The map equation

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a network's structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a system's network structure was formed, as we are in how a network's extant structure influences the system's behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in system-wide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash application, see http://www.tp.umu.se/~rosvall/livemod/mapequation

Using intraspecific molecular and phenotypic variation to promote multi-functionality of reforestation during climate change – A review of tropical forest case studies in South-east Asia

The study of intraspecific genetic variation in plant traits for use in tropical forest restoration has broad potential for increasing our ability to achieve multi-functional objectives during this era of climate change. Developing seed-sourcing guidelines that optimize phenotypic characteristics best suited to a particular planting site as well as to future conditions imposed by environmental change could be useful for effective reforestation. Because evolution operates differently across tree species, this is an especially cumbersome task in tropical forests that contain thousands of species. Partially due to this high plant diversity, research and application of intraspecific variation in genetics, plant traits, and plant function in tropical forests wane far behind less diverse forest biomes. To examine the potential for improving reforestation efforts in tropical forests by considering intraspecific variation in plant traits and functions, we review the state of knowledge on intraspecific variation in South-east Asia as a case study. We focus on the dipterocarp family (Dipterocarpaceae), a highly diverse family of 16 genera with approximately 695 known species that often dominate lowland tropical rainforests of South-east Asia with many of these forests in a degraded state and in need of restoration. We found that there is research accumulating to understand genetic variation in approximately 10% of these 695 species. Intraspecific molecular variation exists at different spatial scales among species with 74% of species having moderate to high population differentiation (Fst > 0.10) and 92% of species with evidence of fine-scale genetic structure. Although this suggests a high potential for trait variation, few studies associated molecular with phenotypic variation. Seventeen tree species across 11 studies revealed intraspecific variation in traits or functions. Research indicates that intraspecific variation in growth may vary two-fold and drought tolerance four-fold among genotypes highlighting the possibility to pre-adapt trees to climate change during reforestation and to use intraspecific variation to promote the use of native species in commercial forestry. Our review presents opportunities and ideas for developing seed-sourcing guidelines to take advantage of intraspecific variation in traits and function by identifying how to locate this variation, which species would benefit, and how to test for trait variation. We also highlight an emerging area of research on local adaptation, common garden studies, and adaptive drought conditioning to improve reforestation during climate change

Symphony for the native wood(s): Global reforestation as an opportunity to develop a culture of conservation

1. The stewardship of forests across multiple human generations has potential to lead to cultural innovations fostering sustainable uses. Nevertheless, positive culture-nature interactions are often disrupted due to colonial exploitation and a lack of intrinsic value ascribed to nature in capitalist economies. There is global recognition that restoring degraded ecosystems is critical to promote the welfare of people and nature by reducing the negative impacts of global climate change and diminishing biodiversity. However, with a focus on technical remedies, restoration and reforestation efforts generally fail to address the root causes of ecosystem degradation.2. In this perspective paper, we call for explicit incorporation of cultural values into global reforestation efforts. We focus on music as a cultural ecosystem service as music has been a prominent part of human history with clear sociological and psychological attributes that may invite mass interest and participation. We illustrate the value of musical linkages via three case studies from Europe, Africa and Hawaii focusing on native tree species, their wood, musical ecology and their interaction with culture.3. We show that multi-generational stewardship of native ecosystems in Europe has allowed the refinement of the violin to its current form, one that is culturally significant for millions of people and has created a multi-million dollar industry. This development stems from a 500-year tradition of craftsmanship handed down across generations and illustrates that ecocultural interactions can be a strong dynamo for development of unique commodities.4. In contrast, in regions where extirpation of native plant species was used as a deliberate colonization strategy, many ecocultural linkages face risk of extinction. Our case studies from Africa and Hawaii illustrate how native tree species of particular value for musical expression were nearly lost and along with loss of music, important cultural connections to nature.5. In the context of restoration, there is also evidence that music-based linkages can revitalize nature-culture interactions and promote restoration of native ecosystems. Incorporating native trees in global reforestation efforts is critical for ensuring that reforestation efforts capture the synergies needed for developing new ideologies that promote the well-being of co-dependent humans and all life

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second order, complex, elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning \textit{a priori} almost everywhere non-tangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying \textit{a posteriori} a separate work on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has changed nam

Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples

Extremely narrow spectrum of GRB110920A: further evidence for localised, subphotospheric dissipation

Much evidence points towards that the photosphere in the relativistic outflow in GRBs plays an important role in shaping the observed MeV spectrum. However, it is unclear whether the spectrum is fully produced by the photosphere or whether a substantial part of the spectrum is added by processes far above the photosphere. Here we make a detailed study of the $\gamma-$ray emission from single pulse GRB110920A which has a spectrum that becomes extremely narrow towards the end of the burst. We show that the emission can be interpreted as Comptonisation of thermal photons by cold electrons in an unmagnetised outflow at an optical depth of $\tau \sim 20$. The electrons receive their energy by a local dissipation occurring close to the saturation radius. The main spectral component of GRB110920A and its evolution is thus, in this interpretation, fully explained by the emission from the photosphere including localised dissipation at high optical depths.Comment: 14 pages, 11 figures, accepted to MNRA

Categorization of indoor places by combining local binary pattern histograms of range and reflectance data from laser range finders

This paper presents an approach to categorize typical places in indoor environments using 3D scans provided by a laser range finder. Examples of such places are offices, laboratories, or kitchens. In our method, we combine the range and reflectance data from the laser scan for the final categorization of places. Range and reflectance images are transformed into histograms of local binary patterns and combined into a single feature vector. This vector is later classified using support vector machines. The results of the presented experiments demonstrate the capability of our technique to categorize indoor places with high accuracy. We also show that the combination of range and reflectance information improves the final categorization results in comparison with a single modality