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The default-mode network (DMN) is a set of functionally connected regions that play crucial roles in internal cognitive processing. Previous resting-state fMRI studies have demonstrated that the intrinsic functional organization of the DMN undergoes remarkable reconfigurations during childhood and adolescence. However, these studies have mainly focused on cross-sectional designs with small sample sizes, limiting the consistency and interpretations of the findings. Here, we used a large sample of longitudinal resting-state fMRI data comprising 305 typically developing children (6–12 years of age at baseline, 491 scans in total) and graph theoretical approaches to delineate the developmental trajectories of the functional architecture of the DMN. For each child, the DMN was constructed according to a prior parcellation with 32 brain nodes. We showed that the overall connectivity increased in strength from childhood to adolescence and became spatially similar to that in the young adult group (N = 61, 18–28 years of age). These increases were primarily located in the midline structures. Global and local network efficiency in the DMN also increased with age, indicating an enhanced capability in parallel information communication within the brain system. Based on the divergent developmental rates of nodal centrality, we identified three subclusters within the DMN, with the fastest rates in the cluster mainly comprising the anterior medial prefrontal cortex and posterior cingulate cortex. Together, our findings highlight the developmental patterns of the functional architecture in the DMN from childhood to adolescence, which has implications for the understanding of network mechanisms underlying the cognitive development of individuals.

Executive function (EF) refers as to a set of high-level cognitive abilities that are critical to many aspects of daily life. Despite its importance in human daily life, the neural networks responsible for the development of EF in childhood are not well understood. The present study thus aimed to examine the development of task-dependent brain network organization and its relationship to age-related improvements in EF. To address this issue, we recruited eighty-eight Chinese children ranging in age from 7 to 12 years old, and collected their functional magnetic resonance imaging (fMRI) data when they performed an EF task. By utilizing graph theory, we found that the task-dependent brain network modules became increasingly segregated with age. Specifically, the intra-module connections within the default-mode network (DMN), frontal-parietal network (FPN) and sensorimotor network (SMN) increased significantly with age. In contrast, the inter-module connections of the visual network to both the FPN/SMN decreased significantly with age. Most importantly, modular segregation of the FPN significantly mediated the relationship between age and EF performance. These findings add to our growing understanding of how development changes in task-dependent brain network organization support vast behavioral improvements in EF observed during childhood.

Data from both animal models and deaf children provide evidence for that the maturation of auditory cortex has a sensitive period during the first 2–4 years of life. During this period, the auditory stimulation can affect the development of cortical function to the greatest extent. Thus far, little is known about the brain development trajectory after early auditory deprivation within this period. In this study, independent component analysis (ICA) technique was used to detect the characteristics of brain network development in children with bilateral profound sensorineural hearing loss (SNHL) before 3 years old. Seven resting‐state networks (RSN) were identified in 50 SNHL and 36 healthy controls using ICA method, and further their intra‐and inter‐network functional connectivity (FC) were compared between two groups. Compared with the control group, SNHL group showed decreased FC within default mode network, while enhanced FC within auditory network (AUN) and salience network. No significant changes in FC were found in the visual network (VN) and sensorimotor network (SMN). Furthermore, the inter‐network FC between SMN and AUN, frontal network and AUN, SMN and VN, frontal network and VN were significantly increased in SNHL group. The results implicate that the loss and the compensatory reorganization of brain network FC coexist in SNHL infants. It provides a network basis for understanding the brain development trajectory after hearing loss within early sensitive period. In this study, independent component analysis (ICA) technique was used to detect the characteristics of brain network development in children with bilateral profound sensorineural hearing loss (SNHL) before 3 years old. The results implicate that the loss and the compensatory reorganization of brain network FC coexist in SNHL infants. It provides a network basis for understanding the brain development trajectory after hearing loss within early sensitive period.

Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.

Let us call a simple graph on n ≥ 2 vertices a prime gap graph if its vertex degrees are 1 and the first n - 1 prime gaps. We show that such a graph exists for every large n, and in fact for every n ≥ 2 if we assume the Riemann hypothesis. Moreover, an infinite sequence of prime gap graphs can be generated by the so-called degree preserving growth process. This is the first time a naturally occurring infinite sequence of positive integers is identified as graphic. That is, we show the existence of an interesting, and so far unique, infinite combinatorial object.

The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification—the mechanism of branching by which such networks grow—remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2 π /5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km ² groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9° ± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.

We study the drivers of the emergence of opinion leaders in a networked community where users establish links to others, indicating their \"trust\" for the link receiver's opinion. This leads to the formation of a network, with high in-degree individuals being the opinion leaders. We use a dyad-level proportional hazard model with time-varying covariates to model the growth of this network. To estimate our model, we use Weighted Exogenous Sampling with Bayesian Inference , a methodology that we develop for fast estimation of dyadic models on large network data sets. We find that, in the Epinions network, both the widely studied \"preferential attachment\" effect based on the existing number of inlinks (i.e., a network-based property of a node) and the number and quality of reviews written (i.e., an intrinsic property of a node) are significant drivers of new incoming trust links to a reviewer (i.e., inlinks to a node). Interestingly, we find that time is an important moderator of these effects-intrinsic node characteristics are a stronger short-term driver of additional inlinks, whereas the preferential attachment effect has a smaller impact but it persists for a longer time. Our novel insights have important managerial implications for the design of online review communities. This paper was accepted by Sandra Slaughter, information systems.

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle α=2π/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.

Skeletal fragility in the elderly does not simply result from a loss of bone mass. However, the mechanisms underlying the concurrent decline in bone mass, quality, and mechanosensitivity with age remain unclear. The important role of osteocytes in these processes and the age-related degeneration of the intricate lacunocanalicular network (LCN) in which osteocytes reside point to a primary role for osteocytes in bone aging. Since LCN complexity severely limits experimental dissection of these mechanisms in vivo, we used two in silico approaches to test the hypothesis that LCN degeneration, due to aging or an osteocyte-intrinsic defect in transforming growth factor beta (TGF-β) signaling (TβRIIocy−/−), is sufficient to compromise essential osteocyte responsibilities of mass transport and exposure to mechanical stimuli. Using reconstructed confocal images of bone with fluorescently labeled osteocytes, we found that osteocytes from aged and TβRIIocy−/− mice had 33 to 45% fewer, and more tortuous, canaliculi. Connectomic network analysis revealed that diminished canalicular density is sufficient to impair diffusion even with intact osteocyte numbers and overall LCN architecture. Computational fluid dynamics predicts that the corresponding drop in shear stress experienced by aged or TβRIIocy−/− osteocytes is highly sensitive to canalicular surface area but not tortuosity. Simulated expansion of the osteocyte pericellular space to mimic osteocyte perilacunar/canalicular remodeling restored predicted shear stress for aged osteocytes to young levels. Overall, these models show how loss of LCN volume through LCN pruning may lead to impaired fluid dynamics and osteocyte exposure to mechanostimulation. Furthermore, osteocytes emerge as targets of age-related therapeutic efforts to restore bone health and function.

Recent work investigating the development of the phonological lexicon, where edges between words represent phonological similarity, have suggested that phonological network growth may be partly driven by a process that favors the acquisition of new words that are phonologically similar to several existing words in the lexicon. To explore this growth mechanism, we conducted a simulation study to examine the properties of networks grown by inverse preferential attachment, where new nodes added to the network tend to connect to existing nodes with fewer edges. Specifically, we analyzed the network structure and degree distributions of artificial networks generated via either preferential attachment, an inverse variant of preferential attachment, or combinations of both network growth mechanisms. The simulations showed that network growth initially driven by preferential attachment followed by inverse preferential attachment led to densely-connected network structures (i.e., smaller diameters and average shortest path lengths), as well as degree distributions that could be characterized by non-power law distributions, analogous to the features of real-world phonological networks. These results provide converging evidence that inverse preferential attachment may play a role in the development of the phonological lexicon and reflect processing costs associated with a mature lexicon structure.