Network synchronization: Optimal and Pessimal Scale-Free Topologies

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex Networks 2007

The spectral dimension of random trees

We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favor of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section I

Entangled networks, synchronization, and optimal network topology

A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node-distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community-structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost-optimal in many senses, and with plenty of potential applications computer science or neuroscience.Comment: Slightly modified version, as accepted in Phys. Rev. Let

Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that

We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological implications of having large spectral gaps. We also introduce related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we discuss two different dynamical feautures of networks: synchronizability and flow of random walkers and so that they are optimized if the corresponding Laplacian matrix have a large spectral gap. From this, we show, by developing a numerical optimization algorithm that maximum synchronizability and fast random walk spreading are obtained for a particular type of extremely homogeneous regular networks, with long loops and poor modular structure, that we call entangled networks. These turn out to be related to Ramanujan and Cage graphs. We argue also that these graphs are very good finite-size approximations to Bethe lattices, and provide almost or almost optimal solutions to many other problems as, for instance, searchability in the presence of congestion or performance of neural networks. Finally, we study how these results are modified when studying dynamical processes controlled by a normalized (weighted and directed) dynamics; much more heterogeneous graphs are optimal in this case. Finally, a critical discussion of the limitations and possible extensions of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted for pub. in JSTA

Confinement orientation effects in S/D tunneling

The most extensive research of scaled electronic devices involves the inclusion of quantum effects in the transport direction as transistor dimensions approach nanometer scales. Moreover, it is necessary to study how these mechanisms affect different transistor architectures to determine which one can be the best candidate to implement future nodes. This work implements Source-to-Drain Tunneling mechanism (S/D tunneling) in a Multi-Subband Ensemble Monte Carlo (MS-EMC) simulator showing the modification in the distribution of the electrons in the subbands, and, consequently, in the potential profile due to different confinement direction between DGSOIs and FinFETs.Spanish Ministry of Science and Innovation (TEC2014-59730-R), H2020 - REMINDER (687931), and H2020 - WAYTOGO-FAST (662175

Impact of non uniform strain configuration on transport properties for FD14+ devices

As device dimensions are scaled down, the use of non-geometrical performance boosters becomes of special relevance. In this sense, strained channels are proposed for the 14 nm FDSOI node. However this option may introduce a new source of variability since strain distribution inside the channel is not uniform at such scales. In this work, a MS-EMC study of different strain configurations including non-uniformities is presented showing drain current degradation because of the increase of intervalley phonon scattering and the subsequent variations of transport effective mass and drift velocity. This effect, which has an intrinsic statistical origin, will make necessary further optimizations to keep the expected boosting capabilities of strained channels

A thorough study of Si nanowire FETs with 3D Multi-Subband Ensemble Monte Carlo simulations

We thoroughly compare the DC electrical behavior of n-MOS transistors based on Si nanowires with 〈 1 0 0 〉 and 〈 1 1 0 〉 channel orientations by means of Multi-Subband Ensemble Monte Carlo simulations. We find that the drain current depends on the nanowire diameter and it is slightly, but consistently, larger for 〈 1 0 0 〉 than for 〈 1 1 0 〉 nanowires. The observed differences in mobility, velocity and spatial charge distribution are interpreted in terms of the effective masses and populations of the different Si conduction band valleys, whose sixfold degeneracy is lifted by quantum confinement in narrow nanowires. Finally, we study the scaling behavior for channel lengths down to 8 nm, concluding that the differences observed between orientations are minimal