Analyzing multiple spike trains with nonparametric granger causality

Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger causality has proven an effective method for this purpose. However, the basis for Granger causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons limultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.

Analyzing information flow in brain networks with nonparametric Granger causality

Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate both pairwise and conditional measures of Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

Is Granger Causality a Viable Technique for Analyzing fMRI Data?

Multivariate neural data provide the basis for assessing interactions in brain networks. Among myriad connectivity measures, Granger causality (GC) has proven to be statistically intuitive, easy to implement, and generate meaningful results. Although its application to functional MRI (fMRI) data is increasing, several factors have been identified that appear to hinder its neural interpretability: (a) latency differences in hemodynamic response function (HRF) across different brain regions, (b) low-sampling rates, and (c) noise. Recognizing that in basic and clinical neuroscience, it is often the change of a dependent variable (e.g., GC) between experimental conditions and between normal and pathology that is of interest, we address the question of whether there exist systematic relationships between GC at the fMRI level and that at the neural level. Simulated neural signals were convolved with a canonical HRF, down-sampled, and noise-added to generate simulated fMRI data. As the coupling parameters in the model were varied, fMRI GC and neural GC were calculated, and their relationship examined. Three main results were found: (1) GC following HRF convolution is a monotonically increasing function of neural GC; (2) this monotonicity can be reliably detected as a positive correlation when realistic fMRI temporal resolution and noise level were used; and (3) although the detectability of monotonicity declined due to the presence of HRF latency differences, substantial recovery of detectability occurred after correcting for latency differences. These results suggest that Granger causality is a viable technique for analyzing fMRI data when the questions are appropriately formulated.

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

Effect of measurement noise on Granger causality

Most of the signals recorded in experiments are inevitably contaminated by measurement noise. Hence, it is important to understand the effect of such noise on estimating causal relations between such signals. A primary tool for estimating causality is Granger causality. Granger causality can be computed by modeling the signal using a bivariate autoregressive (AR) process. In this paper, we greatly extend the previous analysis of the effect of noise by considering a bivariate AR process of general order p. From this analysis, we analytically obtain the dependence of Granger causality on various noise-dependent system parameters. In particular, we show that measurement noise can lead to spurious Granger causality and can suppress true Granger causality. These results are verified numerically. Finally, we show how true causality can be recovered numerically using the Kalman expectation maximization algorithm.

Denoising neural data with state-space smoothing: Method and application

Neural data are inevitably contaminated by noise. When such noisy data are subjected to statistical analysis, misleading conclusions can be reached. Here we attempt to address this problem by applying a state-space smoothing method, based on the combined use of the Kalman filter theory and the Expectation–Maximization algorithm, to denoise two datasets of local field potentials recorded from monkeys performing a visuomotor task. For the first dataset, it was found that the analysis of the high gamma band (60–90 Hz) neural activity in the prefrontal cortex is highly susceptible to the effect of noise, and denoising leads to markedly improved results that were physiologically interpretable. For the second dataset, Granger causality between primary motor and primary somatosensory cortices was not consistent across two monkeys and the effect of noise was suspected. After denoising, the discrepancy between the two subjects was significantly reduced.

New Ventures’ influence on the Growth of SME Employment, Production and Exports in India: Does Institutional Credit matter?

New ventures are considered to be a major source of small firm growth. In Indian context the contribution of new ventures in terms of new employment, production and exports has largely remained unexplored. It is equally important and unexplored, the significance of the contribution of bank credit to the growth of new ventures in India. This paper is an attempt to throw light on these two aspects. The research is based on secondary data of the liberalized period provided by Ministry of Micro, Small and Medium Enterprises, Government of India and Reserve Bank of India. To analyze the influence of bank credit growth on new ventures and the influence of new ventures on growth of additional employment, additional production and additional exports, we used a Bi-Variate Vector Auto Regression. Based on the model generated, Granger causality tests are conducted to obtain the results. The study found that rate of growth of bank credit causes the number of new ventures, implying any increase in the rate of growth of bank credit will be beneficial to the growth of new ventures. The study also concluded that new ventures are not causing the growth of additional employment or additional production. However new ventures cause the growth of additional exports. This is reasonable as entrepreneurs start their new ventures with minimum possible employment and relatively low rate of capacity utilization and they come up to take advantage of the process of globalization by catering to the international market.

A Cause and Effect Analysis of Motion Trajectories for Modeling Actions

An action is typically composed of different parts of the object moving in particular sequences. The presence of different motions (represented as a 1D histogram) has been used in the traditional bag-of-words (BoW) approach for recognizing actions. However the interactions among the motions also form a crucial part of an action. Different object-parts have varying degrees of interactions with the other parts during an action cycle. It is these interactions we want to quantify in order to bring in additional information about the actions. In this paper we propose a causality based approach for quantifying the interactions to aid action classification. Granger causality is used to compute the cause and effect relationships for pairs of motion trajectories of a video. A 2D histogram descriptor for the video is constructed using these pairwise measures. Our proposed method of obtaining pairwise measures for videos is also applicable for large datasets. We have conducted experiments on challenging action recognition databases such as HMDB51 and UCF50 and shown that our causality descriptor helps in encoding additional information regarding the actions and performs on par with the state-of-the art approaches. Due to the complementary nature, a further increase in performance can be observed by combining our approach with state-of-the-art approaches.

A new two point method of obtaining Cv from a consolidation test: Discussion

Careful study of various aspects presented in the note reveals basic fallacies in the concept and final conclusions.The Authors claim to have presented a new method of determining C-v. However, the note does not contain a new method. In fact, the method proposed is an attempt to generate settlement vs. time data using only two values of (t,8). The Authors have used a rectangular hyperbola method to determine C-v from the predicated 8- t data. In this context, the title of the paper itself is misleading and questionable. The Authors have compared C-v values predicated with measured values, both of them being the results of the rectangular hyperbola method.

T chart to evaluate consolidation test results

Using Terzaghi's degree of consolidation, U, and the time factor, T, relationship, if M-U1 and M-U2 (M-U1 not equal M-U2) are slopes of the U-root T curve at any two time factors T-U1 and T-U2, then it can be shown that a unique relationship exists between T-U2/T-U1, M-U1/M-U2, and TU, (or TU2), and knowing any two of these, the third can be uniquely determined. A chart, called the T chart, has been plotted using these three variables for quickly determining T and U at any experimental time, t, to determine the coefficient of consolidation, c(v), corrected zero settlement, delta(o), and ultimate primary settlement, delta(100). The chart can be used even in those cases where settlement and time, at the instant of load increment, are not known.

Improved root t method to evaluate consolidation test results - Discussion

Taylor (1948) suggested the method for determination of the settlement, d, corresponding to 90% consolidation utilizing the characteristics of the degree of consolidation, U, versus the square root of the time factor, square root of T, plot. Based on the properties of the slope of U versus square root of T curve, a new method is proposed to determine d corresponding to any U above 70% consolidation for evaluation of the coefficient of consolidation, Cn. The effects of the secondary consolidation on the Cn value at different percentages of consolidation can be studied. Cn, closer to the field values, can be determined in less time as compared to Taylor's method. At any U in between 75 and 95% consolidation, Cn(U) due to the new method lies in between Taylor's Cn and Casagrande's Cn.

In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains

The test based on comparison of the characteristic coefficients of the adjancency matrices of the corresponding graphs for detection of isomorphism in kinematic chains has been shown to fail in the case of two pairs of ten-link, simple-jointed chains, one pair corresponding to single-freedom chains and the other pair corresponding to three-freedom chains. An assessment of the merits and demerits of available methods for detection of isomorphism in graphs and kinematic chains is presented, keeping in view the suitability of the methods for use in computerized structural synthesis of kinematic chains. A new test based on the characteristic coefficients of the “degree” matrix of the corresponding graph is proposed for detection of isomorphism in kinematic chains. The new test is found to be successful in the case of a number of examples of graphs where the test based on characteristic coefficients of adjancency matrix fails. It has also been found to be successful in distinguishing the structures of all known simple-jointed kinematic chains in the categories of (a) single-freedom chains with up to 10 links, (b) two-freedom chains with up to 9 links and (c) three-freedom chains with up to 10 links.

Laboratory Test Methods For The Evaluation Of Flammability Of Polymers

Combustion is a complex phenomena involving a multiplicity of variables. Some important variables measured in flame tests follow [1]. In order to characterize ignition, such related parameters as ignition time, ease of ignition, flash ignition temperature, and self-ignition temperature are measured. For studying the propagation of the flame, parameters such as distance burned or charred, area of flame spread, time of flame spread, burning rate, charred or melted area, and fire endurance are measured. Smoke characteristics are studied by determining such parameters as specific optical density, maximum specific optical density, time of occurrence of the densities, maximum rate of density increase, visual obscuration time, and smoke obscuration index. In addition to the above variables, there are a number of specific properties of the combustible system which could be measured. These are soot formation, toxicity of combustion gases, heat of combustion, dripping phenomena during the burning of thermoplastics, afterglow, flame intensity, fuel contribution, visual characteristics, limiting oxygen concentration (OI), products of pyrolysis and combustion, and so forth. A multitude of flammability tests measuring one or more of these properties have been developed [2]. Admittedly, no one small scale test is adequate to mimic or assess the performance of a plastic in a real fire situation. The conditions are much too complicated [3, 4]. Some conceptual problems associated with flammability testing of polymers have been reviewed [5, 6].

Reaginic allergy to Parthenium pollen: evaluation by skin test and RAST

The pollen of Parthenium hysterophorus, an alien weed growing wild in India was found to be a potential source of allergic rhinitis. A clinical survey showed that 34% of the patients suffering from rhinitis and 12% suffering from bronchial asthma gave positive skin-prick test reactions to Parthenium pollen antigen extracts. Parthenium-specific IgE was detected in the sera of sixteen out of twenty-four patients suffering from seasonal rhinitis. There was 66% correlation between skin test and RAST.

Salt-Fog Pollution Test-A Modification to Suit Natural Conditions

Salt-fog tests as per International Electrotechnical Commission (IEC) recommendations were conducted on stationtype insulators with large leakage lengths. Later, tests were conducted to simulate natural conditions. From these tests, it was understood that the pollution flashover would occur because of nonuniform pollution layers causing nonuniform voltage distribution during a natural drying-up period. The leakage current during test conditions was very small and the evidence was that the leakage current did not play any significant role in causing flashovers. In the light of the experimental results, some modification of the test procedure is suggested.