This paper explores and critically discusses a new concept with relevance to outdoor and environmental education: Ecological Restoration Education (ERE). The background of ERE is a recently launched ...project by the Swedish Anglers Association (SAA) called ‘Skolbäcken’ with an aim to teach children about fish and fish habitats, and how to protect and conserve both, through practical restoration activities. The project is a reaction to an awakening concern about children’s reduced contact with and understanding of nature, both in the Scandinavian countries and elsewhere in the world. With a point of departure in this concern and project Skolbäcken, the paper explores the idea and practice of ERE, drawing from its conceptual roots; ‘ecological restoration’ and ‘outdoor education’. Results show a concept that is both timely and relevant as it not only emphasizes the critique of the children-nature disconnect, but also contributes with strategies to meet the critique with solutions that are appreciated both by the children and their teachers. However, there are also important challenges, including concerns about normative education and the ‘projectification’ of ERE and how these factors may influence the short or long term success and potential continuation of ERE as a learning strategy in schools. Future needs in terms of further grounding of ERE are also discussed.
Wood pastures are some of the most species-rich environments found in Europe and therefore essential habitats for biodiversity conservation. Society also puts faith in multiple values of trees, ...ranging from climate change mitigation to socio-cultural traditions. Therefore, the seemingly arbitrary tree density limit for pasture environments imposed by the EU through its Common Agricultural Policy (CAP) threatened both biological and societal values. In this study on farmers' perspectives, we target the effects of the CAP tree density limit on management of wood pastures in a low-intensively managed agricultural landscape of southern Sweden. The case of simplifying nature by using simple number limitations was used as an entry point in semi-structured, open-ended, interviews with farmers and officials about their view on trees and pasture management in relation to policy directives. The interviews showed that the policy incentive shifted the management focus from grazing quality to the number of trees and that farmers are willing to cut in order to get subsidies and timber revenues, however not unreflectingly. Farmers had high knowledge about the wide ranging social, cultural and natural values of trees, and are often themselves as good regulators of tree management as policies intend to be. Our study reveals many difficulties in managing the complex relations within landscapes with simplified legal measures, opening up for further discussion about improving policy instruments to preserve both social and biological values of wood pastures. However, although the tree density limit has been criticised on many points related to biodiversity conservation, this study shows that other values linked to pasture trees, e.g. the aesthetic values and their importance as shelter for grazing animals, could be an argument to actually keep the focus on trees as indicators of pasture management quality. We suggest that trees in general and wood-pastures in particular therefore are good starting points, or boundary-objects, for collaboration between production and conservation interests of farming and environmental management.
•Wood-pastures are trapped in the in the dichotomy between agriculture and forestry.•Sensory experiences are important to consider within agri-environmental management.•Farmers have knowledge about a wide range of values associated with pasture trees.•Farmers highlight aesthetic values of trees and their role for grazing animals.•Wood-pastures are good starting points for stakeholder collaboration.
Inexpensive numerical methods are key to enabling simulations of systems of a large number of particles of different shapes in Stokes flow and several approximate methods have been introduced for ...this purpose. We study the accuracy of the multiblob method for solving the Stokes mobility problem in free space, where the 3D geometry of a particle surface is discretised with spherical blobs and the pair-wise interaction between blobs is described by the RPY-tensor. The paper aims to investigate and improve on the magnitude of the error in the solution velocities of the Stokes mobility problem using a combination of two different techniques: an optimally chosen grid of blobs and a pair-correction inspired by Stokesian dynamics. Different optimisation strategies to determine a grid with a given number of blobs are presented with the aim of matching the hydrodynamic response of a single accurately described ideal particle, alone in the fluid. It is essential to obtain small errors in this self-interaction, as they determine the basic error level in a system of well-separated particles. With an optimised grid, reasonable accuracy can be obtained even with coarse blob-resolutions of the particle surfaces. The error in the self-interaction is however sensitive to the exact choice of grid parameters and simply hand-picking a suitable geometry of blobs can lead to errors several orders of magnitude larger in size. The pair-correction is local and cheap to apply, and reduces the error for moderately separated particles and particles in close proximity. Two different types of geometries are considered: spheres and axisymmetric rods with smooth caps. The error in solutions to mobility problems is quantified for particles of varying inter-particle distances for systems containing a few particles, comparing to an accurate solution based on a second kind BIE-formulation where the quadrature error is controlled by employing quadrature by expansion (QBX).
•Rigid rods and spheres are studied in Stokes flow in 3D free space.•The accuracy of the multiblob method is improved at no extra cost.•An optimal grid of blobs matches the hydrodynamic interaction of a model particle.•A self-interaction error dominant in the far-field is reduced with the optimal grid.•Pair-corrections of Stokesian dynamics type reduce errors in near-field.
The convergence of reachable sets for nonconvex differential inclusions is considered. When the right-hand side in the differential inclusion is a compact-valued, Lipschitz continuous set-valued ...function it is shown that the convergence in Hausdorff distance of reachable sets for a forward Euler discretization is linear in the time step.
Abstract
Estimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $\bar z_{\ell +1}=\bar z_\ell + \textrm {Re}\sum _{k=1}^K\bar b_{\ell ...k}\,e^{\textrm {i}\omega _{\ell k}\bar z_\ell }+ \textrm {Re}\sum _{k=1}^K\bar c_{\ell k}\,e^{\textrm {i}\omega ^{\prime}_{\ell k}\cdot x}$. An optimal distribution for the frequencies $(\omega _{\ell k},\omega ^{\prime}_{\ell k})$ of the random Fourier features $e^{\textrm {i}\omega _{\ell k}\bar z_\ell }$ and $e^{\textrm {i}\omega ^{\prime}_{\ell k}\cdot x}$ is derived. This derivation is based on the corresponding generalization error for the approximation of the function values $f(x)$. The generalization error turns out to be smaller than the estimate ${\|\hat f\|^2_{L^1({\mathbb {R}}^d)}}/{(KL)}$ of the generalization error for random Fourier features, with one hidden layer and the same total number of nodes $KL$, in the case of the $L^\infty $-norm of $f$ is much less than the $L^1$-norm of its Fourier transform $\hat f$. This understanding of an optimal distribution for random features is used to construct a new training method for a deep residual network. Promising performance of the proposed new algorithm is demonstrated in computational experiments.
•We review key issues regarding digital approaches to UGI planning and management.•We summarize the risks or opportunities of automated UGIs.•We develop an assessment framework of the implications of ...automated UGIs.•Risks and opportunities of automated UGIs are not fixed but are dynamic.•Further research is needed from a social, ecological, technological approach.
Contemporary society is increasingly impacted by automation; however, few studies have considered the potential consequences of automation on ecosystems and their management (hereafter the automation of urban green infrastructure or UGI). This Perspective Essay takes up this discussion by asking how a digital approach to UGI planning and management mediates the configuration and development of UGI and to whose benefit? This is done through a review of key issues and trends in digital approaches to UGI planning and management. We first conceptualize automation from a social, ecological, and technological interactions perspective and use this lens to present an overview of the risks and opportunities of UGI automation with respect to selected case studies. Results of this analysis are used to develop a conceptual framework for the assessment of the material and governance implications of automated UGIs. We find that, within any given perspective, the automation of UGI entails a complex dialectic between efficiency, human agency and empowerment. Further, risks and opportunities associated with UGI automation are not fixed but are dynamic properties of changing contextual tensions concerning power, actors, rules of the game and discourse at multiple scales. We conclude the paper by outlining a research agenda on how to consider different digital advances within a social-ecological-technological approach.
Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature the
ab initio
molecular dynamics potential energy is based on the ground ...state electron eigenvalue problem and the accuracy has been proven to be
O
(
M
-1
), provided the first electron eigenvalue gap is sufficiently large compared to the given temperature and
M
is the ratio of nuclei and electron masses. For higher temperature eigenvalues corresponding to excited electron states are required to obtain
O
(
M
-1
) accuracy and the derivations assume that all electron eigenvalues are separated, which for instance excludes conical intersections. This work studies a mean-field molecular dynamics approximation where the mean-field Hamiltonian for the nuclei is the partial trace
h
:=
Tr
(
He
−
βH
)/
Tr
(e
−
βH
) with respect to the electron degrees of freedom and
H
is the Weyl symbol corresponding to a quantum many body Hamiltonian ̂
H
. It is proved that the mean-field molecular dynamics approximates canonical quantum correlation observables with accuracy
O
(
M
-1
+
tϵ
2
), for correlation time
t
where
ϵ
2
is related to the variance of mean value approximation
h
. Furthermore, the proof derives a precise asymptotic representation of the Weyl symbol of the Gibbs density operator using a path integral formulation. Numerical experiments on a model problem with one nuclei and two electron states show that the mean-field dynamics has similar or better accuracy than standard molecular dynamics based on the ground state electron eigenvalue.
It is known that ab initio molecular dynamics based on the electron ground-state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low ...compared to the first electron eigenvalue gap. This work proves that a certain weighted average of the different ab initio dynamics, corresponding to each electron eigenvalue, approximates quantum observables for any temperature. The proof uses the semiclassical Weyl law to show that canonical quantum observables of nuclei–electron systems, based on matrix-valued Hamiltonian symbols, can be approximated by ab initio molecular dynamics with the error proportional to the electron–nuclei mass ratio. The result covers observables that depend on time correlations. A combination of the Hilbert–Schmidt inner product for quantum operators and Weyl’s law shows that the error estimate holds for observables and Hamiltonian symbols that have three and five bounded derivatives, respectively, provided the electron eigenvalues are distinct for any nuclei position and the observables are in the diagonal form with respect to the electron eigenstates.
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