33 research outputs found
Correction to “Effects of Heteroatoms of Tetracene and Pentacene Derivatives on Their Stability and Singlet Fission”
Correction
to “Effects of Heteroatoms of Tetracene and Pentacene Derivatives
on Their Stability and Singlet Fission
Effects of Heteroatoms of Tetracene and Pentacene Derivatives on Their Stability and Singlet Fission
The effects of the introduction of
an sp<sup>2</sup>-hybridized
nitrogen atom (î—»Nî—¸) and thiophene ring on the structure
geometries, frontier molecular orbital energies, and excited state
energies related to singlet fission (SF) for some tetracene and pentacene
derivatives were theoretically investigated by quantum chemical methods.
The introduction of a nitrogen atom significantly decreases the energies
of frontier molecular orbitals and hence improves their stabilities
in air and light illumination. More importantly, it is helpful for
reducing the energy loss of the exothermic singlet fission of pentacene
derivatives. For fused benzene-thiophene structures, the (α,
β) connection pattern could stabilize the frontier molecular
orbitals, while the (β, β) connection pattern can promote
the thermodynamic driving force of singlet fission. These facts provide
a theoretical ground for rational design of SF materials
Modularity of original Macaque network and reconstructed networks.
<p>(A) Layout placement of 103 areas and the connections of the Macaque cortical network. (B) The two modules of the real network (open and filled circles) are compared to the two spatial clusters (blue and red). The corresponding modularity is . (C) As in (A), but for a reconstructed network at . The blue and red colors of the nodes represent the two spatial clusters. (D) The same as (B), but the modules are from the reconstructed network in (C), with . (E) Mismatch between the module partitions of the reconstructed and real networks. The mismatching areas are indicated by the pentagrams. (F) shows the fraction of mismatching areas between reconstructed and original networks in module partition, with respect to . The result did not include where the reconstructed networks did not show strong modularity. Blue bars are for the mismatching areas appearing in more than of all 50 realizations at each , while white bars are for the mismatching areas appearing at least once in the 50 realizations at the given . The dashed line represents the mismatching rate between the real networks and shuffled modules (see section “Matching between partitions” in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002937#s4" target="_blank"><i>Materials and Methods</i></a>).</p
Trade-off between Multiple Constraints Enables Simultaneous Formation of Modules and Hubs in Neural Systems
<div><p>The formation of the complex network architecture of neural systems is subject to multiple structural and functional constraints. Two obvious but apparently contradictory constraints are low wiring cost and high processing efficiency, characterized by short overall wiring length and a small average number of processing steps, respectively. Growing evidence shows that neural networks are results from a trade-off between physical cost and functional value of the topology. However, the relationship between these competing constraints and complex topology is not well understood quantitatively. We explored this relationship systematically by reconstructing two known neural networks, Macaque cortical connectivity and <i>C. elegans</i> neuronal connections, from combinatory optimization of wiring cost and processing efficiency constraints, using a control parameter , and comparing the reconstructed networks to the real networks. We found that in both neural systems, the reconstructed networks derived from the two constraints can reveal some important relations between the spatial layout of nodes and the topological connectivity, and match several properties of the real networks. The reconstructed and real networks had a similar modular organization in a broad range of , resulting from spatial clustering of network nodes. Hubs emerged due to the competition of the two constraints, and their positions were close to, and partly coincided, with the real hubs in a range of values. The degree of nodes was correlated with the density of nodes in their spatial neighborhood in both reconstructed and real networks. Generally, the rebuilt network matched a significant portion of real links, especially short-distant ones. These findings provide clear evidence to support the hypothesis of trade-off between multiple constraints on brain networks. The two constraints of wiring cost and processing efficiency, however, cannot explain all salient features in the real networks. The discrepancy suggests that there are further relevant factors that are not yet captured here.</p> </div
Features of spatial and functional segregation and integration of the primate connectome revealed by trade-off between wiring cost and efficiency
<div><p>The primate connectome, possessing a characteristic global topology and specific regional connectivity profiles, is well organized to support both segregated and integrated brain function. However, the organization mechanisms shaping the characteristic connectivity and its relationship to functional requirements remain unclear. The primate brain connectome is shaped by metabolic economy as well as functional values. Here, we explored the influence of two competing factors and additional advanced functional requirements on the primate connectome employing an optimal trade-off model between neural wiring cost and the representative functional requirement of processing efficiency. Moreover, we compared this model with a generative model combining spatial distance and topological similarity, with the objective of statistically reproducing multiple topological features of the network. The primate connectome indeed displays a cost-efficiency trade-off and that up to 67% of the connections were recovered by optimal combination of the two basic factors of wiring economy and processing efficiency, clearly higher than the proportion of connections (56%) explained by the generative model. While not explicitly aimed for, the trade-off model captured several key topological features of the real connectome as the generative model, yet better explained the connectivity of most regions. The majority of the remaining 33% of connections unexplained by the best trade-off model were long-distance links, which are concentrated on few cortical areas, termed long-distance connectors (LDCs). The LDCs are mainly non-hubs, but form a densely connected group overlapping on spatially segregated functional modalities. LDCs are crucial for both functional segregation and integration across different scales. These organization features revealed by the optimization analysis provide evidence that the demands of advanced functional segregation and integration among spatially distributed regions may play a significant role in shaping the cortical connectome, in addition to the basic cost-efficiency trade-off. These findings also shed light on inherent vulnerabilities of brain networks in diseases.</p></div
Comparison between the data of [45] and the present dataset.
<p>(A) Distribution of (binary) links with respect to distance between cortical areas for all the links in data of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>] (white bars) and the links overlapping with our data (black bars). (B) As in A, but for the distribution of the projection weights. The inset shows the average projection weight vs. distance. Here the gray bars are for the new links in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>] non-overlapping with our data. (C) The portion of the total projection weights within each distance bin in the data of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>] occupied by the two core LDC areas (5 and 46, red bars) and the other non-core LDC areas (2 and 7b, blue bars). (D) The total projection cost of each of the 24 targeted area in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>], with respect to that in the corresponding randomized networks, weighted l<sub><i>p</i></sub>/<i>l</i><sub><i>pran</i></sub>, is compared to the corresponding l<sub><i>p</i></sub>/<i>l</i><sub><i>pran</i></sub> from the present data (binary global network, similar to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.g004" target="_blank">Fig 4C</a>, but only concerning the afferent direction here). The red stars show the 2 areas of the data of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>] (5 and 46) appearing in the 6 core LDC areas in our data. The blue stars show the 2 areas of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>] (2 and 7b) appearing in the non-core LDC areas. (E) Each bar corresponds to the weighted ratio l<sub><i>p</i></sub>/<i>l</i><sub><i>pran</i></sub> for each of the 24 targeted areas in new dataset [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005776#pcbi.1005776.ref045" target="_blank">45</a>]. The first 4 bars refer to the 4 LDC areas in our data, which is ordered by the value of l<sub><i>p</i></sub>/<i>l</i><sub><i>pran</i></sub>. The following 20 areas are also ordered by the l<sub><i>p</i></sub>/<i>l</i><sub><i>pran</i></sub> values.</p
Degrees of nodes in the reconstructed and real networks.
<p>(A) and (B) Correlation between degrees and neighborhood density vs. the normalized radius for reconstructed () and real networks. (A) for Macaque and (B) for <i>C. elegans</i>. The results differ for the output (blue line), input (red line) and total degree (green line) in the real network, but are almost the same in the reconstructed network (black dashed line). The horizontal black line represents of significance level. The error-bar is from 50 realizations of the reconstructed networks.</p
Constructed networks in a 1D model.
<p>There are 200 nodes uniformly placed on a one-dimensional circle linked by a total of 2000 directed connections. Shown are the adjacency matrices obtained at various values, as indicated on the top of the plots. The nodes are indexed by their locations on the circle, common for all panels. (A) , (B) , (C) , (D) , (E) and (F) .</p
Comparison of reconstructed and original connectivity of Macaque cortical network.
<p>The left two plots (A and B) are for the original network. (A) Layout placement of 103 areas and connections between them. (B) Adjacency matrix, the output () and input () degrees of the areas. The right four plots (C–F) show adjacency matrices and the degrees of areas in the reconstructed networks at various values of . (C) , (D) , (E) and (F) . The index of the cortical areas is the same for (C–F) and the names of the areas are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002937#pcbi.1002937.s011" target="_blank">Table S1</a> of Supporting Information (SI).</p
Modularity of original <i>C. elegans</i> neuronal network and reconstructed networks.
<p>(A) Layout placement of 276 neurons and the connections of the network. (B) The four modules of the real network (open, filled circles, plus and asterisk) are compared to the three spatial clusters (blue, green and red). The corresponding modularity is . (C) As in (A), but for a reconstructed network at . The red, blue, and green colors of the nodes represent the three spatial clusters. In (A) and (C), we used different scales for the and axis for clear presentation. The connections among dense nodes cannot be seen. The inset of (B) shows the positions and clusters of neurons in identical scales. (D) The same as (B), but the modules are from the reconstructed network in (C), with . (E) Mismatch between the module partition of the reconstructed and real networks. The mismatched areas are indicated by the pentagrams. (F) shows the ratio of mismatched areas between reconstructed and original networks in module partition, with respect to . The result did not include and where the reconstructed networks did not show strong modularity. Blue bars are for mismatched areas appearing in more than of all 50 realizations, while white bars are for mismatched areas appearing at least once in the 50 realizations for a given . The dashed line represents the mismatching rate between the real network and the shuffled modules.</p