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Error hypersurfaces are very valuable to study because of their unique status in multilayer perceptron research. Given the architecture of a multilayer perceptron, if the pattern sets are different, so are the respective error hypersurfaces in the multilayer perceptron. Using the theory of groups and Polya Theorem, this paper constructs classes of congruent pattern sets and classes of congruent error hypersurfaces, and proves that the number of classes of congruent pattern sets is equal to the number of congruent error hypersurfaces. Calculation results lead to much fewer classes of congruent error hypersurfaces than the total error hypersurfaces, and show that as the input dimension N increases, the former number increases at a much lower rate than the latter number, thus simplifying the understanding of the complexity of classes of error hypersurfaces.

Organized brain activity is the result of dynamical, segregated neuronal signals that may be used to investigate synchronization effects using sophisticated neuroengineering techniques. Phase synchrony analysis, in particular, has emerged as a promising methodology to study transient and frequency-specific coupling effects across multi-site signals. In this study, we investigated phase synchronization in intracellular recordings of interictal and ictal epileptiform events recorded from pairs of cells in the whole (intact) mouse hippocampus. In particular, we focused our analysis on the background noise-like activity (NLA), previously reported to exhibit complex neurodynamical properties. Our results show evidence for increased linear and nonlinear phase coupling in NLA across three frequency bands [theta (4–10 Hz), beta (12–30 Hz) and gamma (30–80 Hz)] in the ictal compared to interictal state dynamics. We also present qualitative and statistical evidence for increased phase synchronization in the theta, beta and gamma frequency bands from paired recordings of ictal NLA. Overall, our results validate the use of background NLA in the neurodynamical study of epileptiform transitions and suggest that what is considered "neuronal noise" is amenable to synchronization effects in the spatiotemporal domain.

A complex network approach is combined with time dynamics in order to conduct a space–time analysis applicable to longitudinal studies aimed to characterize the progression of Alzheimer's disease (AD) in individual patients. The network analysis reveals how patient-specific patterns are associated with disease progression, also capturing the widespread effect of local disruptions. This longitudinal study is carried out on resting electroence phalography (EEGs) of seven AD patients. The test is repeated after a three months' period. The proposed methodology allows to extract some averaged information and regularities on the patients' cohort and to quantify concisely the disease evolution. From the functional viewpoint, the progression of AD is shown to be characterized by a loss of connected areas here measured in terms of network parameters (characteristic path length, clustering coefficient, global efficiency, degree of connectivity and connectivity density). The differences found between baseline and at follow-up are statistically significant. Finally, an original topographic multiscale approach is proposed that yields additional results.

Background: Transcranial magnetic stimulation combined with electroencephalogram (TMS-EEG) can be used to explore the dynamical state of neuronal networks. In patients with epilepsy, TMS can induce epileptiform discharges (EDs) with a stochastic occurrence despite constant stimulation parameters. This observation raises the possibility that the pre-stimulation period contains multiple covert states of brain excitability some of which are associated with the generation of EDs. Objective: To investigate whether the interictal period contains "high excitability" states that upon brain stimulation produce EDs and can be differentiated from "low excitability" states producing normal appearing TMS-EEG responses. Methods: In a cohort of 25 patients with Genetic Generalized Epilepsies (GGE) we identified two subjects characterized by the intermittent development of TMS-induced EDs. The high-excitability in the pre-stimulation period was assessed using multiple measures of univariate time series analysis. Measures providing optimal discrimination were identified by feature selection techniques. The "high excitability" states emerged in multiple loci (indicating diffuse cortical hyperexcitability) and were clearly differentiated on the basis of 14 measures from "low excitability" states (accuracy = 0.7). Conclusion: In GGE, the interictal period contains multiple, quasi-stable covert states of excitability a class of which is associated with the generation of TMS-induced EDs. The relevance of these findings to theoretical models of ictogenesis is discussed.

A multivariate sample entropy metric of signal complexity is applied to EEG data recorded when subjects were viewing four prior-labeled emotion-inducing video clips from a publically available, validated database. Besides emotion category labels, the video clips also came with arousal scores. Our subjects were also asked to provide their own emotion labels. In total 30 subjects with age range 19–70 years participated in our study. Rather than relying on predefined frequency bands, we estimate multivariate sample entropy over multiple data-driven scales using the multivariate empirical mode decomposition (MEMD) technique and show that in this way we can discriminate between five self-reported emotions ($p<0.05$). These results could not be obtained by analyzing the relation between arousal scores and video clips, signal complexity and arousal scores, and self-reported emotions and traditional power spectral densities and their hemispheric asymmetries in the theta, alpha, beta, and gamma frequency bands. This shows that multivariate, multiscale sample entropy is a promising technique to discriminate multiple emotional states from EEG recordings.

All complex life on Earth is composed of ‘eukaryotic’ cells. Eukaryotes arose just once in 4 billion years, via an endosymbiosis — bacteria entered a simple host cell, evolving into mitochondria, the ‘powerhouses’ of complex cells. Mitochondria lost most of their genes, retaining only those needed for respiration, giving eukaryotes ‘multi-bacterial’ power without the costs of maintaining thousands of complete bacterial genomes. These energy savings supported a substantial expansion in nuclear genome size, and far more protein synthesis from each gene.

The efficiency of complex industrialized farming systems are compared to that of natural environmental systems while taking into account economic and environmental benefit as well as the needs of farmers and cattle.