BACKGROUND: Currently, the most popular methods for missing DNA-methylation value imputation rely on exploiting methylation patterns across multiple samples from the same population. However, if there is significant variability between individuals or limited data available, these methods might produce biased results. This situation has prompted researchers to seek alternative approaches for handling single-sample data, particularly in the context of personalized medicine. Accordingly, we propose One-Sample Methyl Imputation (OSMI), an imputation method that can also be used in single-sample applications. RESULTS: The proposed method in single-subject cases yielded an average imputation accuracy of RMSE = 0.2713 (95%-CI from 0.2696 to 0.2730) in β-value units (range: 0-1) based on real 450 K BeadChip data sets of 3,402 individuals. It is possible to take the affiliation of individual CpGs to CpG islands into account during the imputation of missing methylation values. This improves the imputation accuracy. In addition, the accuracy of imputation depends in general on the density of CpG sites on DNA-methylation microarrays and increases as the CpG site density increases. OSMI has low memory and computational requirements. CONCLUSIONS: OSMI uses a single methylome to impute missing values quickly at very low memory constraints. Its imputation accuracy is inferior to other methods if multiple samples are available and these samples are reasonably similar, but OSMI represents a useful addition to the imputation toolbox for the case of single-sample applications.

PURPOSE: Here we aimed to automatically classify human emotion earlier than is typically attempted. There is increasing evidence that the human brain differentiates emotional categories within 100-300 ms after stimulus onset. Therefore, here we evaluate the possibility of automatically classifying human emotions within the first 300 ms after the stimulus and identify the time-interval of the highest classification performance. METHODS: To address this issue, MEG signals of 17 healthy volunteers were recorded in response to three different picture stimuli (pleasant, unpleasant, and neutral pictures). Six Linear Discriminant Analysis (LDA) classifiers were used based on two binary comparisons (pleasant versus neutral and unpleasant versus neutral) and three different time-intervals (100-150 ms, 150-200 ms, and 200-300 ms post-stimulus). The selection of the feature subsets was performed by Genetic Algorithm and LDA. RESULTS: We demonstrated significant classification performances in both comparisons. The best classification performance was achieved with a median AUC of 0.83 (95 %- CI [0.71; 0.87]) classifying brain responses evoked by unpleasant and neutral stimuli within 100-150 ms, which is at least 850 ms earlier than attempted by other studies. CONCLUSION: Our results indicate that using the proposed algorithm, brain emotional responses can be significantly classified at very early stages of cortical processing (within 300 ms). Moreover, our results suggest that emotional processing in the human brain occurs within the first 100-150 ms.

In science and engineering mathematical modeling serves as a tool for the understanding of processes and systems and as a testing bed for several hypotheses, e.g., concerning the testing (prediction) of functional limits by simulations. A brief overview of current modeling strategies in brain research is given, spatial scales ranging from single neuron to large scale activity of and between brain regions are considered. The models are mainly time-invariant. Three time-variant modeling strategies, which enable a model-based signal analysis, are described and applied to large scale signals. The first is derived from adaptive filter theory and covers linear system and linear as well as nonlinear process models. The second is based on modeled brain source signals, i.e., the inverse problem must be solved. The third strategy consists of a generalization of Dynamic Causal Modeling (DCM); DCM is frequently used for analysis of directed interactions between brain structures. Examples are derived from neonatal electroencephalography (EEG) monitoring of preterm and fullterm newborns. A further example is based on high-density recordings of event-related potentials (ERPs) and shows the combination of a time-variant ERP-based source model, as a part of a realistic head model, with a multivariate process model to analyze the time evolution of interactions between source processes before and during the execution of a complex motoric task. In two other examples hemodynamic signals (functional magnetic resonance imaging-fMRI) are utilized for analysis of interactions between brain regions, where nonlinear, multivariate models are used.

This work addresses the problem of improving the generalization capabilities of continuous recurrent neural networks. The learning task is transformed into an optimal control framework in which the weights and the initial network state are treated as unknown controls. A new learning algorithm based on a variational formulation of Pontrayagin's maximum principle is proposed. Under reasonable assumptions, its convergence is discussed. Numerical examples are given that demonstrate an essential improvement of generalization capabilities after the learning process of a dynamic network.

This paper addresses the problem of training trajectories by means of continuous recurrent neural networks whose feedforward parts are multilayer perceptrons. Such networks can approximate a general nonlinear dynamic system with arbitrary accuracy. The learning process is transformed into an optimal control framework where the weights are the controls to be determined. A training algorithm based upon a variational formulation of Pontryagin's maximum principle is proposed for such networks. Computer examples demonstrating the efficiency of the given approach are also presented.

The problem of learning multiple continuous trajectories by means of recurrent neural networks with (in general) time-varying weights is addressed. The learning process is transformed into an optimal control framework where both the weights and the initial network state to be found are treated as controls. For such a task, a learning algorithm is proposed which is based on a variational formulation of Pontryagin's maximum principle. The convergence of this algorithm, under reasonable assumptions, is also investigated. Numerical examples of learning nontrivial two-class problems are presented which demonstrate the efficiency of the approach proposed.

This study addresses a problem of learning multiple continuous trajectories by means of recurrent neural networks with (in general) time-varying weights. The learning task is transformed into an optimal control problem where both the weights and initial network state to be found are treated as controls. Based on a variational formulation of Pontryagin's maximum principle, a new learning algorithm is proposed which generalizes the one given given previously (1999). Under reasonable assumptions, its convergence is also discussed. A numerical example of learning a two-class problem is presented which demonstrates the efficiency of the approach proposed.

This paper is concerned with a general learning (with arbitrary criterion and state-dependent constraints) of continuous trajectories by means of recurrent neural networks with time-varying weights. The learning process is transformed into an optimal control framework, where the weights to be found are treated as controls. A new learning algorithm based on a variational formulation of Pontryagin's maximum principle is proposed. This algorithm is shown to converge, under reasonable conditions, to an optimal solution. The neural networks with time-dependent weights make it possible to efficiently find an admissible solution (i.e., initial weights satisfying state constraints) which then serves as an initial guess to carry out a proper minimization of a given criterion. The proposed methodology may be directly applicable to both classification of temporal sequences and to optimal tracking of nonlinear dynamic systems. Numerical examples are also given which demonstrate the efficiency of the approach presented.