Comparison of Different Spike Sorting Subtechniques Based on Rat Brain Basolateral Amygdala Neuronal Activity

Developing electrophysiological recordings of brain neuronal activity and their analysis provide a basis for exploring the structure of brain function and nervous system investigation. The recorded signals are typically a combination of spikes and noise. High amounts of background noise and possibility of electric signaling recording from several neurons adjacent to the recording site have led scientists to develop neuronal signal processing tools such as spike sorting to facilitate brain data analysis. Spike sorting plays a pivotal role in understanding the electrophysiological activity of neuronal networks. This process prepares recorded data for interpretations of neurons interactions and understanding the overall structure of brain functions. Spike sorting consists of three steps: spike detection, feature extraction, and spike clustering. There are several methods to implement each of spike sorting steps. This paper provides a systematic comparison of various spike sorting sub-techniques applied to real extracellularly recorded data from a rat brain basolateral amygdala. An efficient sorted data resulted from careful choice of spike sorting sub-methods leads to better interpretation of the brain structures connectivity under different conditions, which is a very sensitive concept in diagnosis and treatment of neurological disorders. Here, spike detection is performed by appropriate choice of threshold level via three different approaches. Feature extraction is done through PCA and Kernel PCA methods, which Kernel PCA outperforms. We have applied four different algorithms for spike clustering including K-means, Fuzzy C-means, Bayesian and Fuzzy maximum likelihood estimation. As one requirement of most clustering algorithms, optimal number of clusters is achieved through validity indices for each method. Finally, the sorting results are evaluated using inter-spike interval histograms.Comment: 8 pages, 12 figure

Randomized opinion dynamics over networks: influence estimation from partial observations

In this paper, we propose a technique for the estimation of the influence matrix in a sparse social network, in which $n$ individual communicate in a gossip way. At each step, a random subset of the social actors is active and interacts with randomly chosen neighbors. The opinions evolve according to a Friedkin and Johnsen mechanism, in which the individuals updates their belief to a convex combination of their current belief, the belief of the agents they interact with, and their initial belief, or prejudice. Leveraging recent results of estimation of vector autoregressive processes, we reconstruct the social network topology and the strength of the interconnections starting from \textit{partial observations} of the interactions, thus removing one of the main drawbacks of finite horizon techniques. The effectiveness of the proposed method is shown on randomly generation networks

WeA04.6 Hybrid System Identification via Sparse Polynomial Optimization

Abstract — In this paper, the problem of identifying discrete time affine hybrid systems with measurement noise is considered. Given a finite collection of measurements and a bound on the noise, the objective is to identify a hybrid system with the smallest number of sub-systems that is compatible with the a priori information. While this problem has been addressed in the literature if the input/output data is noise-free or corrupted by process noise, it remains open for the case of measurement noise. To handle this case, we propose a new approach based on recasting the problem into a polynomial optimization form and exploiting its inherent sparse structure to obtain computationally tractable problems. Combining these ideas with a randomized Hit and Run type approach leads to further computational complexity reduction, allowing for solving realistically sized problems. Numerical examples are provided, illustrating the effectiveness of the algorithm and its potential to handle large size problems. I

On the Design of Robust Controllers for Arbitrary Uncertainty Structures

The focal point of this note is the design of robust controllers for linear time-invariant uncertain systems. Given bounds on performance (defined by a convex performance evaluator) the algorithm converges to a controller that robustly satisfies the specifications. The procedure introduced has its basis on stochastic gradient algorithms and it is proven that the probability of performance violation tends to zero with probability one. Moreover, this algorithm can be applied to any uncertain plant, independently of the uncertainty structure. As an example of application of this new approach, we demonstrate its usefulness in the design of robust H2 controllers

Decentralized Optimal Traffic Engineering in Connectionless Networks

This paper addresses the problem of optimal traffic engineering in a connectionless autonomous system. Based on Nonlinear Control Theory, the approach taken in this paper provides a family of optimal adaptation laws. These laws enable each node in the network to independently distribute traffic among any given set of next-hops in an optimal way, as measured by a given global utility function of a general form. This optimal traffic distribution is achieved with minimum information exchange between neighboring nodes. Furthermore, this approach not only allows for optimal multiple forwarding paths but also enables multiple Classes of Service; e.g., classes of service defined in the DiffServ architecture. Moreover, the proposed decentralized control scheme enables optimal traffic redistribution in the case of link failures. Suboptimal control laws are also presented in an effort to reduce the computational burden imposed on the nodes of the network. Finally, an implementation of these laws with currently available technology is discussed