Mean-field analysis of directed modular networks.

We considered a modular network with a binomial degree distribution and related the analytical relationships of the network properties (modularity, average clustering coefficient, and small-worldness) with structural parameters that define the network, i.e., number of nodes, number of modules, average node degree, and ratio of intra-modular to total connections. Even though modular networks are universally found in real-world systems and are consequently of broad interest in complex network science, the relationship between network properties and structural parameters has not yet been formulated. Here, we show that a series of equations for predicting the network properties can be related using a mean-field connectivity matrix that is defined on the basis of the structural parameters in the network generation algorithm. The theoretical results are then compared with values calculated numerically using the original connectivity matrix and are found to agree well, except when the connections between modules are sparse. Representation of the structure of the network using simple parameters is expected to be conducive for elucidating the structure-dynamics relationship.

Carrier properties of B atomic-layer-doped Si films grown by ECR Ar plasma-enhanced CVD without substrate heating.

The atomic-layer (AL) doping technique in epitaxy has attracted attention as a low-resistive ultrathin semiconductor film as well as a two-dimensional (2-D) carrier transport system. In this paper, we report carrier properties for B AL-doped Si films with suppressed thermal diffusion. B AL-doped Si films were formed on Si(100) by B AL formation followed by Si cap layer deposition in low-energy Ar plasma-enhanced chemical-vapor deposition without substrate heating. After fabrication of Hall-effect devices with the B AL-doped Si films on unstrained and 0.8%-tensile-strained Si(100)-on-insulator substrates (maximum process temperature 350°C), carrier properties were electrically measured at room temperature. Typically for the initial B amount of 2 × 1014 cm-2 and 7 × 1014 cm-2, B concentration depth profiles showed a clear decay slope as steep as 1.3 nm/decade. Dominant carrier was a hole and the maximum sheet carrier densities as high as 4 × 1013 cm-2 and 2 × 1013 cm-2 (electrical activity ratio of about 7% and 3.5%) were measured respectively for the unstrained and 0.8%-tensile-strained Si with Hall mobility around 10-13 cm2 V-1 s-1. Moreover, mobility degradation was not observed even when sheet carrier density was increased by heat treatment at 500-700 °C. There is a possibility that the local carrier (ionized B atom) concentration around the B AL in Si reaches around 1021 cm-3 and 2-D impurity-band formation with strong Coulomb interaction is expected. The behavior of carrier properties for heat treatment at 500-700 °C implies that thermal diffusion causes broadening of the B AL in Si and decrease of local B concentration.

Impact of modular organization on dynamical richness in cortical networks.

As in many naturally formed networks, the brain exhibits an inherent modular architecture that is the basis of its rich operability, robustness, and integration-segregation capacity. However, the mechanisms that allow spatially segregated neuronal assemblies to swiftly change from localized to global activity remain unclear. Here, we integrate microfabrication technology with in vitro cortical networks to investigate the dynamical repertoire and functional traits of four interconnected neuronal modules. We show that the coupling among modules is central. The highest dynamical richness of the network emerges at a critical connectivity at the verge of physical disconnection. Stronger coupling leads to a persistently coherent activity among the modules, while weaker coupling precipitates the activity to be localized solely within the modules. An in silico modeling of the experiments reveals that the advent of coherence is mediated by a trade-off between connectivity and subquorum firing, a mechanism flexible enough to allow for the coexistence of both segregated and integrated activities. Our results unveil a new functional advantage of modular organization in complex networks of nonlinear units.

Size-dependent regulation of synchronized activity in living neuronal networks.

We study the effect of network size on synchronized activity in living neuronal networks. Dissociated cortical neurons form synaptic connections in culture and generate synchronized spontaneous activity within 10 days in vitro. Using micropatterned surfaces to extrinsically control the size of neuronal networks, we show that synchronized activity can emerge in a network as small as 12 cells. Furthermore, a detailed comparison of small (∼20 cells), medium (∼100 cells), and large (∼400 cells) networks reveal that synchronized activity becomes destabilized in the small networks. A computational modeling of neural activity is then employed to explore the underlying mechanism responsible for the size effect. We find that the generation and maintenance of the synchronized activity can be minimally described by: (1) the stochastic firing of each neuron in the network, (2) enhancement in the network activity in a positive feedback loop of excitatory synapses, and (3) Ca-dependent suppression of bursting activity. The model further shows that the decrease in total synaptic input to a neuron that drives the positive feedback amplification of correlated activity is a key factor underlying the destabilization of synchrony in smaller networks. Spontaneous neural activity plays a critical role in cortical information processing, and our work constructively clarifies an aspect of the structural basis behind this.

Measurement of large low-order aberrations by using a series of through-focus Ronchigrams.

A method for measuring large aberrations up to second order (defocus, 2-fold astigmatism and axial coma), which uses a through-focus series of Ronchigrams, is proposed. The method is based on the principle that line-focus conditions in Ronchigrams can be locally detected and low-order aberrations can thereby be measured. The proposed method provides auto-tuning of large low-order aberration; in particular, iterative aberration measurement and correction reduce low-order aberrations from several thousand nanometers to less than a few hundred nanometers, which can be handled by conventional fine-aberration tuning methods.