4,227 research outputs found
Navigation on a Poisson point process
On a locally finite point set, a navigation defines a path through the point
set from one point to another. The set of paths leading to a given point
defines a tree known as the navigation tree. In this article, we analyze the
properties of the navigation tree when the point set is a Poisson point process
on . We examine the local weak convergence of the navigation
tree, the asymptotic average of a functional along a path, the shape of the
navigation tree and its topological ends. We illustrate our work in the
small-world graphs where new results are established.Comment: Published in at http://dx.doi.org/10.1214/07-AAP472 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Processes on Unimodular Random Networks
We investigate unimodular random networks. Our motivations include their
characterization via reversibility of an associated random walk and their
similarities to unimodular quasi-transitive graphs. We extend various theorems
concerning random walks, percolation, spanning forests, and amenability from
the known context of unimodular quasi-transitive graphs to the more general
context of unimodular random networks. We give properties of a trace associated
to unimodular random networks with applications to stochastic comparison of
continuous-time random walk.Comment: 66 pages; 3rd version corrects formula (4.4) -- the published version
is incorrect --, as well as a minor error in the proof of Proposition 4.10;
4th version corrects proof of Proposition 7.1; 5th version corrects proof of
Theorem 5.1; 6th version makes a few more minor correction
Ecosystem properties and principles of living systems as foundation for sustainable agriculture – Critical reviews of environmental assessment tools, key findings and questions from a course process
With increasing demands on limited resources worldwide, there is a growing interest in sustainable patterns of utilisation and production. Ecological agriculture is a response to these concerns.
To assess progress and compliance, standard and comprehensive measures of resource requirements, impacts and agro-ecological health are needed. Assessment tools should also be rapid, standardized, userfriendly, meaningful to public policy and applicable to management. Fully considering these requirements confounds the development of integrated methods.
Currently, there are many methodologies for monitoring performance, each with its own foundations, assumptions, goals, and outcomes, dependent upon agency agenda or academic orientation. Clearly, a concept of sustainability must address biophysical, ecological, economic, and sociocultural foundations.
Assessment indicators and criteria, however, are generally limited, lacking integration, and at times in conflict with one another. A result is that certification criteria, indicators, and assessment methods are not based on a consistent, underlying conceptual framework and often lack a management focus.
Ecosystem properties and principles of living systems, including self-organisation, renewal, embeddedness, emergence and commensurate response provide foundation for sustainability assessments and may be appropriate focal points for critical thinking in an evaluation of current methods and standards. A systems framework may also help facilitate a comprehensive approach and promote a context for meaningful discourse. Without holistic accounts, sustainable progress remains an illdefined concept and an elusive goal.
Our intent, in the work with this report, was to use systems ecology as a pedagogic basis for learning and discussion to:
- Articulate general and common characteristics of living systems.
- Identify principles, properties and patterns inherent in natural ecosystems.
- Use these findings as foci in a dialogue about attributes of sustainability to:
a. develop a model for communicating scientific rationale.
b. critically evaluate environmental assessment tools for application in land-use.
c. propose appropriate criteria for a comprehensive assessment and expanded definition of ecological land use
- …