Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities.

In both the East and West, traditional teachings say that the mind and heart are somehow closely correlated, especially during spiritual practice. One difficulty in proving this objectively is that the natures of brain and heart activities are quite different. In this paper, we propose a methodology that uses wavelet entropy to measure the chaotic levels of both electroencephalogram (EEG) and electrocardiogram (ECG) data and show how this may be used to explore the potential coordination between the mind and heart under different experimental conditions. Furthermore, Statistical Parametric Mapping (SPM) was used to identify the brain regions in which the EEG wavelet entropy was the most affected by the experimental conditions. As an illustration, the EEG and ECG were recorded under two different conditions (normal rest and mindful breathing) at the beginning of an 8-week standard Mindfulness-based Stress Reduction (MBSR) training course (pretest) and after the course (posttest). Using the proposed method, the results consistently showed that the wavelet entropy of the brain EEG decreased during the MBSR mindful breathing state as compared to that during the closed-eye resting state. Similarly, a lower wavelet entropy of heartrate was found during MBSR mindful breathing. However, no difference in wavelet entropy during MBSR mindful breathing was found between the pretest and posttest. No correlation was observed between the entropy of brain waves and the entropy of heartrate during normal rest in all participants, whereas a significant correlation was observed during MBSR mindful breathing. Additionally, the most well-correlated brain regions were located in the central areas of the brain. This study provides a methodology for the establishment of evidence that mindfulness practice (i.e., mindful breathing) may increase the coordination between mind and heart activities.

Attention during functional tasks is associated with motor performance in children with developmental coordination disorder: A cross-sectional study.

This cross-sectional and exploratory study aimed to compare motor performance and electroencephalographic (EEG) attention levels in children with developmental coordination disorder (DCD) and those with typical development, and determine the relationship between motor performance and the real-time EEG attention level in children with DCD.Eighty-six children with DCD [DCD: n = 57; DCD and attention deficit hyperactivity disorder (ADHD): n = 29] and 99 children with typical development were recruited. Their motor performance was assessed with the Movement Assessment Battery for Children (MABC) and attention during the tasks of the MABC was evaluated by EEG.All children with DCD had higher MABC impairment scores and lower EEG attention scores than their peers (P < 0.05). After accounting for age, sex, body mass index, and physical activity level, the attention index remained significantly associated with the MABC total impairment score and explained 14.1% of the variance in children who had DCD but not ADHD (P = 0.009) and 17.5% of the variance in children with both DCD and ADHD (P = 0.007). Children with DCD had poorer motor performance and were less attentive to movements than their peers. Their poor motor performance may be explained by inattention.

Normalization of Pain-Evoked Neural Responses Using Spontaneous EEG Improves the Performance of EEG-Based Cross-Individual Pain Prediction.

An effective physiological pain assessment method that complements the gold standard of self-report is highly desired in pain clinical research and practice. Recent studies have shown that pain-evoked electroencephalography (EEG) responses could be used as a readout of perceived pain intensity. Existing EEG-based pain assessment is normally achieved by cross-individual prediction (i.e., to train a prediction model from a group of individuals and to apply the model on a new individual), so its performance is seriously hampered by the substantial inter-individual variability in pain-evoked EEG responses. In this study, to reduce the inter-individual variability in pain-evoked EEG and to improve the accuracy of cross-individual pain prediction, we examined the relationship between pain-evoked EEG, spontaneous EEG, and pain perception on a pain EEG dataset, where a large number of laser pulses (>100) with a wide energy range were delivered. Motivated by our finding that an individual's pain-evoked EEG responses is significantly correlated with his/her spontaneous EEG in terms of magnitude, we proposed a normalization method for pain-evoked EEG responses using one's spontaneous EEG to reduce the inter-individual variability. In addition, a nonlinear relationship between the level of pain perception and pain-evoked EEG responses was obtained, which inspired us to further develop a new two-stage pain prediction strategy, a binary classification of low-pain and high-pain trials followed by a continuous prediction for high-pain trials only, both of which used spontaneous-EEG-normalized magnitudes of evoked EEG responses as features. Results show that the proposed normalization strategy can effectively reduce the inter-individual variability in pain-evoked responses, and the two-stage pain prediction method can lead to a higher prediction accuracy.

Decoding Subjective Intensity of Nociceptive Pain from Pre-stimulus and Post-stimulus Brain Activities.

Pain is a highly subjective experience. Self-report is the gold standard for pain assessment in clinical practice, but it may not be available or reliable in some populations. Neuroimaging data, such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), have the potential to be used to provide physiology-based and quantitative nociceptive pain assessment tools that complements self-report. However, existing neuroimaging-based nociceptive pain assessments only rely on the information in pain-evoked brain activities, but neglect the fact that the perceived intensity of pain is also encoded by ongoing brain activities prior to painful stimulation. Here, we proposed to use machine learning algorithms to decode pain intensity from both pre-stimulus ongoing and post-stimulus evoked brain activities. Neural features that were correlated with intensity of laser-evoked nociceptive pain were extracted from high-dimensional pre- and post-stimulus EEG and fMRI activities using partial least-squares regression (PLSR). Further, we used support vector machine (SVM) to predict the intensity of pain from pain-related time-frequency EEG patterns and BOLD-fMRI patterns. Results showed that combining predictive information in pre- and post-stimulus brain activities can achieve significantly better performance in classifying high-pain and low-pain and in predicting the rating of perceived pain than only using post-stimulus brain activities. Therefore, the proposed pain prediction method holds great potential in basic research and clinical applications.

N1 Magnitude of Auditory Evoked Potentials and Spontaneous Functional Connectivity Between Bilateral Heschl's Gyrus Are Coupled at Interindividual Level.

N1 component of auditory evoked potentials is extensively used to investigate the propagation and processing of auditory inputs. However, the substantial interindividual variability of N1 could be a possible confounding factor when comparing different individuals or groups. Therefore, identifying the neuronal mechanism and origin of the interindividual variability of N1 is crucial in basic research and clinical applications. This study is aimed to use simultaneously recorded electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data to investigate the coupling between N1 and spontaneous functional connectivity (FC). EEG and fMRI data were simultaneously collected from a group of healthy individuals during a pure-tone listening task. Spontaneous FC was estimated from spontaneous blood oxygenation level-dependent (BOLD) signals that were isolated by regressing out task evoked BOLD signals from raw BOLD signals and then was correlated to N1 magnitude across individuals. It was observed that spontaneous FC between bilateral Heschl's gyrus was significantly and positively correlated with N1 magnitude across individuals (Spearman's R = 0.829, p < 0.001). The specificity of this observation was further confirmed by two whole-brain voxelwise analyses (voxel-mirrored homotopic connectivity analysis and seed-based connectivity analysis). These results enriched our understanding of the functional significance of the coupling between event-related brain responses and spontaneous brain connectivity, and hold the potential to increase the applicability of brain responses as a probe to the mechanism underlying pathophysiological conditions.

Entrainment of chaotic activities in brain and heart during MBSR mindfulness training.

The activities of the brain and the heart are dynamic, chaotic, and possibly intrinsically coordinated. This study aims to investigate the effect of Mindfulness-Based Stress Reduction (MBSR) program on the chaoticity of electronic activities of the brain and the heart, and to explore their potential correlation. Electroencephalogram (EEG) and electrocardiogram (ECG) were recorded at the beginning of an 8-week standard MBSR training course and after the course. EEG spectrum analysis was carried out, wavelet entropies (WE) of EEG (together with reconstructed cortical sources) and heart rate were calculated, and their correlation was investigated. We found enhancement of EEG power of alpha and beta waves and lowering of delta waves power during MBSR training state as compared to normal resting state. Wavelet entropy analysis indicated that MBSR mindfulness meditation could reduce the chaotic activities of both EEG and heart rate as a change of state. However, longitudinal change of trait may need more long-term training. For the first time, our data demonstrated that the chaotic activities of the brain and the heart became more coordinated during MBSR training, suggesting that mindfulness training may increase the entrainment between mind and body. The 3D brain regions involved in the change in mental states were identified.

Repetitive Religious Chanting Modulates the Late-Stage Brain Response to Fear- and Stress-Provoking Pictures.

Chanting and praying are among the most popular religious activities, which are said to be able to alleviate people's negative emotions. However, the neural mechanisms underlying this mental exercise and its temporal course have hardly been investigated. Here, we used event-related potentials (ERPs) to explore the effects of chanting the name of a Buddha (Amitabha) on the brain's response to viewing negative pictures that were fear- and stress-provoking. We recorded and analyzed electroencephalography (EEG) data from 21 Buddhists with chanting experience as they viewed negative and neutral pictures. Participants were instructed to chant the names of Amitabha or Santa Claus silently to themselves or simply remain silent (no-chanting condition) during picture viewing. To measure the physiological changes corresponding to negative emotions, electrocardiogram and galvanic skin response data were also collected. Results showed that viewing negative pictures (vs. neutral pictures) increased the amplitude of the N1 component in all the chanting conditions. The amplitude of late positive potential (LPP) also increased when the negative pictures were viewed under the no-chanting and the Santa Claus condition. However, increased LPP was not observed when chanting Amitabha. The ERP source analysis confirmed this finding and showed that increased LPP mainly originated from the central-parietal regions of the brain. In addition, the participants' heart rates decreased significantly when viewing negative pictures in the Santa Claus condition. The no-chanting condition had a similar decreasing trend although not significant. However, while chanting Amitabha and viewing negative pictures participants' heart rate did not differ significantly from that observed during neutral picture viewing. It is possible that the chanting of Amitabha might have helped the participants to develop a religious schema and neutralized the effect of the negative stimuli. These findings echo similar research findings on Christian religious practices and brain responses to negative stimuli. Hence, prayer/religious practices may have cross-cultural universality in emotion regulation. This study shows for the first time that Buddhist chanting, or in a broader sense, repetition of religious prayers will not modulate brain responses to negative stimuli during the early perceptual stage, but only during the late-stage emotional/cognitive processing.

Alpha and gamma oscillation amplitudes synergistically predict the perception of forthcoming nociceptive stimuli.

Ongoing fluctuations of intrinsic cortical networks determine the dynamic state of the brain, and influence the perception of forthcoming sensory inputs. The functional state of these networks is defined by the amplitude and phase of ongoing oscillations of neuronal populations at different frequencies. The contribution of functionally different cortical networks has yet to be elucidated, and only a clear dependence of sensory perception on prestimulus alpha oscillations has been clearly identified. Here, we combined electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) in a large sample of healthy participants to investigate how ongoing fluctuations in the activity of different cortical networks affect the perception of subsequent nociceptive stimuli. We observed that prestimulus EEG oscillations in the alpha (at bilateral central regions) and gamma (at parietal regions) bands negatively modulated the perception of subsequent stimuli. Combining information about alpha and gamma oscillations predicted subsequent perception significantly more accurately than either measure alone. In a parallel experiment, we found that prestimulus fMRI activity also modulated the perception of subsequent stimuli: perceptual ratings were higher when the BOLD signal was higher in nodes of the sensorimotor network and lower in nodes of the default mode network. Similar to what observed in the EEG data, prediction accuracy was improved when the amplitude of prestimulus BOLD signals in both networks was combined. These findings provide a comprehensive physiological basis to the idea that dynamic changes in brain state determine forthcoming behavioral outcomes. Hum Brain Mapp 37:501-514, 2016. © 2015 Wiley Periodicals, Inc.

Task-related functional connectivity dynamics in a block-designed visual experiment.

Studying task modulations of brain connectivity using functional magnetic resonance imaging (fMRI) is critical to understand brain functions that support cognitive and affective processes. Existing methods such as psychophysiological interaction (PPI) and dynamic causal modeling (DCM) usually implicitly assume that the connectivity patterns are stable over a block-designed task with identical stimuli. However, this assumption lacks empirical verification on high-temporal resolution fMRI data with reliable data-driven analysis methods. The present study performed a detailed examination of dynamic changes of functional connectivity (FC) in a simple block-designed visual checkerboard experiment with a sub-second sampling rate (TR = 0.645 s) by estimating time-varying correlation coefficient (TVCC) between BOLD responses of different brain regions. We observed reliable task-related FC changes (i.e., FCs were transiently decreased after task onset and went back to the baseline afterward) among several visual regions of the bilateral middle occipital gyrus (MOG) and the bilateral fusiform gyrus (FuG). Importantly, only the FCs between higher visual regions (MOG) and lower visual regions (FuG) exhibited such dynamic patterns. The results suggested that simply assuming a sustained FC during a task block may be insufficient to capture distinct task-related FC changes. The investigation of FC dynamics in tasks could improve our understanding of condition shifts and the coordination between different activated brain regions.

Joint source separation of simultaneous EEG-fMRI recording in two experimental conditions using common spatial patterns.

Simultaneous collection of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data has become increasingly popular in neuroscientific studies, because it can provide neural information with both high spatial and temporal resolution. In order to maximally utilize the information contained in simultaneous EEG-fMRI recording, many sophisticated multimodal data-mining methods, such as joint ICA, have been developed. However, these methods normally deal with data recorded in one experimental condition, and they cannot effectively extract information on activities that are distinct in two conditions. In this paper, a new data decomposition method called joint common spatial pattern (jCSP) is proposed. Compared with previous methods, the jCSP method exploits inter-conditional difference in the strength of brain source activities to achieve source separation, and is able to uncover the source activities with the strongest discriminative power. A group analysis based on clustering is further proposed to reveal distinctive jCSP patterns at group level. We applied joint CSP to a simultaneous EEG-fMRI dataset collected from 21 subjects under two different resting-state conditions (eyes-closed and eyes-open). Results show a distinct dynamic pattern shared by EEG alpha power and fMRI signal during eyes-open resting-state.

An automated and fast approach to detect single-trial visual evoked potentials with application to brain-computer interface.

OBJECTIVE: This study aims (1) to develop an automated and fast approach for detecting visual evoked potentials (VEPs) in single trials and (2) to apply the single-trial VEP detection approach in designing a real-time and high-performance brain-computer interface (BCI) system. METHODS: The single-trial VEP detection approach uses common spatial pattern (CSP) as a spatial filter and wavelet filtering (WF) a temporal-spectral filter to jointly enhance the signal-to-noise ratio (SNR) of single-trial VEPs. The performance of the joint spatial-temporal-spectral filtering approach was assessed in a four-command VEP-based BCI system. RESULTS: The offline classification accuracy of the BCI system was significantly improved from 67.6±12.5% (raw data) to 97.3±2.1% (data filtered by CSP and WF). The proposed approach was successfully implemented in an online BCI system, where subjects could make 20 decisions in one minute with classification accuracy of 90%. CONCLUSIONS: The proposed single-trial detection approach is able to obtain robust and reliable VEP waveform in an automatic and fast way and it is applicable in VEP based online BCI systems. SIGNIFICANCE: This approach provides a real-time and automated solution for single-trial detection of evoked potentials or event-related potentials (EPs/ERPs) in various paradigms, which could benefit many applications such as BCI and intraoperative monitoring.

Genome-wide analysis of DNA copy number alterations and loss of heterozygosity in intracranial germ cell tumors.

BACKGROUNDS: Intracranial germ cell tumors (GCTs) are rare and heterogeneous with very little is known about their pathogenesis and underlying genetic abnormalities. PROCEDURES: In order to identify candidate genes and pathways which are involved in the pathogenesis of these tumors, we have profiled 62 intracranial GCTs for DNA copy number alterations (CNAs) and loss of heterozygosity (LOH) by using single nucleotide polymorphism (SNP) array and quantitative real time PCR (qPCR). RESULTS: Initially 27 cases of tumor tissues with matched blood samples were fully analyzed by SNP microarray and qPCR. Statistical analysis using the genomic identification of significant targets in cancer (GISTIC) tool identified 10 regions of significant copy number gain and 11 regions of significant copy number loss. While overall pattern of genomic aberration was similar between germinoma and nongerminomatous germ cell tumors (NGGCTs), a few subtype-specific peak regions were identified. Analysis by SNP array and qPCR was replicated using an independent cohort of 35 cases. CONCLUSIONS: Frequent aberrations of CCND2 (12p13) and RB1 (13q14) suggest that Cyclin/CDK-RB-E2F pathway might play a critical role in the pathogenesis of intracranial GCTs. Frequent gain of PRDM14 (8q13) implies that transcriptional regulation of primordial germ cell specification might be an important factor in the development of this tumor.

Single-trial laser-evoked potentials feature extraction for prediction of pain perception.

Pain is a highly subjective experience, and the availability of an objective assessment of pain perception would be of great importance for both basic and clinical applications. The objective of the present study is to develop a novel approach to extract pain-related features from single-trial laser-evoked potentials (LEPs) for classification of pain perception. The single-trial LEP feature extraction approach combines a spatial filtering using common spatial pattern (CSP) and a multiple linear regression (MLR). The CSP method is effective in separating laser-evoked EEG response from ongoing EEG activity, while MLR is capable of automatically estimating the amplitudes and latencies of N2 and P2 from single-trial LEP waveforms. The extracted single-trial LEP features are used in a Naïve Bayes classifier to classify different levels of pain perceived by the subjects. The experimental results show that the proposed single-trial LEP feature extraction approach can effectively extract pain-related LEP features for achieving high classification accuracy.

Single-trial detection of visual evoked potentials by common spatial patterns and wavelet filtering for brain-computer interface.

Event-related potentials (ERPs) are widely used in brain-computer interface (BCI) systems as input signals conveying a subject's intention. A fast and reliable single-trial ERP detection method can be used to develop a BCI system with both high speed and high accuracy. However, most of single-trial ERP detection methods are developed for offline EEG analysis and thus have a high computational complexity and need manual operations. Therefore, they are not applicable to practical BCI systems, which require a low-complexity and automatic ERP detection method. This work presents a joint spatial-time-frequency filter that combines common spatial patterns (CSP) and wavelet filtering (WF) for improving the signal-to-noise (SNR) of visual evoked potentials (VEP), which can lead to a single-trial ERP-based BCI.

Time-varying correlation coefficients estimation and its application to dynamic connectivity analysis of fMRI.

Exploration of the dynamics of functional brain connectivity based on the correlation coefficients of functional magnetic resonance imaging (fMRI) data is important for understanding the brain mechanisms. Because fMRI data are time-varying in nature, the functional connectivity shows substantial fluctuations and dynamic characteristics. However, an effective method for estimating time-varying functional connectivity is lacking, which is mainly due to the difficulty in choosing an appropriate window to localize the time-varying correlation coefficients (TVCC). This paper introduces a novel method for adaptively estimating the TVCC of non-stationary signals and studies its application to infer dynamic functional connectivity of fMRI data in a visual task. The proposed method employs a sliding window having a certain bandwidth to estimate the TVCC locally and the window bandwidths are selected adaptively by a local plug-in rule to minimize the mean squared error. The results show that the functional connectivity changes in the visual task are transient, which suggests that simply assuming sustained connectivity changes during task period might not be sufficient to capture dynamic connectivity changes induced by tasks.

Gene regulatory network discovery using pairwise Granger causality.

Discovery of gene regulatory network from gene expression data can yield a useful insight to drug development. Among the methods applied to time-series data, Granger causality (GC) has emerged as a powerful tool with several merits. Since gene expression data usually have a much larger number of genes than time points therefore a full model cannot be applied in a straightforward manner, GC is often applied to genes pair wisely. In this study, the authors first investigate with synthetic data how spurious causalities (false discoveries) may arise because of the use of pairwise rather than full-model GC detection. Furthermore, spurious causalities may also arise if the order of the vector autoregressive model is not high enough. As a remedy, the authors demonstrate that model validation techniques can effectively reduce the number of false discoveries. Then, they apply pairwise GC with model validation to the real human HeLa cell-cycle dataset. They find that Akaike information criterion is generally most suitable for determining model order, but precaution should be taken for extremely short time series. With the authors proposed implementation, degree distributions and network hubs are obtained and compared with existing results, giving a new observation that the hubs tend to act as sources rather than receivers of interactions.

An integrated approach for identifying wrongly labelled samples when performing classification in microarray data.

BACKGROUND: Using hybrid approach for gene selection and classification is common as results obtained are generally better than performing the two tasks independently. Yet, for some microarray datasets, both classification accuracy and stability of gene sets obtained still have rooms for improvement. This may be due to the presence of samples with wrong class labels (i.e. outliers). Outlier detection algorithms proposed so far are either not suitable for microarray data, or only solve the outlier detection problem on their own. RESULTS: We tackle the outlier detection problem based on a previously proposed Multiple-Filter-Multiple-Wrapper (MFMW) model, which was demonstrated to yield promising results when compared to other hybrid approaches (Leung and Hung, 2010). To incorporate outlier detection and overcome limitations of the existing MFMW model, three new features are introduced in our proposed MFMW-outlier approach: 1) an unbiased external Leave-One-Out Cross-Validation framework is developed to replace internal cross-validation in the previous MFMW model; 2) wrongly labeled samples are identified within the MFMW-outlier model; and 3) a stable set of genes is selected using an L1-norm SVM that removes any redundant genes present. Six binary-class microarray datasets were tested. Comparing with outlier detection studies on the same datasets, MFMW-outlier could detect all the outliers found in the original paper (for which the data was provided for analysis), and the genes selected after outlier removal were proven to have biological relevance. We also compared MFMW-outlier with PRAPIV (Zhang et al., 2006) based on same synthetic datasets. MFMW-outlier gave better average precision and recall values on three different settings. Lastly, artificially flipped microarray datasets were created by removing our detected outliers and flipping some of the remaining samples' labels. Almost all the 'wrong' (artificially flipped) samples were detected, suggesting that MFMW-outlier was sufficiently powerful to detect outliers in high-dimensional microarray datasets.

Detecting outlier samples in microarray data.

In this paper, we address the problem of detecting outlier samples with highly different expression patterns in microarray data. Although outliers are not common, they appear even in widely used benchmark data sets and can negatively affect microarray data analysis. It is important to identify outliers in order to explore underlying experimental or biological problems and remove erroneous data. We propose an outlier detection method based on principal component analysis (PCA) and robust estimation of Mahalanobis distances that is fully automatic. We demonstrate that our outlier detection method identifies biologically significant outliers with high accuracy and that outlier removal improves the prediction accuracy of classifiers. Our outlier detection method is closely related to existing robust PCA methods, so we compare our outlier detection method to a prominent robust PCA method.

Genome-scale cluster analysis of replicated microarrays using shrinkage correlation coefficient.

BACKGROUND: Currently, clustering with some form of correlation coefficient as the gene similarity metric has become a popular method for profiling genomic data. The Pearson correlation coefficient and the standard deviation (SD)-weighted correlation coefficient are the two most widely-used correlations as the similarity metrics in clustering microarray data. However, these two correlations are not optimal for analyzing replicated microarray data generated by most laboratories. An effective correlation coefficient is needed to provide statistically sufficient analysis of replicated microarray data. RESULTS: In this study, we describe a novel correlation coefficient, shrinkage correlation coefficient (SCC), that fully exploits the similarity between the replicated microarray experimental samples. The methodology considers both the number of replicates and the variance within each experimental group in clustering expression data, and provides a robust statistical estimation of the error of replicated microarray data. The value of SCC is revealed by its comparison with two other correlation coefficients that are currently the most widely-used (Pearson correlation coefficient and SD-weighted correlation coefficient) using statistical measures on both synthetic expression data as well as real gene expression data from Saccharomyces cerevisiae. Two leading clustering methods, hierarchical and k-means clustering were applied for the comparison. The comparison indicated that using SCC achieves better clustering performance. Applying SCC-based hierarchical clustering to the replicated microarray data obtained from germinating spores of the fern Ceratopteris richardii, we discovered two clusters of genes with shared expression patterns during spore germination. Functional analysis suggested that some of the genetic mechanisms that control germination in such diverse plant lineages as mosses and angiosperms are also conserved among ferns. CONCLUSION: This study shows that SCC is an alternative to the Pearson correlation coefficient and the SD-weighted correlation coefficient, and is particularly useful for clustering replicated microarray data. This computational approach should be generally useful for proteomic data or other high-throughput analysis methodology.

Fast network component analysis (FastNCA) for gene regulatory network reconstruction from microarray data.

MOTIVATION: Recently developed network component analysis (NCA) approach is promising for gene regulatory network reconstruction from microarray data. The existing NCA algorithm is an iterative method which has two potential limitations: computational instability and multiple local solutions. The subsequently developed NCA-r algorithm with Tikhonov regularization can help solve the first issue but cannot completely handle the second one. Here we develop a novel Fast Network Component Analysis (FastNCA) algorithm which has an analytical solution that is much faster and does not have the above limitations. RESULTS: Firstly FastNCA is compared to NCA and NCA-r using synthetic data. The reconstruction of FastNCA is more accurate than that of NCA-r and comparable to that of properly converged NCA. FastNCA is not sensitive to the correlation among the input signals, while its performance does degrade a little but not as dramatically as that of NCA. Like NCA, FastNCA is not very sensitive to small inaccuracies in a priori information on the network topology. FastNCA is about several tens times faster than NCA and several hundreds times faster than NCA-r. Then, the method is applied to real yeast cell-cycle microarray data. The activities of the estimated cell-cycle regulators by FastNCA and NCA-r are compared to the semi-quantitative results obtained independently by Lee et al. (2002). It is shown here that there is a greater agreement between the results of FastNCA and Lee's, which is represented by the ratio 23/33, than that between the results of NCA-r and Lee's, which is 14/33. AVAILABILITY: Software and supplementary materials are available from http://www.eee.hku.hk/~cqchang/FastNCA.htm