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In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.

In this paper, we apply a new time-frequency spectral estimation method for multichannel data to epileptiform electroencephalography (EEG). The method is based on the smooth localized complex exponentials (SLEX) functions which are time-frequency localized versions of the Fourier functions and, hence, are ideal for analyzing nonstationary signals whose spectral properties evolve over time. The SLEX functions are simultaneously orthogonal and localized in time and frequency because they are obtained by applying a projection operator rather than a window or taper. In this paper, we present the Auto-SLEX method which is a statistical method that 1) computes the periodogram using the SLEX transform, 2) automatically segments the signal into approximately stationary segments using an objective criterion that is based on log energy, and 3) automatically selects the optimal bandwidth of the spectral smoothing window. The method is applied to the intracranial EEG from a patient with temporal lobe epilepsy. This analysis reveals a reduction in average duration of stationarity in preseizure epochs of data compared to baseline. These changes begin up to hours prior to electrical seizure onset in this patient.

We develop a procedure for analyzing multivariate nonstationary time series using the SLEX library (smooth localized complex exponentials), which is a collection of bases, each basis consisting of waveforms that are orthogonal and time-localized versions of the Fourier complex exponentials. Under the SLEX framework, we build a family of multivariate models that can explicitly characterize the time- varying spectral and coherence properties. Every model has a spectral representation in terms of a unique SLEX basis. Before selecting a model, we first decompose the multivariate time series into nonstationary components with uncorrelated (nonredundant) spectral information. The best SLEX model is selected using the penalized log energy criterion, which we derive in this article to be the Kullback-Leibler distance between a model and the SLEX principal components of the multivariate time series. The model selection criterion takes into account all of the pairwise cross-correlation simultaneously in the multivariate time series. The proposed SLEX analysis gives results that are easy to interpret, because it is an automatic time-dependent generalization of the classical Fourier analysis of stationary time series. Moreover, the SLEX method uses computationally efficient algorithms and hence is able to provide a systematic framework for extracting spectral features from a massive dataset. We illustrate the SLEX analysis with an application to a multichannel brain wave dataset recorded during an epileptic seizure. [ABSTRACT FROM AUTHOR]