Network Geometry and Complexity

(28 pages, 11 figures)Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. More in general, higher-order networks can be cell-complexes formed by gluing convex polytopes along their faces. Interestingly, higher order networks have a natural geometric interpretation and therefore constitute a natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. This model, originally proposed for capturing the evolution of simplicial complexes, is here extended to cell-complexes formed by subsequently gluing different copies of an arbitrary regular polytope. We reveal the interplay between complexity and geometry of the higher order networks generated by the model by studying the emergent community structure and the degree distribution as a function of the regular polytope forming its building blocks. Additionally, we discuss the underlying hyperbolic nature of the emergent geometry and we relate the spectral dimension of the higher-order network to the dimension and nature of its building blocks

Development and analysis of the Soil Water Infiltration Global database.

In this paper, we present and analyze a novel global database of soil infiltration measurements, the Soil Water Infiltration Global (SWIG) database. In total, 5023 infiltration curves were collected across all continents in the SWIG database. These data were either provided and quality checked by the scientists who performed the experiments or they were digitized from published articles. Data from 54 different countries were included in the database with major contributions from Iran, China, and the USA. In addition to its extensive geographical coverage, the collected infiltration curves cover research from 1976 to late 2017. Basic information on measurement location and method, soil properties, and land use was gathered along with the infiltration data, making the database valuable for the development of pedotransfer functions (PTFs) for estimating soil hydraulic properties, for the evaluation of infiltration measurement methods, and for developing and validating infiltration models. Soil textural information (clay, silt, and sand content) is available for 3842 out of 5023 infiltration measurements (~76%) covering nearly all soil USDA textural classes except for the sandy clay and silt classes. Information on land use is available for 76% of the experimental sites with agricultural land use as the dominant type (~40%). We are convinced that the SWIG database will allow for a better parameterization of the infiltration process in land surface models and for testing infiltration models. All collected data and related soil characteristics are provided online in *.xlsx and *.csv formats for reference, and we add a disclaimer that the database is for public domain use only and can be copied freely by referencing it. Supplementary data are available at https://doi.org/10.1594/PANGAEA.885492 (Rahmati et al., 2018). Data quality assessment is strongly advised prior to any use of this database. Finally, we would like to encourage scientists to extend and update the SWIG database by uploading new data to it

Development and analysis of the Soil Water Infiltration Global database

In this paper, we present and analyze a novel global database of soil infiltration measurements, the Soil Water Infiltration Global (SWIG) database. In total, 5023 infiltration curves were collected across all continents in the SWIG database. These data were either provided and quality checked by the scientists who performed the experiments or they were digitized from published articles. Data from 54 different countries were included in the database with major contributions from Iran, China, and the USA. In addition to its extensive geographical coverage, the collected infiltration curves cover research from 1976 to late 2017. Basic information on measurement location and method, soil properties, and land use was gathered along with the infiltration data, making the database valuable for the development of pedotransfer functions (PTFs) for estimating soil hydraulic properties, for the evaluation of infiltration measurement methods, and for developing and validating infiltration models. Soil textural information (clay, silt, and sand content) is available for 3842 out of 5023 infiltration measurements ( ∼ 76%) covering nearly all soil USDA textural classes except for the sandy clay and silt classes. Information on land use is available for 76% of the experimental sites with agricultural land use as the dominant type ( ∼ 40%). We are convinced that the SWIG database will allow for a better parameterization of the infiltration process in land surface models and for testing infiltration models. All collected data and related soil characteristics are provided online in *.xlsx and *.csv formats for reference, and we add a disclaimer that the database is for public domain use only and can be copied freely by referencing it. Supplementary data are available at https://doi.org/10.1594/PANGAEA.885492 (Rahmati et al., 2018). Data quality assessment is strongly advised prior to any use of this database. Finally, we would like to encourage scientists to extend and update the SWIG database by uploading new data to it

Motion planning in spaces with small fundamental groups

We establish sharp upper bounds for the topological complexity TC(X) of motion planning algorithms in topological spaces X such that the fundamental group is "small", i.e. when π1(X) is cyclic of order ≤ 3 or has small cohomological dimension