Topological graph dimension

AbstractIn the invited chapter Discrete Spatial Models of the book Handbook of Spatial Logics, we have introduced the concept of dimension for graphs, which is inspired by Evako’s idea of dimension of graphs [A.V. Evako, R. Kopperman, Y.V. Mukhin, Dimensional properties of graphs and digital spaces, J. Math. Imaging Vision 6 (1996) 109–119]. Our definition is analogous to that of (small inductive) dimension in topology. Besides the expected properties of isomorphism-invariance and monotonicity with respect to subgraph inclusion, it has the following distinctive features: •Local aspect. That is, dimension at a vertex is basic, and the dimension of a graph is obtained as the sup over its vertices.•Dimension of a strong product G×H is dim(G)+dim(H) (for non-empty graphs G,H). In this paper we present a short account of the basic theory, with several new applications and results

Foreword

Digitalitzat per Artypla

06341 Abstracts Collection -- Computational Structures for Modelling Space, Time and Causality

From 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

04351 Summary -- Spatial Representation: Discrete vs. Continuous Computational Models

Topological notions and methods are used in various areas of the physical sciences and engineering, and therefore computer processing of topological data is important. Separate from this, but closely related, are computer science uses of topology: applications to programming language semantics and computing with exact real numbers are important examples. The seminar concentrated on an important approach, which is basic to all these applications, i.e. spatial representation

04351 Abstracts Collection -- Spatial Representation: Discrete vs. Continuous Computational Models

From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351 ``Spatial Representation: Discrete vs. Continuous Computational Models\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Maker Movements, Do-It-Yourself Cultures and Participatory Design: Implications for HCI Research

Falling costs and the wider availability of computational components, platforms and ecosystems have enabled the expansion of maker movements and DIY cultures. This can be considered as a form of democratization of technology systems design, in alignment with the aims of Participatory Design approaches. However, this landscape is constantly evolving, and long-term implications for the HCI community are far from clear. The organizers of this one-day workshop invite participants to present their case studies, experiences and perspectives on the topic with the goal of increasing understanding within this area of research. The outcomes of the workshop will include the articulation of future research directions with the purpose of informing a research agenda, as well as the establishment of new collaborations and networks

Predicting Postfire Sediment Yields of Small Steep Catchments Using Airborne Lidar Differencing

Predicting sediment yield from recently burned areas remains a challenge but is important for hazard and resource management as wildfire impacts increase. Here we use lidar-based monitoring of two fires in southern California, USA to study the movement of sediment during pre-rainfall periods and postfire periods of flooding and debris flows over multiple storm events. Using a data-driven approach, we examine the relative importance of terrain, vegetation, burn severity, and rainfall amounts through time on sediment yield. We show that incipient fire-activated dry sediment loading and pre-fire colluvium were rapidly flushed out by debris flows and floods but continued erosion occurred later in the season from soil erosion and, in ∼9% of catchments, from shallow landslides. Based on these observations, we develop random forest regression models to predict dry ravel and incipient runoff-driven sediment yield applicable to small steep headwater catchments in southern California

Are coastal habitats important nurseries? A meta-analysis

Nearshore‐structured habitats—including underwater grasses, mangroves, coral, and other biogenic reefs, marshes, and complex abiotic substrates—have long been postulated to function as important nurseries for juvenile fishes and invertebrates. Here, we review the evolution of the “nursery habitat hypothesis” and use \u3e11,000 comparisons from 160 peer‐reviewed studies to test whether and which structured habitats increase juvenile density, growth, and survival. In general, almost all structured habitats significantly enhanced juvenile density—and in some cases growth and survival—relative to unstructured habitats. Underwater grasses and mangroves also promoted juvenile density and growth beyond what was observed in other structured habitats. These conclusions were robust to variation among studies, although there were significant differences with latitude and among some phyla. Our results confirm the basic nursery function of certain structured habitats, which lends further support to their conservation, restoration, and management at a time when our coastal environments are becoming increasingly impacted. They also reveal a dearth of evidence from many other systems (e.g., kelp forests) and for responses other than density. Although recent studies have advocated for increasingly complex approaches to evaluating nurseries, we recommend a renewed emphasis on more straightforward assessments of juvenile growth, survival, reproduction, and recruitment