Improved measures of phase-coupling between spikes and the Local Field Potential

An important tool to study rhythmic neuronal synchronization is provided by relating spiking activity to the Local Field Potential (LFP). Two types of interdependent spike-LFP measures exist. The first approach is to directly quantify the consistency of single spike-LFP phases across spikes, referred to here as point-field phase synchronization measures. We show that conventional point-field phase synchronization measures are sensitive not only to the consistency of spike-LFP phases, but are also affected by statistical dependencies between spike-LFP phases, caused by e.g. non-Poissonian history-effects within spike trains such as bursting and refractoriness. To solve this problem, we develop a new pairwise measure that is not biased by the number of spikes and not affected by statistical dependencies between spike-LFP phases. The second approach is to quantify, similar to EEG-EEG coherence, the consistency of the relative phase between spike train and LFP signals across trials instead of across spikes, referred to here as spike train to field phase synchronization measures. We demonstrate an analytical relationship between point-field and spike train to field phase synchronization measures. Based on this relationship, we prove that the spike train to field pairwise phase consistency (PPC), a quantity closely related to the squared spike-field coherence, is a monotonically increasing function of the number of spikes per trial. This derived relationship is exact and analytic, and takes a linear form for weak phase-coupling. To solve this problem, we introduce a corrected version of the spike train to field PPC that is independent of the number of spikes per trial. Finally, we address the problem that dependencies between spike-LFP phase and the number of spikes per trial can cause spike-LFP phase synchronization measures to be biased by the number of trials. We show how to modify the developed point-field and spike train to field phase synchronization measures in order to make them unbiased by the number of trials.     

Emergence of Metastable State Dynamics in Interconnected Cortical Networks with Propagation Delays

The importance of the large number of thin-diameter and unmyelinated axons that connect different cortical areas is unknown. The pronounced propagation delays in these axons may prevent synchronization of cortical networks and therefore hinder efficient information integration and processing. Yet, such global information integration across cortical areas is vital for higher cognitive function. We hypothesized that delays in communication between cortical areas can disrupt synchronization and therefore enhance the set of activity trajectories and computations interconnected networks can perform. To evaluate this hypothesis, we studied the effect of long-range cortical projections with propagation delays in interconnected large-scale cortical networks that exhibited spontaneous rhythmic activity. Long-range connections with delays caused the emergence of metastable, spatio-temporally distinct activity states between which the networks spontaneously transitioned. Interestingly, the observed activity patterns correspond to macroscopic network dynamics such as globally synchronized activity, propagating wave fronts, and spiral waves that have been previously observed in neurophysiological recordings from humans and animal models. Transient perturbations with simulated transcranial alternating current stimulation (tACS) confirmed the multistability of the interconnected networks by switching the networks between these metastable states. Our model thus proposes that slower long-range connections enrich the landscape of activity states and represent a parsimonious mechanism for the emergence of multistability in cortical networks. These results further provide a mechanistic link between the known deficits in connectivity and cortical state dynamics in neuropsychiatric illnesses such as schizophrenia and autism, as well as suggest non-invasive brain stimulation as an effective treatment for these illnesses.     

Synchronization between beating cilia.

A novel quantitative parameter is proposed to define and measure the degree of synchronization between two small ciliary areas. These areas can be close to or far from one another. The Pearson correlation factor is used to define the degree of synchronization by a single number. This approach is based on a computerized, dual photoelectric method which simulataneously measures the scattered light from two small areas on the ciliary epithelium or its tissue culture. The measurements were performed on tissue culture from frog's palate epithelium. It was found that: (a) the degree of synchronization decreases, as a function of distance; (b) the correlation is fairly high even at relatively large separations, when measured on the same patch; (c) on a given patch the synchronization factor is independent of the direction of the metachronal wave; (d) close disconnected ciliary cells exhibit fairly high correlation; (e) disconnected randomly choosen ciliary cells at relatively large separation distances exhibit relatively low correlation, smaller by a factor of 2 than the correlation factor at the same distances when measured along the metachronal wave; (f) the average frequencies' ratio and the metachronal wavelength can be used as first-order indicators of ciliary synchronization; (g) there is a spread of metachronal wavelengths even over a single well-organized patch.     

The relationship between radiosensitivity and cell kinetic effects after low- and high-dose-rate irradiation in five human tumors in nude mice

Radiation-induced synchronization of cells in the radiosensitive G2 phase can, theoretically, be applied to individual tailoring of fractionation schemes, possibly rendering radiotherapy more effective. For that purpose, cell cycle perturbations were studied in five xenografts by flow cytometry. A dose-dependent increase of cells in G2 phase was noticed in all five tumor cell lines after high-dose-rate irradiation, and in four tumor cell lines after low-dose-rate irradiation. The timing of maximum accumulation was not related to dose, but coincided with the cell cycle time of the respective tumors. Furthermore, the increase in the number of cells in G2 phase correlated with the radiosensitivity of the tumors as assessed by measurements of regrowth delays. The observed synchronization provides a basis for further investigations on the relevance of radiation-induced cell cycle synchrony to the effectiveness of fractionated radiotherapy.     

Adaptive Cluster Synchronization of Directed Complex Networks with Time Delays

This paper studied the cluster synchronization of directed complex networks with time delays. It is different from undirected networks, the coupling configuration matrix of directed networks cannot be assumed as symmetric or irreducible. In order to achieve cluster synchronization, this paper uses an adaptive controller on each node and an adaptive feedback strategy on the nodes which in-degree is zero. Numerical example is provided to show the effectiveness of main theory. This method is also effective when the number of clusters is unknown. Thus, it can be used in the community recognizing of directed complex networks.     

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others.     

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.     

USE OF INDIVIDUAL DIFFERENCES SCALING FOR SENSORY STUDIES: SIMULATED RECOVERY OF STRUCTURE UNDER VARIOUS MISSING VALUE RATES AND ERROR LEVELS

The use of Individual Differences Scaling in sensory studies has been limited because the number of pairwise comparisons in a complete design can be prohibitively large. This study examines the effect of different levels of error and missing data on recovery of true structure by Individual Difference Scaling for the normal range of assessors and stimuli (8–16) used by sensory workers. Recovery was very good for a missing value rate of 20%. It was good for 40% provided that the number of stimuli was high, but deteriorated sharply at 60% missing data. The effect of superimposing random error on to the true structure indicated that a large error rate gave poor recovery. It is concluded that up to 40% of the distances in a complete design could be excluded, provided that replicate measurements indicated error levels were not severe.     

Optimal stepwise experimental design for pairwise functional interaction studies

MOTIVATION: Pairwise experimental perturbation is increasingly used to probe gene and protein function because these studies offer powerful insight into the activity and regulation of biological systems. Symmetric two-dimensional datasets, such as pairwise genetic interactions are amenable to an optimally designed measurement procedure because of the equivalence of cases and conditions where fewer experimental measurements may be required to extract the underlying structure. RESULTS: We show that optimal experimental design can provide improvements in efficiency when collecting data in an iterative manner. We develop a method built on a statistical clustering model for symmetric data and the Fisher information uncertainty estimates, and we also provide simple heuristic approaches that have comparable performance. Using yeast epistatic miniarrays as an example, we show that correct assignment of the major subnetworks could be achieved with <50% of the measurements in the complete dataset. Optimization is likely to become critical as pairwise functional studies extend to more complex mammalian systems where all by all experiments are currently intractable.     

An iterative refinement algorithm for consistency based multiple structural alignment methods

MOTIVATION: Multiple STructural Alignment (MSTA) provides valuable information for solving problems such as fold recognition. The consistency-based approach tries to find conflict-free subsets of alignments from a pre-computed all-to-all Pairwise Alignment Library (PAL). If large proportions of conflicts exist in the library, consistency can be hard to get. On the other hand, multiple structural superposition has been used in many MSTA methods to refine alignments. However, multiple structural superposition is dependent on alignments, and a superposition generated based on erroneous alignments is not guaranteed to be the optimal superposition. Correcting errors after making errors is not as good as avoiding errors from the beginning. Hence it is important to refine the pairwise library to reduce the number of conflicts before any consistency-based assembly. RESULTS: We present an algorithm, Iterative Refinement of Induced Structural alignment (IRIS), to refine the PAL. A new measurement for the consistency of a library is also proposed. Experiments show that our algorithm can greatly improve T-COFFEE performance for less consistent pairwise alignment libraries. The final multiple alignment outperforms most state-of-the-art MSTA algorithms at assembling 15 transglycosidases. Results on three other benchmarks showed that the algorithm consistently improves multiple alignment performance. AVAILABILITY: The C++ code of the algorithm is available upon request.     

Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach

This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.     

The number of segregating sites in expanding human populations, with implications for estimates of demographic parameters

The frequency distribution of pairwise differences between sequences of mtDNA has recently been used to estimate the size of human populations before and after a hypothetical episode of rapid population growth and the time at which the population grew. To test the internal consistency of this method, we used three different sets of human mtDNA data and the corresponding demographic parameters estimated from the distribution of pairwise differences to determine by simulation the expected number of segregating sites, S, and its empirical distribution. The results indicate that the observed values of S are significantly lower than expected in two of three cases under the assumption of the infinite-sites model. Further simulations in which mutations were allowed to occur more than once at the same site and in which there was variation in mutation rate among sites show that the expected number of segregating sites can be much lower than under the infinite-site assumption. Nevertheless, the observed value of S is still significantly different from the value expected under the expansion hypothesis in two of three cases.      

A polynomial time solvable formulation of multiple sequence alignment.

Since traditional multiple alignment formulations are NP-hard, heuristics are commonly employed to find acceptable alignments with no guaranteed performance bound. This causes a substantial difficulty in understanding what the resulting alignment means and in assessing the quality of these alignments. We propose an alternative formulation of multiple alignment based on the idea of finding a multiple alignment of k sequences which preserves k - 1 pairwise alignments as specified by edges of a given tree. Although it is well known that such a preserving alignment always exists, it did not become a mainstream method for multiple alignment since it seems that a lot of information is lost from ignoring pairwise similarities outside the tree. In contrast, by using pairwise alignments that incorporate consistency information from other sequences, we show that it is possible to obtain very good accuracy with the preserving alignment formulation. We show that a reasonable objective function to use is to find the shortest preserving alignment, and, by a reduction to a graph-theoretic problem, that the problem of finding the shortest preserving multiple alignment can be solved in polynomial time. We demonstrate the success of this approach on three sets of benchmark multiple alignments by using consistency-based pairwise alignments from the first stage of two of the best performing progressive alignment algorithms TCoffee and ProbCons and replace the second heuristic progressive step of these algorithms by the exact preserving alignment step. We apply this strategy to TCoffee and show that our approach outperforms TCoffee on two of the three test sets. We apply the strategy to a variant of ProbCons with no iterative refinements and show that our approach achieves similar or better accuracy except on one test set. We also compare our performance to ProbCons with iterative refinements and show that our approach achieves similar or better accuracy on many subcategories even without further refinements. The most important advantage of the preserving alignment formulation is that we are certain that we can solve the problem in polynomial time without using a heuristic. A software program implementing this approach (PSAlign) is available at http://faculty.cs.tamu.edu/shsze/psalign.     

Statistical Properties of Pairwise Distances between Leaves on a Random Yule Tree

A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number of pairs separated by a certain time distance. This number turns out to follow a increasing exponential function. This property of a Yule tree can serve as a simple test for empirical data to be well described by a Yule process. We further use this recursive method to calculate the expected number of the n-most closely related pairs of leaves and the number of cherries separated by a certain time distance. To make our results more useful for realistic scenarios, we explicitly take into account that the leaves of a tree may be incompletely sampled and derive a criterion for poorly sampled phylogenies. We show that our result can account for empirical data, using two families of birds species.     

Synchronized dynamics of cortical neurons with time-delay feedback

The dynamics of three mutually coupled cortical neurons with time delays in the coupling are explored numerically and analytically. The neurons are coupled in a line, with the middle neuron sending a somewhat stronger projection to the outer neurons than the feedback it receives, to model for instance the relay of a signal from primary to higher cortical areas. For a given coupling architecture, the delays introduce correlations in the time series at the time-scale of the delay. It was found that the middle neuron leads the outer ones by the delay time, while the outer neurons are synchronized with zero lag times. Synchronization is found to be highly dependent on the synaptic time constant, with faster synapses increasing both the degree of synchronization and the firing rate. Analysis shows that pre-synaptic input during the inter-spike interval stabilizes the synchronous state, even for arbitrarily weak coupling, and independent of the initial phase. The finding may be of significance to synchronization of large groups of cells in the cortex that are spatially distanced from each other.     

Online Detection of Fetal Acidemia during Labour by Testing Synchronization of EEG and Heart Rate: A Prospective Study in Fetal Sheep

Severe fetal acidemia during labour can result in life-lasting neurological deficits, but the timely detection of this condition is often not possible. This is because the positive predictive value (PPV) of fetal heart rate (FHR) monitoring, the mainstay of fetal health surveillance during labour, to detect concerning fetal acidemia is around 50%. In fetal sheep model of human labour, we reported that severe fetal acidemia (pH<7.00) during repetitive umbilical cord occlusions (UCOs) is preceded ∼60 minutes by the synchronization of electroencephalogram (EEG) and FHR. However, EEG and FHR are cyclic and noisy, and although the synchronization might be visually evident, it is challenging to detect automatically, a necessary condition for bedside utility. Here we present and validate a novel non-parametric statistical method to detect fetal acidemia during labour by using EEG and FHR. The underlying algorithm handles non-stationary and noisy data by recording number of abnormal episodes in both EEG and FHR. A logistic regression is then deployed to test whether these episodes are significantly related to each other. We then apply the method in a prospective study of human labour using fetal sheep model (n = 20). Our results render a PPV of 68% for detecting impending severe fetal acidemia ∼60 min prior to pH drop to less than 7.00 with 100% negative predictive value. We conclude that this method has a great potential to improve PPV for detection of fetal acidemia when it is implemented at the bedside. We outline directions for further refinement of the algorithm that will be achieved by analyzing larger data sets acquired in prospective human pilot studies.     

mILD: a tool for constructing and analyzing matrices of pairwise phylogenetic character incongruence tests

SUMMARY: Pairwise comparisons of disagreement in phylogenetic datasets offer a powerful tool for isolating historical incongruence for closer analysis. Statistically significant phylogenetic character incongruence may reflect important differences in evolutionary history, such as horizontal gene transfer. Such testing can also be used to specify possible combinations of datasets for further phylogenetic analysis. The process of comparing multiple datasets can be very time consuming, and it is sometimes unclear how to combine data partitions given the observed patterns of incongruence. Here we present an application that automates the process of making pairwise comparisons between large numbers of phylogenetic datasets using the Incongruence Length Difference (ILD) test. The application also implements strategies for data combination based on the patterns of incongruence observed in pairwise comparisons.     

Characterizing the Propagation of Uterine Electrophysiological Signals Recorded with a Multi-Sensor Abdominal Array in Term Pregnancies

The objective of this study was to quantify the number of segments that have contractile activity and determine the propagation speed from uterine electrophysiological signals recorded over the abdomen. The uterine magnetomyographic (MMG) signals were recorded with a 151 channel SARA (SQUID Array for Reproductive Assessment) system from 36 pregnant women between 37 and 40 weeks of gestational age. The MMG signals were scored and segments were classified based on presence of uterine contractile burst activity. The sensor space was then split into four quadrants and in each quadrant signal strength at each sample was calculated using center-of-gravity (COG). To this end, the cross-correlation analysis of the COG was performed to calculate the delay between pairwise combinations of quadrants. The relationship in propagation across the quadrants was quantified and propagation speeds were calculated from the delays. MMG recordings were successfully processed from 25 subjects and the average values of propagation speeds ranged from 1.3–9.5 cm/s, which was within the physiological range. The propagation was observed between both vertical and horizontal quadrants confirming multidirectional propagation. After the multiple pairwise test (99% CI), significant differences in speeds can be observed between certain vertical or horizontal combinations and the crossed pair combinations. The number of segments containing contractile activity in any given quadrant pair with a detectable delay was significantly higher in the lower abdominal pairwise combination as compared to all others. The quadrant-based approach using MMG signals provided us with high spatial-temporal information of the uterine contractile activity and will help us in the future to optimize abdominal electromyographic (EMG) recordings that are practical in a clinical setting.     

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen–Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen–Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.     

Exploring interactions by second-stage community analyses

Many biological data sets, from field observations and manipulative experiments, involve crossed factor designs, analysed in a univariate context by higher-way analyses of variance which partition out ‘main’ and ‘interaction’ effects. Indeed, tests for significance of interactions among factors, such as differing Before-After responses at Control and Impact sites, are the basis of the widely used BACI strategy for detecting impacts in the environment. There are difficulties, however, in generalising simple univariate definitions of interaction, from classic linear models, to the robust, non-parametric multivariate methods that are commonly required in handling assemblage data. The size of an interaction term, and even its existence at all, depends crucially on the measurement scale, so it is fundamentally a parametric construct. Despite this, certain forms of interaction can be examined using non-parametric methods, namely those evidenced by changing assemblage patterns over many time periods, for replicate sites from different experimental conditions (types of ‘Beyond BACI’ design) - or changing multivariate structure over space, at many observed times. Second-stage MDS, which can be thought of as an MDS plot of the pairwise similarities between MDS plots (e.g. of assemblage time trajectories), can be used to illustrate such interactions, and they can be formally tested by second-stage ANOSIM permutation tests. Similarities between (first-stage) multivariate patterns are assessed by rank-based matrix correlations, preserving the fully non-parametric approach common in marine community studies. The method is exemplified using time-series data on corals from Thailand, macrobenthos from Tees Bay, UK, and macroalgae from a complex recolonisation experiment carried out in the Ligurian Sea, Italy. The latter data set is also used to demonstrate how the analysis copes straightforwardly with certain repeated-measures designs.