Topology Design for Optimal Network Coherence

We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of the network topology. As a consequence, a simple greedy algorithm is guaranteed to produce near optimal edge set selections. We also show that fast rank one updates of the Laplacian pseudoinverse using generalizations of the Sherman-Morrison formula and an accelerated variant of the greedy algorithm can speed up the algorithm by several orders of magnitude in practice. These allow our algorithms to scale to network sizes far beyond those that can be handled by convex relaxation heuristics

Advances in photonic reservoir computing on an integrated platform

Reservoir computing is a recent approach from the fields of machine learning and artificial neural networks to solve a broad class of complex classification and recognition problems such as speech and image recognition. As is typical for methods from these fields, it involves systems that were trained based on examples, instead of using an algorithmic approach. It originated as a new training technique for recurrent neural networks where the network is split in a reservoir that does the `computation' and a simple readout function. This technique has been among the state-of-the-art. So far implementations have been mainly software based, but a hardware implementation offers the promise of being low-power and fast. We previously demonstrated with simulations that a network of coupled semiconductor optical amplifiers could also be used for this purpose on a simple classification task. This paper discusses two new developments. First of all, we identified the delay in between the nodes as the most important design parameter using an amplifier reservoir on an isolated digit recognition task and show that when optimized and combined with coherence it even yields better results than classical hyperbolic tangent reservoirs. Second we will discuss the recent advances in photonic reservoir computing with the use of resonator structures such as photonic crystal cavities and ring resonators. Using a network of resonators, feedback of the output to the network, and an appropriate learning rule, periodic signals can be generated in the optical domain. With the right parameters, these resonant structures can also exhibit spiking behaviour

Exact reconstruction of gene regulatory networks using compressive sensing.

BackgroundWe consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network's sparseness.ResultsFor the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.ConclusionsThe method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies

Cycle-accurate evaluation of reconfigurable photonic networks-on-chip

There is little doubt that the most important limiting factors of the performance of next-generation Chip Multiprocessors (CMPs) will be the power efficiency and the available communication speed between cores. Photonic Networks-on-Chip (NoCs) have been suggested as a viable route to relieve the off- and on-chip interconnection bottleneck. Low-loss integrated optical waveguides can transport very high-speed data signals over longer distances as compared to on-chip electrical signaling. In addition, with the development of silicon microrings, photonic switches can be integrated to route signals in a data-transparent way. Although several photonic NoC proposals exist, their use is often limited to the communication of large data messages due to a relatively long set-up time of the photonic channels. In this work, we evaluate a reconfigurable photonic NoC in which the topology is adapted automatically (on a microsecond scale) to the evolving traffic situation by use of silicon microrings. To evaluate this system's performance, the proposed architecture has been implemented in a detailed full-system cycle-accurate simulator which is capable of generating realistic workloads and traffic patterns. In addition, a model was developed to estimate the power consumption of the full interconnection network which was compared with other photonic and electrical NoC solutions. We find that our proposed network architecture significantly lowers the average memory access latency (35% reduction) while only generating a modest increase in power consumption (20%), compared to a conventional concentrated mesh electrical signaling approach. When comparing our solution to high-speed circuit-switched photonic NoCs, long photonic channel set-up times can be tolerated which makes our approach directly applicable to current shared-memory CMPs