New delay-dependent stability criteria for recurrent neural networks with time-varying delays

Dimirovski, Georgi M. (Dogus Author)This work is concerned with the delay-dependentstability problem for recurrent neural networks with time-varying delays. A new improved delay-dependent stability criterion expressed in terms of linear matrix inequalities is derived by constructing a dedicated Lyapunov-Krasovskii functional via utilizing Wirtinger inequality and convex combination approach. Moreover, a further improved delay-dependent stability criterion is established by means of a new partitioning method for bounding conditions on the activation function and certain new activation function conditions presented. Finally, the application of these novel results to an illustrative example from the literature has been investigated and their effectiveness is shown via comparison with the existing recent ones

In silico case studies of compliant robots: AMARSI deliverable 3.3

In the deliverable 3.2 we presented how the morphological computing ap- proach can significantly facilitate the control strategy in several scenarios, e.g. quadruped locomotion, bipedal locomotion and reaching. In particular, the Kitty experimental platform is an example of the use of morphological computation to allow quadruped locomotion. In this deliverable we continue with the simulation studies on the application of the different morphological computation strategies to control a robotic system

Reverse engineering of genetic networks with time delayed recurrent neural networks and clustering techniques

In the iterative process of experimentally probing biological networks and computationally inferring models for the networks, fast, accurate and flexible computational frameworks are needed for modeling and reverse engineering biological networks. In this dissertation, I propose a novel model to simulate gene regulatory networks using a specific type of time delayed recurrent neural networks. Also, I introduce a parameter clustering method to select groups of parameter sets from the simulations representing biologically reasonable networks. Additionally, a general purpose adaptive function is used here to decrease and study the connectivity of small gene regulatory networks modules. In this dissertation, the performance of this novel model is shown to simulate the dynamics and to infer the topology of gene regulatory networks derived from synthetic and experimental time series gene expression data. Here, I assess the quality of the inferred networks by the use of graph edit distance measurements in comparison to the synthetic and experimental benchmarks. Additionally, I compare between edition costs of the inferred networks obtained with the time delay recurrent networks and other previously described reverse engineering methods based on continuous time recurrent neural and dynamic Bayesian networks. Furthermore, I address questions of network connectivity and correlation between data fitting and inference power by simulating common experimental limitations of the reverse engineering process as incomplete and highly noisy data. The novel specific type of time delay recurrent neural networks model in combination with parameter clustering substantially improves the inference power of reverse engineered networks. Additionally, some suggestions for future improvements are discussed, particularly under the data driven perspective as the solution for modeling complex biological systems

Model-free reconstruction of neuronal network connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio