The neuromorphic Mosaic: re-configurable in-memory small-world graphs

Thanks to their non-volatile and multi-bit properties, memristors have been extensively used as synaptic weight elements in neuromorphic architectures. However, their use to define and re-program the network connectivity has been overlooked. Here, we propose, implement and experimentally demonstrate Mosaic, a neuromorphic architecture based on a systolic array of memristor crossbars. For the first time, we use distributed non-volatile memristors not only for computation, but also for routing (i.e., to define the network connectivity). Mosaic is particularly well-suited for the implementation of re-configurable small-world graphical models, with dense local and sparse global connectivity - found extensively in the brain. We mathematically show that, as the networks scale up, the Mosaic requires less memory than in conventional memristor approaches. We map a spiking recurrent neural network on the Mosaic to solve an Electrocardiogram (ECG) anomaly detection task. While the performance is either equivalent or better than software models, the advantage of the Mosaic was clearly seen in respective one and two orders of magnitude reduction in energy requirements, compared to a micro-controller and address-event representation-based processor. Mosaic promises to open up a new approach to designing neuromorphic hardware based on graph-theoretic principles with less memory and energy.

TECHNOLOGICAL MODEL AND SUSTAINABILITY ASSESSMENT METHODOLOGY OF THE MULTISERVICE COMMUNICATION NETWORK FUNCTIONING

The modern development of multiservice communication networks (MÑN) is characterized by the desire of operators to provide users with an unlimited range of services with guaranteed quality of service (QoS). QoS is determined by the stability of the network’s functioning, that is, its ability to function without errors. The existing routing algorithms in modern networks focus the main load on the most productive sections, while the rest of the network is used quite poorly. This is confirmed by the results of studies [1,2], in which the structure of modern global communication networks is assigned to the class of small-world graphs. Obviously, that the increased connectivity of such networks determines high indicators of its stability, but at the same time, this route redundancy is poorly used by existing routing protocols to provide QoS when transmitting different traffic (triple-play: audio, video, and data) [3, 4]. There is also no work devoted to the analysis of the possibilities of sharing different routes (route parallelism) for the implementation of QoS enhancement mechanisms in the MÑN. This article discusses the technological concept of a network with route parallelism in communication networks built on the basis of the IP protocol family.

On small world non-Sunada twins and cellular Voronoi diagrams

Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic. We say that a family of non-Sunada twins is unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. If all Gi and Hi are edge-transitive we have a balanced family of small world non-Sunada twins. We say that a family of non-Sunada twins is strongly unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. We use term edge disbalanced for the family of non-Sunada twins such that all graphs Gi and Hi are edge-intransitive. We present explicit constructions of the above defined families. Two new families of distance-regular—but not distance-transitive—graphs will be introduced.

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τt ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τt ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τt ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.