Classes of Symmetric Cayley Graphs over Finite Abelian Groups of Degrees 4 and 6

The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.Comment: 12 pages. A previous version of some of the results in this paper where first announced at 2010 International Workshop on Optimal Interconnection Networks (IWONT 2010). It is accessible at http://upcommons.upc.edu/revistes/handle/2099/1037

Symmetric L-graphs

In this paper we characterize symmetric L-graphs, which are either Kronecker products of two cycles or Gaussian graphs. Vertex symmetric networks have the property that the communication load is uniformly distributed on all the vertices so that there is no point of congestion. A stronger notion of symmetry, edge symmetry, requires that every edge in the graph looks the same. Such property ensures that the communication load is uniformly distributed over all the communication links, so that there is no congestion at any link.Peer Reviewe

A computation of the shortest paths in optimal two-dimensional circulant networks

Для семейства оптимальных двумерных циркулянтных сетей с аналитическим описанием получены две новые улучшенные версии алгоритма поиска кратчайших путей с константной оценкой сложности. Дано простое, основанное на геометрической модели циркулянтных графов, доказательство формул, используемых для алгоритма поиска кратчайших путей. Представлены алгоритмы парных обменов и даны их оценки для сетей на кристалле с топологией в виде рассмотренных графов. Новые версии алгоритма улучшают также предложенный ранее автором алгоритм поиска кратчайших путей для оптимальных обобщённых графов Петерсена с аналитическим описанием

Symmetric Interconnection Networks from Cubic Crystal Lattices

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of these networks. By using integral matrices to deal with Cayley graphs over Abelian groups, we have been able to propose and analyze a family of high-dimensional grid-based interconnection networks. As they are built over $n$-dimensional grids that induce a regular tiling of the space, these topologies have been denoted \textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling symmetric 3D networks. Other higher dimensional networks can be composed over these graphs, as illustrated in this research. Easy network partitioning can also take advantage of this network composition operation. Minimal routing algorithms are also provided for these new topologies. Finally, some practical issues such as implementability and preliminary performance evaluations have been addressed

Design of a Neuromemristive Echo State Network Architecture

Echo state neural networks (ESNs) provide an efficient classification technique for spatiotemporal signals. The feedback connections in the ESN enable feature extraction in both spatial and temporal components in time series data. This property has been used in several application domains such as image and video analysis, anomaly detection, and speech recognition. The software implementations of the ESN demonstrated efficiency in processing such applications, and have low design cost and flexibility. However, hardware implementation is necessary for power constrained resources applications such as therapeutic and mobile devices. Moreover, software realization consumes an order or more power compared to the hardware realization. In this work, a hardware ESN architecture with neuromemristive system is proposed. A neuromemristive system is a brain inspired computing system that uses memristive devises for synaptic plasticity. The memristive devices in neuromemristive systems have several interesting properties such as small footprint, simple device structure, and most importantly zero static power dissipation. The proposed architecture is reconfigurable for different ESN topologies. 2-D mesh architecture and toroidal networks are exploited in the reservoir layer. The relation between performance of the proposed reservoir architecture and reservoir metrics are analyzed. The proposed architecture is tested on a suite of medical and human computer interaction applications. The benchmark suite includes epileptic seizure detection, speech emotion recognition, and electromyography (EMG) based finger motion recognition. The proposed ESN architecture demonstrated an accuracy of $90\%$, $96\%$, and $84\%$ for epileptic seizure detection, speech emotion recognition and EMG prosthetic fingers control respectively