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Concept: Topology


Recent advances in nanophotonic light trapping open up the new gateway to enhance the absorption of solar energy beyond the so called Yablonovitch Limit. It addresses the urgent needs in developing low cost thin-film solar photovoltaic technologies. However, current design strategy mainly relies on the parametric approach that is subject to the predefined topological design concepts based on physical intuition. Incapable of dealing with the topological variation severely constrains the design of optimal light trapping structure. Inspired by natural evolution process, here we report a design framework driven by topology optimization based on genetic algorithms to achieve a highly efficient light trapping structure. It has been demonstrated that the optimal light trapping structures obtained in this study exhibit more than 3-fold increase over the Yablonovitch Limit with the broadband absorption efficiency of 48.1%, beyond the reach of intuitive designs.

Concepts: Evolution, Energy, Topology, Solar cell, Photovoltaics, Design, Solar energy, Solar thermal energy


Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.

Concepts: Mathematics, Structure, Topology, Graph theory, Topological space, Metric space, Graph, Architecture


Many studies show that open access (OA) articles-articles from scholarly journals made freely available to readers without requiring subscription fees-are downloaded, and presumably read, more often than closed access/subscription-only articles. Assertions that OA articles are also cited more often generate more controversy. Confounding factors (authors may self-select only the best articles to make OA; absence of an appropriate control group of non-OA articles with which to compare citation figures; conflation of pre-publication vs. published/publisher versions of articles, etc.) make demonstrating a real citation difference difficult. This study addresses those factors and shows that an open access citation advantage as high as 19% exists, even when articles are embargoed during some or all of their prime citation years. Not surprisingly, better (defined as above median) articles gain more when made OA.

Concepts: Mathematics, Topology, Peer review, Metric space, Open set, Open access, Wealth condensation, The rich get richer and the poor get poorer


Topological networks lie at the heart of our cities and social milieu. However, it remains unclear how and when the brain processes topological structures to guide future behaviour during everyday life. Using fMRI in humans and a simulation of London (UK), here we show that, specifically when new streets are entered during navigation of the city, right posterior hippocampal activity indexes the change in the number of local topological connections available for future travel and right anterior hippocampal activity reflects global properties of the street entered. When forced detours require re-planning of the route to the goal, bilateral inferior lateral prefrontal activity scales with the planning demands of a breadth-first search of future paths. These results help shape models of how hippocampal and prefrontal regions support navigation, planning and future simulation.

Concepts: Brain, Topology, Manifold, Graph theory, Topological space, Metric space, Open set, Network topology


As the cost of sequencing continues to decrease and the amount of sequence data generated grows, new paradigms for data storage and analysis are increasingly important. The relative scaling behavior of these evolving technologies will impact genomics research moving forward.

Concepts: Series, Topology, Sequence, Computer data storage, The Real, Real analysis, Limit of a sequence, Cauchy sequence


-Small studies have suggested that high intensity interval training (HIIT) is superior to moderate continuous training (MCT) in reversing cardiac remodeling and increasing aerobic capacity in heart failure patients with reduced ejection fraction (HFrEF). The present multicenter trial compared 12 weeks supervised interventions of HIIT, MCT, or a recommendation of regular exercise (RRE).

Concepts: Myocardial infarction, Cardiology, Heart failure, Ejection fraction, Exercise, Topology, Exercise physiology, High-intensity interval training


Knots may ultimately prove just as versatile and useful at the nanoscale as at the macroscale. However, the lack of synthetic routes to all but the simplest molecular knots currently prevents systematic investigation of the influence of knotting at the molecular level. We found that it is possible to assemble four building blocks into three braided ligand strands. Octahedral iron(II) ions control the relative positions of the three strands at each crossing point in a circular triple helicate, while structural constraints on the ligands determine the braiding connections. This approach enables two-step assembly of a molecular 819 knot featuring eight nonalternating crossings in a 192-atom closed loop ~20 nanometers in length. The resolved metal-free 819 knot enantiomers have pronounced features in their circular dichroism spectra resulting solely from topological chirality.

Concepts: Knot, Chirality, Topology, Circular dichroism, Loop, Rope, Ropework, Knots


During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them.

Concepts: Human, Mathematics, Series, Geometry, Topology, Sequence, Group, Set


By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.

Concepts: Sociology, Topology, Topological space, Simplex, Algebraic topology, Polytope, Simplicial complex, Simplicial set


The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive “pruning” of short-distance functional connections in schizophrenia.

Concepts: Brain, Magnetic resonance imaging, Cerebral cortex, Topology, Graph theory, Frontal lobe, Metric space, Network topology