Nature-inspired interconnects for self-assembled large-scale network-on-chip designs

Damage spreading in spatial and small-world random Boolean networks

The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean networks (RBNs) are commonly used as a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other nonrandom connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the Hamming distance at very low connectivities (K ≪ 1) and that the critical connectivity of stability K(s) changes compared to random networks. At higher K, this scaling remains unchanged. We also show that the Hamming distance of spatially local networks scales with a power law as the system size N increases, but with a different exponent for local and small-world networks. The scaling arguments for small-world networks are obtained with respect to the system sizes and strength of spatially local connections. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.

On the nature and shape of tubulin trails: implications on microtubule self-organization

Microtubules, major elements of the cell skeleton are, most of the time, well organized in vivo, but they can also show self-organizing behaviors in time and/or space in purified solutions in vitro. Theoretical studies and models based on the concepts of collective dynamics in complex systems, reaction-diffusion processes and emergent phenomena were proposed to explain some of these behaviors. In the particular case of microtubule spatial self-organization, it has been advanced that microtubules could behave like ants, self-organizing by 'talking to each other' by way of hypothetic (because never observed) concentrated chemical trails of tubulin that are expected to be released by their disassembling ends. Deterministic models based on this idea yielded indeed like-looking spatio-temporal self-organizing behaviors. Nevertheless the question remains of whether microscopic tubulin trails produced by individual or bundles of several microtubules are intense enough to allow microtubule self-organization at a macroscopic level. In the present work, by simulating the diffusion of tubulin in microtubule solutions at the microscopic scale, we measure the shape and intensity of tubulin trails and discuss about the assumption of microtubule self-organization due to the production of chemical trails by disassembling microtubules. We show that the tubulin trails produced by individual microtubules or small microtubule arrays are very weak and not elongated even at very high reactive rates. Although the variations of concentration due to such trails are not significant compared to natural fluctuations of the concentration of tubuline in the chemical environment, the study shows that heterogeneities of biochemical composition can form due to microtubule disassembly. They could become significant when produced by numerous microtubule ends located in the same place. Their possible formation could play a role in certain conditions of reaction. In particular, it gives a mesoscopic basis to explain the collective dynamics observed in excitable microtubule solutions showing the propagation of concentration waves of microtubules at the millimeter scale, although we doubt that individual microtubules or bundles can behave like molecular ants.

Interplay between structural randomness, composite disorder, and electrical response: resonances and transient delays in complex impedance networks

We study the interplay between structural and conductivity (composite) disorder and the collective electrical response in random network models. Translating the problem of time-dependent electrical response (resonance and transient relaxation) in binary random composite networks to the framework of generalized eigenvalues, we study and analyze the scaling behavior of the density of resonances in these structures. We found that by controlling the density of shortcuts (topological randomness) and/or the composite ratio of the binary links (conductivity disorder), one can effectively shape resonance landscapes or suppress or enhance long transient delays in the corresponding random impedance networks.

Investigating the properties of self-organization and synchronization in electronic systems

Nonlinear cooperative behavior appears naturally in many systems, such as cardiac cell oscillations; cellular calcium oscillations; oscillatory chemical reactions, and fireflies. Such systems have been studied in detail due to their inherent properties of robustness, adaptability, scalability, and emergence. In this paper, such nonlinear cooperative behaviors are considered within the domain of electronic system design. We investigate these desirable properties in a system composed of electronic oscillators. The paper presents a series of circuit simulation results showing that self-organizing principles, which can be emulated in an electronic circuit, enable the systems to show a phase transition to synchronization, in a manner similar to those of natural systems. Circuit simulation results presented here show that the circuits are robust to the unreliable performance of the electronic oscillators and tolerant to their run-time faults. These are important findings for future engineering applications in which the system's elements are likely to be unreliable and faulty, such as in molecular- and nanoelectronic systems.

Inorganic molecular-scale MoSI nanowire-gold nanoparticle networks exhibit self-organized critical self-assembly

We investigate for the first time the topological characteristics of large molecular-scale inorganic networks self-assembled in solution using the unique sulfur-bonding chemistry of conducting MoSI molecular wires and gold nanoparticles (GNPs). The network self-assembly is shown to display power-law distribution of graph edges, indicating an intrinsic tendency to self-organize into scale-invariant critical state, without any external control parameter. We discuss the electronic transport properties of such networks particularly with regard to the possibility of data processing.

Introduction: optimization in networks

The recent surge in the network modeling of complex systems has set the stage for a new era in the study of fundamental and applied aspects of optimization in collective behavior. This Focus Issue presents an extended view of the state of the art in this field and includes articles from a large variety of domains in which optimization manifests itself, including physical, biological, social, and technological networked systems.