and end points with least-cost-path analyses. The results indicate that spatial resolution has a critical influence in the modelling: the similarity between routes modelled at a same spatial resolution with distinct cost functions considerably surpasses that of routes simulated at varying resolutions with a same cost function. Furthermore, employing finer resolutions enhances the similarity between routes mapped with different cost functions, while also improving the accuracy of predicted moving times. These findings provide evidence that DEM resolution should receive prime attention in the modelling of trails with slope-dependent cost functions.
The built landscape of Nuragic Sardinia is an exceptional case for geostatistical analysis, allowing for a discussion of long-held assumptions and ideas. The function of nuraghi (ca. 1700–1100 BCE), the most prominent settled monument of the Sardinian Bronze Age, has been addressed via a multiplicity of landscape approaches, mainly relying on intuitive assessments of their spatial properties: nuraghi were assumed as means of territorial control. The series of nuraghi crowning the mesa plateau named Giara of Gesturi (South-Central Sardinia) provides a significant case for the study of their relations with visibility and movement. Context-oriented GIS models based on viewsheds and least-cost paths have been devised as targeted tools. The results show a certain correlation between nuraghi and potential movement on the slopes, thanks to the selection of plateau morphologies such as outward crests. Anyway, nuraghi do not stand exactly at the most accessible points of the plateau. Nuraghi offered ample visual control, especially at large distances, but not specifically over the closest accessible ways. This suggests that the function of nuraghi is somehow connected to defense and visibility, but it is not explained directly by local territorial control: a role as landmarks and multifaceted monuments has likely to be envisioned.
This paper describes the contribution of path modelling to the ancient settlement pattern study over the long term. The path modelling methodology is a stimulating tool, which is complementary to the hierarchical approaches in the landscape archaeology since it contributes to the understanding of the spatial relation between archaeological sites. The existing methodology was enhanced by enlarging the set of path reconstitution parameters (visibility) and by modelling in two scales. The proposed model is based on parameters derived merely from the relief because its changes should be insignificant even over a long period time.
Societies exchange knowledge, ideas and merchandise throughout their territories. Topography plays a fundamental role in the trajectory of such movement s while helps explaining the distribution of human constructions. Standard GIS functions have been employed widely to simulate communication routes between settlements, but the straight application of published least cost route models proved inadequate for Mediterranean alluvial plain areas. The objective of this study is the production of a new model, using topographic and hydrologic factors as variables from which it would be possible to simulate a route , and test it against known Roman itineraries. The s elected Roman stretches are Girona - Coll de Pannisars and Tarrago na - Montblanc. The new model shows the need to consider each case individually but also stresses the hydrologic facto r, expressed in seasonal floods, as being of prime importance in th e creation and development of Roman roads in Mediterranean alluvial plains.
GIS: A Computing Perspective, Second Edition, provides a full, up-to-date overview of GIS, both Geographic Information Systems and the study of Geographic Information Science. Analyzing the subject from a computing perspective, the second edition explores conceptual and formal models needed to understand spatial information, and examines the representations and data structures needed to support adequate system performance. This volume also covers the special-purpose interfaces and architectures required to interact with and share spatial information, and explains the importance of uncertainty and time. The material on GIS architectures and interfaces as well as spatiotemporal information systems is almost entirely new.The second edition contains substantial new information, and has been completely reformatted to improve accessibility. Changes include:
* A new chapter on spatial uncertainty* Complete revisions of the bibliography, index, and supporting diagrams* Supplemental material is offset at the top of the page, as are references and links for further study* Definitions of new terms are in the margins of pages where they appear, with corresponding entries in the index
Book description:
Geographical Information Systems has moved from the domain of the computer specialist into the wider archaeological community, providing it with an exciting new research method. This clearly written but rigorous book provides a comprehensive guide to that use. Topics covered include: the theoretical context and the basics of GIS; data acquisition including database design; interpolation of elevation models; exploratory data analysis including spatial queries; statistical spatial analysis; map algebra; spatial operations including the calculation of slope and aspect, filtering and erosion modeling; methods for analysing regions; visibility analysis; network analysis including hydrological modeling; the production of high quality output for paper and electronic publication; and the use and production of metadata. Offering an extensive range of archaeological examples, it is an invaluable source of practical information for all archaeologists, whether engaged in cultural resource management or academic research. This is essential reading for both the novice and the advanced user.
1. The metabolic cost and the mechanical work at different speeds during uphill, level and downhill walking have been measured in four subjects. 2. The mechanical work has been partitioned into the internal work (W(int)), due to the speed changes of body segment with respect to the body centre of mass (BCM), and the external work (W(ext)), related to the position and speed changes of the BCM in the environment. 3. W(ext) has been further divided into a positive part W+ext) and a negative one (W-(ext)), associated with the energy increases and decreases, respectively, over the stride period. 4. For all constant speeds the most economical gradient has been found to be -10.2% (+/- 0.8 S.D.). 5. At each gradient there is a unique W+ext/W-ext ratio (= 1 in level walking), regardless of speed, with a tendency for W-ext and W+ext to vanish above +15% and below -15% gradient, respectively. 6. W(int) is constant at each speed regardless of gradient. This is partly explained by an only slight decrease in stride frequency at increasing gradient. W(int) constancy implies that it has no role in determining the optimum gradient. 7. A linear multiple regression relating W+ext and W-ext to the metabolic cost at different gradients showed that negative (eff-) and positive (eff+) efficiencies decrease with increasing speed (from 0.912 to 0.726, and from 0.182 to 0.146, respectively). The eff-/eff+ ratio, however, remains rather constant (4.995 +/- 0.125 S.D.). 8. We conclude that the measured W(ext), the W+ext/W-ext partitioning and eff-/eff+ ratio, i.e. the different efficiency of the muscles used as force and brake generators, can explain the metabolic optimum gradient at about -10%.
By combining the experiment results of R. Margaria (Atti Accad. Naz. Lincei Memorie 7: 299-368, 1938), regarding the metabolic cost of gradient locomotion, together with recent insights on gait biomechanics, a prediction about the most economical gradient of mountain paths (approximately 25%) is obtained and interpreted. The pendulum-like mechanism of walking produces a waste of mechanical work against gravity within the gradient range of up to 15% (the overall efficiency is dominated by the low transmission efficiency), whereas for steeper values only the muscular efficiency is responsible for the (slight) metabolic change (per meter of vertical displacement) with respect to gradient. The speeds at the optimum gradient turned out to be approximately 0.65 m/s (+0.16 m/s vertical) and 1.50 m/s (-0.36 m/s vertical), for uphill and downhill walking, respectively, and the ascensional energy expenditure was 0.4 and 2.0 ml O2.kg body mass-1.vertical m-1 climbed or descended. When the metabolic power becomes a burden, as in high-altitude mountaineering, the optimum gradient should be reduced. A sample of real mountain path gradients, experimentally measured, mimics the obtained predictions.
The costs of walking (Cw) and running (Cr) were measured on 10 runners on a treadmill inclined between -0.45 to +0.45 at different speeds. The minimum Cw was 1.64 +/- 0.50 J. kg(-1). m(-1) at a 1.0 +/- 0.3 m/s speed on the level. It increased on positive slopes, attained 17.33 +/- 1.11 J. kg(-1). m(-1) at +0.45, and was reduced to 0.81 +/- 0.37 J. kg(-1). m(-1) at -0.10. At steeper slopes, it increased to reach 3.46 +/- 0.95 J. kg(-1). m(-1) at -0.45. Cr was 3.40 +/- 0.24 J. kg(-1). m(-1) on the level, independent of speed. It increased on positive slopes, attained 18.93 +/- 1.74 J. kg(-1). m(-1) at +0.45, and was reduced to 1.73 +/- 0.36 J. kg(-1). m(-1) at -0.20. At steeper slopes, it increased to reach 3.92 +/- 0.81 J. kg(-1). m(-1) at -0.45. The mechanical efficiencies of walking and running above +0.15 and below -0.15 attained those of concentric and eccentric muscular contraction, respectively. The optimum gradients for mountain paths approximated 0.20-0.30 for both gaits. Downhill, Cr was some 40% lower than reported in the literature for sedentary subjects. The estimated maximum running speeds on positive gradients corresponded to those adopted in uphill races; on negative gradients they were well above those attained in downhill competitions.