A method for dense packing discovery

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting \textit{de novo} (from-scratch) searches for dense packings becomes crucial. In this paper, we use the \textit{divide and concur} framework to develop a general search method for the solution of periodic constraint problems, and we apply it to the discovery of dense periodic packings. An important feature of the method is the integration of the unit cell parameters with the other packing variables in the definition of the configuration space. The method we present led to improvements in the densest-known tetrahedron packing which are reported in [arXiv:0910.5226]. Here, we use the method to reproduce the densest known lattice sphere packings and the best known lattice kissing arrangements in up to 14 and 11 dimensions respectively (the first such numerical evidence for their optimality in some of these dimensions). For non-spherical particles, we report a new dense packing of regular four-dimensional simplices with density $\phi=128/219\approx0.5845$ and with a similar structure to the densest known tetrahedron packing.Comment: 15 pages, 5 figure

Implementing the Vision: The Atlanta BeltLine Corridor, Georgia, USA

The Atlanta BeltLine is a 22-mile transformative corridor project that will connect 45 neighborhoods through transit, open space and trails. As a repurposed series of abandoned railroad segments that run across the valleys and ridges of the Piedmont plateau region, the physical design of the corridor actively responds to both the physiographic and cultural diversity of its context. It is a comprehensive example of landscape infrastructure that will serve to organize, engage and guide future development in one of America’s fastest growing metropolitan areas (Figure 1)

Scaling migrations to communities: An empirical case of migration network in the Arctic

Seasonal migrants transport energy, nutrients, contaminants, parasites and diseases, while also connecting distant food webs between communities and ecosystems, which contributes to structuring meta-communities and meta-ecosystems. However, we currently lack a framework to characterize the structure of the spatial connections maintained by all migratory species reproducing or wintering in a given community. Here, we use a network approach to represent and characterize migratory pathways at the community level and provide an empirical description of this pattern from a High-Arctic terrestrial community. We define community migration networks as multipartite networks representing different biogeographic regions connected with a focal community through the seasonal movements of its migratory species. We focus on the Bylot Island High-Arctic terrestrial community, a summer breeding ground for several migratory species. We define the non-breeding range of each species using tracking devices, or range maps refined by flyways and habitat types. We show that the migratory species breeding on Bylot Island are found across hundreds of ecoregions on several continents during the non-breeding period and present a low spatial overlap. The migratory species are divided into groups associated with different sets of ecoregions. The non-random structure observed in our empirical community migration network suggests evolutionary and geographic constraints as well as ecological factors act to shape migrations at the community level. Overall, our study provides a simple and generalizable framework as a starting point to better integrate migrations at the community level. Our framework is a far-reaching tool that could be adapted to address the seasonal transport of energy, contaminants, parasites and diseases in ecosystems, as well as trophic interactions in communities with migratory species

Remarks on the notion of quantum integrability

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2

Ecological equivalence: a realistic assumption for niche theory as a testable alternative to neutral theory

Hubbell's 2001 neutral theory unifies biodiversity and biogeography by modelling steady-state distributions of species richness and abundances across spatio-temporal scales. Accurate predictions have issued from its core premise that all species have identical vital rates. Yet no ecologist believes that species are identical in reality. Here I explain this paradox in terms of the ecological equivalence that species must achieve at their coexistence equilibrium, defined by zero net fitness for all regardless of intrinsic differences between them. I show that the distinction of realised from intrinsic vital rates is crucial to evaluating community resilience. An analysis of competitive interactions reveals how zero-sum patterns of abundance emerge for species with contrasting life-history traits as for identical species. I develop a stochastic model to simulate community assembly from a random drift of invasions sustaining the dynamics of recruitment following deaths and extinctions. Species are allocated identical intrinsic vital rates for neutral dynamics, or random intrinsic vital rates and competitive abilities for niche dynamics either on a continuous scale or between dominant-fugitive extremes. Resulting communities have steady-state distributions of the same type for more or less extremely differentiated species as for identical species. All produce negatively skewed log-normal distributions of species abundance, zero-sum relationships of total abundance to area, and Arrhenius relationships of species to area. Intrinsically identical species nevertheless support fewer total individuals, because their densities impact as strongly on each other as on themselves. Truly neutral communities have measurably lower abundance/area and higher species/abundance ratios. Neutral scenarios can be parameterized as null hypotheses for testing competitive release, which is a sure signal of niche dynamics. Ignoring the true strength of interactions between and within species risks a substantial misrepresentation of community resilience to habitat los

Arduous implementation: Does the Normalisation Process Model explain why it's so difficult to embed decision support technologies for patients in routine clinical practice

Background: decision support technologies (DSTs, also known as decision aids) help patients and professionals take part in collaborative decision-making processes. Trials have shown favorable impacts on patient knowledge, satisfaction, decisional conflict and confidence. However, they have not become routinely embedded in health care settings. Few studies have approached this issue using a theoretical framework. We explained problems of implementing DSTs using the Normalization Process Model, a conceptual model that focuses attention on how complex interventions become routinely embedded in practice.Methods: the Normalization Process Model was used as the basis of conceptual analysis of the outcomes of previous primary research and reviews. Using a virtual working environment we applied the model and its main concepts to examine: the 'workability' of DSTs in professional-patient interactions; how DSTs affect knowledge relations between their users; how DSTs impact on users' skills and performance; and the impact of DSTs on the allocation of organizational resources.Results: conceptual analysis using the Normalization Process Model provided insight on implementation problems for DSTs in routine settings. Current research focuses mainly on the interactional workability of these technologies, but factors related to divisions of labor and health care, and the organizational contexts in which DSTs are used, are poorly described and understood.Conclusion: the model successfully provided a framework for helping to identify factors that promote and inhibit the implementation of DSTs in healthcare and gave us insights into factors influencing the introduction of new technologies into contexts where negotiations are characterized by asymmetries of power and knowledge. Future research and development on the deployment of DSTs needs to take a more holistic approach and give emphasis to the structural conditions and social norms in which these technologies are enacte

Large-scale synchrony of gap dynamics and the distribution of understory tree species in maple-beech forests

Large-scale synchronous variations in community dynamics are well documented for a vast array of organisms, but are considerably less understood for forest trees. Because of temporal variations in canopy gap dynamics, forest communities—even old-growth ones—are never at equilibrium at the stand scale. This paucity of equilibrium may also be true at the regional scale. Our objectives were to determine (1) if nonequilibrium dynamics caused by temporal variations in the formation of canopy gaps are regionally synchronized, and (2) if spatiotemporal variations in canopy gap formation aVect the relative abundance of tree species in the understory. We examined these questions by analyzing variations in the suppression and release history of Acer saccharum Marsh. and Fagus grandifolia Ehrh. from 481 growth series of understory saplings taken from 34 mature stands. We observed that (1) the proportion of stems in release as a function of time exhibited a U-shaped pattern over the last 35 years, with the lowest levels occurring during 1975–1985, and that (2) the response to this in terms of species composition was that A. saccharum became more abundant at sites that had the highest proportion of stems in release during 1975–1985. We concluded that the understory dynamics, typically thought of as a stand-scale process, may be regionally synchronized