Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times

Assessing forest availability for wood supply in Europe

The quantification of forests available for wood supply (FAWS) is essential for decision-making with regard to the maintenance and enhancement of forest resources and their contribution to the global carbon cycle. The provision of harmonized forest statistics is necessary for the development of forest associated policies and to support decision-making. Based on the National Forest Inventory (NFI) data from 13 European countries, we quantify and compare the areas and aboveground dry biomass (AGB) of FAWS and forest not available for wood supply (FNAWS) according to national and reference definitions by determining the restrictions and associated thresholds considered at country level to classify forests as FAWS or FNAWS. FAWS represent between 75 and 95 % of forest area and AGB for most of the countries in this study. Economic restrictions are the main factor limiting the availability of forests for wood supply, accounting for 67 % of the total FNAWS area and 56 % of the total FNAWS AGB, followed by environmental restrictions. Profitability, slope and accessibility as economic restrictions, and protected areas as environmental restrictions are the factors most frequently considered to distinguish between FAWS and FNAWS. With respect to the area of FNAWS associated with each type of restriction, an overlap among the restrictions of 13.7 % was identified. For most countries, the differences in the FNAWS areas and AGB estimates between national and reference definitions ranged from 0 to 5 %. These results highlight the applicability and reliability of a FAWS reference definition for most of the European countries studied, thereby facilitating a consistent approach to assess forests available for supply for the purpose of international reporting