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Methods ARTICLE
SCoT: a Python toolbox for EEG source connectivity
- Institute for Knowledge Discovery, Graz University of Technology, Graz, Austria
Analysis of brain connectivity has become an important research tool in neuroscience. Connectivity can be estimated between cortical sources reconstructed from the electroencephalogram (EEG). Such analysis often relies on trial averaging to obtain reliable results. However, some applications such as brain-computer interfaces (BCIs) require single-trial estimation methods. In this paper, we present SCoT—a source connectivity toolbox for Python. This toolbox implements routines for blind source decomposition and connectivity estimation with the MVARICA approach. Additionally, a novel extension called CSPVARICA is available for labeled data. SCoT estimates connectivity from various spectral measures relying on vector autoregressive (VAR) models. Optionally, these VAR models can be regularized to facilitate ill posed applications such as single-trial fitting. We demonstrate basic usage of SCoT on motor imagery (MI) data. Furthermore, we show simulation results of utilizing SCoT for feature extraction in a BCI application. These results indicate that CSPVARICA and correct regularization can significantly improve MI classification. While SCoT was mainly designed for application in BCIs, it contains useful tools for other areas of neuroscience. SCoT is a software package that (1) brings combined source decomposition and connectivtiy estimation to the open Python platform, and (2) offers tools for single-trial connectivity estimation. The source code is released under the MIT license and is available online at github.com/SCoT-dev/SCoT.
1. Introduction
Quantifying interactions between brain areas is an important and useful tool in neuroscience (Michel and Murray, 2012). Spatially separated brain areas form dynamic large-scale networks that are described by functional and effective connectivity (Schnitzler and Gross, 2005; Siegel et al., 2012). While functional connectivity measures synchronous activation, effective connectivity explains causal relations between areas (Friston, 1994, 2011). We will use the term connectivity for both functional and effective connectivity throughout this manuscript.
Estimates of connectivity can be deduced from the multi-channel EEG by employing a VAR model. However, fitting such a model requires a large amount of data. In particular, the required number of time samples is proportional to the number of channels and the model order. A common approach to generate enough data is to use repeated trials of the same task. However, the EEG also contains task-related activity that varies from trial to trial, which would disappear when averaging over trials. Such activity can only be studied at the single-trial level (Michel and Murray, 2012). A framework for performing single-trial time-varying system identification and visualization was published recently (Mullen et al., 2013). An important use case for single-trial analysis are BCIs, which extract control signals from ongoing brain activity (Millán et al., 2010). Connectivity measures have already been used in several BCI-related studies (Gysels et al., 2005; Shoker et al., 2005; Brunner et al., 2006; Wei et al., 2007; Hamner et al., 2011; Lim et al., 2011; Daly et al., 2012; Billinger et al., 2013a).
Measuring connectivity from the EEG entails methodological challenges such as volume conduction and multiple comparison problems (Siegel et al., 2012). Due to volume conduction, electrical signals originating from one source in the brain are detected by multiple EEG electrodes. Conversely, each electrode measures a superposition of activity from multiple sources. Thus, interpreting connectivity between EEG channels if of limited usefulness. This can be overcome by transforming the problem from the electrode domain to the source domain. Common approaches to estimate source activities include source localization techniques and independent component analysis (ICA). Source localization attempts to map the scalp potential distribution to current source densities on the cortex. However, this approach requires accurate models of head anatomy and electrical properties, as well as accurate electrode locations (Baillet et al., 2001). In contrast, ICA performs a blind decomposition of EEG channels without having to rely on a head model. Additionally, source signals obtained from ICA can be interpreted as originating from cortical dipoles (Makeig et al., 1996). When measuring connectivity between ICA sources, the seemingly contradictory assumptions of dependence for connectivity estimation and independence for ICA must be carefully taken into account. We give a detailed discussion of this issue in section 2.
Our source connectivity toolbox (short SCoT) is a software package for Python that contains tools for estimating connectivity between cortical sources. While various implementations of connectivity are available on other platforms, source connectivity toolbox (SCoT) is the first Python package dedicated to connectivity estimation. Apart from common multi-trial analysis techniques, SCoT also supports single-trial connectivity. The toolbox contains separate modules for ICA, VAR model fitting, and spectral connectivity measure estimation (supported measures are listed in Table 1). While the tools were originally designed for single-trial BCI feature extraction, they equally work with multiple trials and are useful for functional and effective connectivity analysis of EEG signals. SCoT implements the MVARICA approach (Gómez-Herrero et al., 2008), which combines VAR models and ICA for jointly estimating sources and connectivity. Furthermore, we implemented a novel supervised variant of MVARICA specifically tailored toward classification of BCI data, which we named CSPVARICA. The toolbox contains built-in routines for data processing, but can be configured to use the machine learning package scikit-learn (Pedregosa et al., 2011) or custom routines as backends. Unit tests assure correct functionality of the core routines.
The aim of this article is twofold. First, we want to introduce SCoT to researchers along with code snippets that show basic usage examples. Second, we give a technical overview of the methods we implemented and present our new CSPVARICA.
2. Materials and Methods
2.1. Source Estimation and VAR Model Fitting
The EEG is commonly modeled as a linear mixture of underlying cortical source activations (1). These source activations are modeled as VAR processes (2), which contain information about connectivity (Gómez-Herrero et al., 2008).
The mixing matrix M transforms every sample n of the source activations sn into the observable EEG, which is denoted as xn. VAR model coefficient matrices B(k) and innovation process en form the VAR model of order p that describes the source activations; en is assumed to be a vector of independent non-Gaussian white noise processes.
The most naive approach to connectivity estimation is to ignore the mixing of cortical sources and assume that each EEG sensor corresponds to a unique cortical source. However, volume conduction between EEG sensors is not correctly captured by VAR models and therefore severely limits the usefulness of connectivity at the sensor level (Siegel et al., 2012).
More sophisticated approaches obtain source activations by constructing an unmixing matrix U that mathematically reverses the mixing process so that sn = Uxn (with UM equal to the identity matrix I). ICA performs such a decomposition by attempting to find spatial EEG components with minimal instantaneous cross-dependencies between each other. These components can be interpreted as cortical source activations that are not affected by volume conduction. However, connectivity between sources can also cause instantaneous cross-dependencies (Figure 1). ICA assumes no temporal dependence structure within the data, but connectivity between sources violates this assumption. Thus, ICA treats the signals as though instantaneous cross-dependencies were exclusively caused by the mixing process. This might decrease the reliability of subsequent connectivity estimates, as was demonstrated by Haufe et al. (2010).
Figure 1. Connectivity and correlation in a bivariate AR(1) model of order p = 1 with two signals x and y. The VAR coefficients bij describe the dependency of signal i on the previous sample of signal j. In this example, there is effective connectivity from x to y, but not from y to x. Although no direct interaction between xn and yn exists, the signals are correlated, since both xn and yn depend on xn−1. The strength of this correlation depends on byy, byx, and additive noise (which is not shown in this figure).
We provide an implementation of ICA source decomposition in SCoT. However, limitations and conflicting assumptions of VAR and ICA should be carefully considered before applying this approach. Therefore, we recommend more sophisticated techniques such as MVARICA or our novel CSPVARICA.
SCoT implements the MVARICA approach, which performs joint source decomposition and VAR model fitting while respecting their respective assumptions about dependencies (Gómez-Herrero et al., 2008). MVARICA works in three steps (see Figure 2). First, the EEG is transformed by applying principal component analysis (PCA) as follows:
The signals in yn contain the PCA-transformed EEG. The PCA transformation matrix C is pruned to remove components that contribute least to the total EEG variance. This step reduces the dimensionality for subsequent processing and limits the number of sources found by MVARICA. Second, a VAR model with coefficients A(k) and residual processes rn is fitted to yn:
By combining (2–4) we can relate the VAR model fitted to yn with the VAR model that describes the source activations:
The residuals r contain cross-dependencies that cannot be explained by the VAR model. According to (6), all cross-dependencies remaining in the residuals are due to the transformation CM. In the third step, the residuals are decomposed by ICA in order to obtain an estimate of the transformation . Finally, an estimated unmixing matrix is obtained as so that
Figure 2. Source decomposition with MVARICA and CSPVARICA. Both approaches estimate source activations ŝ from the EEG. The EEG signals x are transformed to y either by PCA (MVARICA) or CSP (CSPVARICA). Subsequently, the residuals r of a VAR model fitted to y are decomposed by ICA to obtain an estimate of the combined matrix CM. This matrix, along with the transformation C is used to obtain estimated source activations ŝ.
Typically, estimates of the VAR coefficients at the source level are obtained by inserting estimates and in (5) and solving for . However, if sources are spatially stationary (constant M), the unmixing estimate can be reused on other data sets to obtain source activations and fit VAR models directly to these activations according to (2). This allows us to determine the unmixing matrix from a set of training data, and subsequently perform connectivity estimation between the same sources on new data.
In general, MVARICA is applied to multi-trial data. Different strategies to obtain the VAR residuals r can be employed, depending on which stationarity assumptions hold on the data. If stationarity can be assumed across all trials, a single VAR model may be fitted to all trials. If stationarity can be assumed only across trials from the same condition, a different VAR model may be fitted for each condition. Finally, if stationarity cannot be assumed across trials, a different VAR model may be fitted for each individual trial. The last approach requires single-trial VAR model fitting, which we will discuss in section 2.6.
MVARICA reduces the input dimensionality by discarding the principal components that contribute least to the total EEG variance. However, EEG components of interest often have a low signal-to-noise ratio. Thus, PCA might remove such components while retaining noise with higher variance. We propose to use common spatial patterns (CSP) instead of PCA. While PCA finds components according to their contribution to the total variance, CSP finds components that explain the differences (in variance) between two conditions (Koles et al., 1990). Thus, we expect CSP to be superior to PCA whenever differences between two conditions (e.g., baseline/task, task/task, etc.) are analyzed. CSPVARICA is implemented in SCoT as a supervised alternative to MVARICA (see Figure 2). CSPVARICA is similar to MVARICA except for the first step, where we replaced PCA with CSP. Equations (3–7) are equally valid for CSPVARICA; only the tranformation matrix C is different because it represents the CSP transform instead of the PCA transform.
2.4. Model Validation
MVARICA and CSPVARICA apply ICA to the residuals of VAR models. ICA assumes no temporal structure in the data. Thus, it is important that the VAR models adequately describe the data so that the residuals are serially uncorrelated.
SCoT implements a multivariate portmanteau test to test for whiteness in the residuals (Hosking, 1980). The test compares the multivariate Li-McLeod statistic Q against the null hypothesis that the residuals are white (Lütkepohl, 2005). When the residuals are normally distributed, Q follows a chi-squared distribution. However, we explicitly assume non-Gaussian residuals. Thus, we estimate the distribution of Q0 under the null hypothesis from surrogate residuals. Temporal structure in the residuals is destroyed by randomly permuting the residuals along the time axis. We repeatedly calculate Q0 from different permutations and calculate the probability of observing a Q0 larger than Q. A probability of less than 0.05 indicates significantly non-white residuals.
2.5. Connectivity
Once source estimates are available, numerous connectivity measures can be extracted from VAR models. Table 1 lists all measures currently implemented in SCoT. Some of the most commonly used measures are summarized in Schlögl and Supp (2006). All these measures may be extracted directly from the VAR coefficients returned by MVARICA or CSPVARICA.
In addition to well known measures, SCoT implements the full frequency partial directed coherence (ffPDC). The ffPDC is obtained by normalizing the partial directed coherence (PDC) over all frequencies instead of each frequency individually:
Here, i and j correspond to the indices of the sink and the source signals, respectively. A is the inverse of the VAR transfer function.
In general, repeatedly applying MVARICA or CSPVARICA to different data segments yields components in different order. This makes tracking of connectivity patterns difficult. However, it is possible to overcome this issue by re-using the unmixing matrix obtained from one decomposition. Applying this unmixing matrix to new portions of data results in varying activations of the same sources, which facilitates three important use cases: single-trial estimation, time-varying analysis, and comparing different conditions.
2.6. Single-Trial Estimation
VAR model fitting typically requires a large amount of data. To obtain a sufficient amount of data, a model can be fitted to multiple trials, assuming stationarity across trials (i.e., each trial is a realization of the same process). However, this is not feasible in applications such as MI BCIs, where trial duration is several seconds or continuous control is required. Instead, connectivity estimates need to be obtained from a single window of data. In SCoT, we perform single-trial connectivity estimation on short windows of source activations, but use a training set of multiple trials to obtain sources that are assumed to be spatially stationary.
One procedure for single-trial connectivity estimation is described in our previous work (Billinger et al., 2013a), where various connectivity measures were estimated on selected ICA sources. This procedure can be improved by replacing ICA and source selection with MVARICA or CSPVARICA. Importantly, single-trial VAR model fitting is prone to overfitting due to the limited amount of data available in a single trial. However, this problem can be alleviated by regularization. Therefore, SCoT supports ridge regression for fitting VAR models to individual and multiple time windows. The scikit-learn backend provides additional model fitting routines including Lasso, Elastic Net, and generalized cross-validation (GCV) for determining the ridge parameter.
The degrees of freedom when fitting a VAR model depends on the model order. Typically, the order of VAR models is determined with cross-validation or selection criteria such as Akaikein formation criterion (AIC) or Bayesian information criterion (BIC). Regularization effectively limits the degrees of freedom, so both model order and regularization penalty can be optimized. For simplicity, we manually set the model order to a reasonably high value and optimize only the regularization penalty.
2.7. Statistics
So far, we have only discussed point estimates of connectivity. However, scientists will usually want to make statistical inferences about connectivity to either determine if there really is connectivity from one source to another, or to determine if there is a difference in connectivity between two conditions.
In SCoT, presence of connectivity is deduced using the method of surrogate data generated by phase randomization. While removing connectivity from each signal pair individually may give better results (Faes et al., 2009), we took a simpler approach, where connectivity is destroyed between all signals simultaneously. We obtain the distribution of connectivity under the null hypothesis of no connectivity by repeatedly estimating connectivity on surrogates. Connectivity estimated from actual data can be compared against this distribution to test if it is significantly non-zero.
Statistical difference in connectivity is obtained by performing bootstrap resampling. Bootstrap samples are drawn at the trial level, thus this method only works for multi-trial data sets. The distribution of difference in connectivity is obtained by bootstrapping both conditions. The difference is significantly different from zero if the confidence interval does not contain 0.
Typically, such tests are performed for each frequency bin and channel pair, which requires correction for multiple testing. However, individual tests are likely to be positively correlated. Thus, controlling for the family-wise error rate is likely to be overly conservative. Instead, controlling for the false discovery rate (Benjamini and Hochberg, 1995) is implemented in SCoT.
2.8. Source Connectivity Workflow
SCoT implements routines for estimating connectivity between EEG sources. Two estimation approaches are possible in SCoT. Too many Ps in approach is to estimate sources and connectivity jointly on the same data set using MVARICA or CSPVARICA. Alternatively, a two-step approach is supported, where sources and connectivity are estimated on different data sets. Both approaches impose strong spatial stationarity assumptions on the sources. However, in the latter approach source activity may vary over time.
Joint estimation is performed by applying MVARICA or CSPVARICA to a data set where sources are spatially and temporally stationary. Two-step estimation consists of separately performing source decomposition and VAR model fitting, possibly on different data sets. MVARICA or CSPVARICA can be employed in the source decomposition step by discarding their VAR estimates. In the second step, the unmixing matrix is used to obtain source activations on a different data set. Connectivity measures are estimated from VAR models fitted to these source activations.
The two-step approach is useful whenever connectivity is expected to vary between spatially stationary sources. Possible applications include comparing different conditions, analyzing time-varying connectivity, and estimating single-trial connectivity.
It is often useful to estimate time-varying connectivity. This can be done on a multi-trial or a single-trial basis, whichever is appropriate for the data and the research question. Time-varying multi-trial connectivity estimation facilitates analysis of cue-locked connectivity dynamics. Here, we estimate connectivity on the first time segment of multiple trials, then for the second (possibly overlapping) segment, and so on. This results in an average time-course of connectivity related to the trial start. Time-varying single-trial connectivity estimation may be employed when connectivity dynamics are not cue locked, or no cues are available such as in continuous BCIs. Here, we estimate connectivity on short (possibly overlapping) windows, resulting in a time course of instantaneous connectivity.
3. Implementation
3.1. Overview
SCoT is distributed as a Python package named scot. The package contains several modules that implement the toolbox's functionality and the two sub-packages scot.backend and scot.builtin. The former contains backend modules that allow SCoT to use different implementations of low-level routines such as PCA, ICA, or model fitting. The other package implements built-in versions of these routines. See Figure 3 for an overview of the package structure.
Figure 3. Overview of the dependency hierarchy in the SCoT API. High-level interfaces are depicted above the interfaces they depend on.
SCoT depends on NumPy, SciPy (Oliphant, 2007), and optionally on scikit-learn (Pedregosa et al., 2011). Matplotlib is required for visualization only. Furthermore, SCoT contains the complementary eegtopo package, which is used for EEG topography plots based on spherical spline interpolation (Perrin et al., 1989).
Development is test-driven, with unit tests covering core functionality as far as the stochastic nature of the implemented algorithms allows. The source code is released under the open source MIT license and is available online at github.com/SCoT-dev/SCoT.
3.2. Backend Mechanism
A design goal of SCoT is to keep external dependencies at a minimum. The backend mechanism provides a common interface that allows SCoT to optionally utilize routines from third-party software without introducing unnecessary dependencies. A backend consists of targets that represent thin wrapper functions, class implementations or even modules. These are stored in a global dictionary, where they can be accessed from within SCoT. The dictionary is updated when including a backend module. Thus, the user can easily select a backend by simply importing the module. SCoT comes with two backends: scot.backend.builtin, which provides basic implementations of backend functionality and scot.backend.sklearn, which provides wrappers for routines implemented in the external scikit-learn package.
The built-in ICA backend calls BINICA to perform Infomax ICA (Makeig et al., 1996). BINICA is an external binary, which is either shipped with EEGLAB (Delorme and Makeig, 2004), or separately available online1 and is downloaded on demand.
Currently, the following backend targets are used by SCoT: ICA (ICA function), PCA (PCA function), VAR (VAR model fitting class), and utils (miscellaneous helper routines). The backend mechanism relies on duck-typing, which allows users to easily create custom backends by simply putting their own functions in the global backend dictionary.
3.3. Workspace
The scot.ooapi module exposes the class Workspace, which provides convenient access to SCoT from interactive Python sessions. This class also serves as an example for usage of the more flexible low-level application programming interface (API), which is described in detail later. An instance of the Workspace class is optionally initialized with sampling rate, desired dimensionality reduction, number of fast Fourier transform (FFT) bins and/or electrode locations. This alleviates the user of the burden to pass these parameters to each individual function call. The Workspace class can perform source decomposition on EEG data, estimate connectivity on the same or a different data set, conduct statistical analysis, and visualize the results.
3.4. Package Structure
Here, we provide a summary of the modules that form the SCoT package. Please refer to the API reference in the SCoT documentation for a more detailed description. A summary of the modules is listed in Table 2.
3.4.1. Internal modules
These are modules mainly intended for internal use in SCoT.
builtin is actually a sub-package. It contains SCoT's own implementations of PCA, CSP, VAR, and a wrapper to the BINICA binary.
The config module defines global variables for configuring SCoT. Currently, it contains only the backend dictionary. This dictionary is populated when importing a backend. Functions like mvarica query this variable to determine which implementations of PCA, ICA, etc., to use.
Internal utility functions are defined in the utils module. These include among others a function for calculating autocovariance matrices and the memoize decorator that caches function return values.
3.4.2. User facing modules
These are modules that users of SCoT will often work with.
backend is actually a sub-package. It contains a separate module for each backend currently available in SCoT. At the moment these are builtin and sklearn.
The connectivity module provides a class for extracting connectivity measures from VAR model coefficients (see Table 1 for a list of available connectivity measures). Some connectivity measures are calculated from other measures (e.g., the dDTF). To avoid unnecessary recalculations of repeatedly used measures, this class makes use of the memoize decorator to quickly get the cached return values of member functions that have been called before.
Functions for statistical evaluation of connectivity are available in connectivity_statistics. These include surrogate estimation under the null-hypothesis of no connectivity, bootstrapping, statistical tests, and correction for multiple testing.
The datatools module contains functions for manipulating EEG data, such as cutting segments from continuous data or applying spatial filters to segmented data. The matfiles module allows loading and saving of MATLAB.mat files. This module converts the result of scipy's loadmat to nested Python dictionaries.
The ooapi modules provides the Workspace class, which is described in detail above.
ICA source decomposition is implemented in the plainica module. It performs optional dimensionality reduction with PCA and subsequent ICA source decomposition.
The plotting module contains visualization routines. This module depends on matplotlib to create plots similar to MATLAB. The dependency is optional and required only for visualization; if matplotlib is not available, the module can still be imported, but the functions cannot be called. The visualization routines rely on the eegtopo package to plot scalp projections of sources.
The VAR module contains the class VARBase, which is the VAR base class for VAR models in SCoT. This class implements routines common to all implementations of VAR models, such as prediction or model validation. However, model fitting routines are provided by the derived classes scot.builtin.var.VAR and scot.backend.sklearn.VAR.
The MVARICA and CSPVARICA procedures are implemented in the varica module. The module exposes one function for each procedure.
Cross-validation strategies are implemented in xvschema. This module contains functions that generate indices for testing and training sets for single-trial and multi-trial optimization. While multi-trial strategy is a normal leave-one-out cross-validation, the single-trial strategy creates training sets that contain only single trials.
4. Results
4.1. Using SCoT
4.1.1. Basic usage
Here, we will demonstrate how to use SCoT to estimate multi-trial connectivity from EEG data. More detailed examples are distributed with the source code.
First, the SCoT package must be made available to the Python interpreter. By default, SCoT uses the built-in routines for PCA and ICA. Alternatively, scikit-learn can be used by importing the sklearn backend.
SCoT works with three-dimensional NumPy arrays. The three dimensions of an EEG data set are time, signals, and trials. An example data set is available with SCoT. This data set contains a recording of 45 EEG channels from one subject performing hand and foot MI. The subject was instructed to perform either MI task by a visual cue. Every 9.5–10.5 s such cues were presented 90 times for each class in randomized order.
In the following code snippets we use the variables raweeg, triggers, classes, and fs. These variables are taken from the example data set and contain the continuous EEG data (samples × channels), a list of trigger locations (sample indices) that mark individual trials, class labels () for each trial, and the sampling rate (Hz).
Convenience functions for basic data manipulation are available. The following example cuts segments of 1 s starting 3 s after each trigger from continuous EEG and arranges them in three dimensions as described above.
eeg =
raweeg, triggers, 3*fs, 4*fs)
The Workspace class provides a high-level interface to the toolbox. As the name suggests, an instance of this class provides a workspace on which SCoT routines operate. The workspace contains data, source and connectivity estimates, and settings.
This command initializes a new workspace with VAR model order 40, dimensionality reduction to four components, and EEG electrode locations described in the variable locs.
If reducedim was not set, it would default to retaining 99 % of the EEG variance. Alternatively, PCA can be disabled by setting reducedim to .
A dataset is passed to the workspace with the set_data method. The optional second argument may contain a list of labels that assigns a class label to each trial in the data. The method do_mvarica decomposes the EEG data into source activations and fits a VAR model in the process. It is important to test the VAR residuals for whiteness. A p-value of less than e.g., 0.05 returned by VAR.test_whiteness would indicate significantly non-white residuals, and the VAR settings would need to be tuned. To obtain separate VAR models for each class, we call set_used_labels() to specify which classes to use in subsequent operations. Once VAR models are fitted with the fit_var method, we can plot spectral connectivity measures with get_connectivity. Finally, show_plots displays the plots.
Figure 4 (left) shows the result of applying these steps to the example data set. By replacing do_mvarica with do_cspvarica, we obtain different sources (Figure 4, right). The two frequency bands μ (8–12 Hz) and β (16–24 Hz) are known to play a part in motor processing (Pfurtscheller, 1981). While MVARICA detects connectivity mostly in the μ band, CSPVARICA reveals connectivity in the μ and β bands. Furthermore, connectivity between the CSPVARICA sources varies more between classes. This difference between MVARICA and CSPVARICA is somewhat expected, because MVARICA selects sources that explain as much of the EEG variance as possible, while CSPVARICA prefers sources with maximally different activations between classes.
Figure 4. Directed connectivity with MVARICA (left) and CSPVARICA (right). The ffDTF between four components is plotted for hand (green) and foot (blue) motor imagery. The estimation window was set from 3 s to 4 s after cue on-set. The x-axes correspond to frequencies from 0 to 30 Hz, and the y-axes are the magnitude of the ffDTF (in arbitrary units). Columns correspond to sources and rows to sinks. Scalp projections are arbitrarily scaled to provide a qualitative representation of the sources. Each source's power spectral density is plotted along the diagonal for reference.
4.1.2. Time-varying connectivity
The plots in Figure 4 only show a snapshot of connectivity in one time segment. In order to get an overview on how connectivity evolves over time, the estimation process is repeated for multiple time-shifted segments. However, source decomposition should not be performed for every time segment individually. Even if the same sources were detected in consecutive windows, their signs and order would change randomly. This in turn would make interpreting the results very difficult. Instead, it is reasonable to re-use the same sources (represented by the unmixing matrix) in each time segment.
In the following example, such time-frequency analysis is performed over the whole trial of the data set. The new data set is prepared by cutting 10 s long slices starting 2 s before each trigger from the continuous EEG.
eeg_long =
raweeg, triggers, -2*fs, 8*fs)
The source decomposition obtained before from the short time segments will be re-used by simply assigning the new data set to the workspace. Time-frequency analysis does not require the user to call fit_var. Instead, separate models are fitted internally for each time segment. The function get_tf_connectivity takes three mandatory arguments: the measure to use, window length, and step size.
The code snippet above produces output similar to the right side of Figure 5. Here, it becomes clear that most of the differences between the classes are due to reduced connectivity during hand motor imagery.
Figure 5. Time/frequency plots as obtained with CSPVARICA. The ffDTF between four components is plotted for foot (left) and hand (right) motor imagery. A 1 s long estimation window was sliding between t = −2 and t = 8. The x-axes correspond to the center of the sliding window which ranges from −1.5 to 7.5 s, where t = 0 represents the trigger (cue). The y-axes correspond to frequencies from 0 to 30 Hz. Columns correspond to sources and rows to sinks, while the diagonal shows the scalp projections of the respective components. Scalp projections are arbitrarily scaled to provide a qualitative representation of the sources.
4.2. BCI Simulation
Using SCoT, we performed a BCI simulation study to demonstrate the efficacy of CSPVARICA and MVARICA on single trial classification on EEG recordings of MI data. Fourteen subjects participated in this study, all of them gave informed consent and were paid for their participation. Each participant took part in two sessions on separate days, with six recording runs of 30 trials in each session. The sessions comprised 90 right hand MI and 90 foot MI trials. Trial duration was 7 s with breaks of varying duration (2.5–3.5 s) between trials. EEG preprocessing included removing electrooculogram (EOG) artifacts (Schlögl et al., 2007) and downsampling to 100 Hz. A more detailed description of the data and preprocessing procedure can be found in Billinger et al. (2013a).
We performed cross-validation per subject and session, using each of the six runs for testing once and the remaining five runs for initializing the procedure. In each cross-validation step, we decomposed the raw EEG into 16 components with either CSPVARICA or MVARICA. Subsequently, we split the component activation signals into segments of 1.5 s length that overlapped by 0.2 s. The following two steps were applied to each segment individually. First, we determined the optimal regularization parameter λ for subsequent single-trial VAR model fitting. Second, we extracted full frequency directed transfer function (ffDTF), ffPDC, and band power (BP) features in two frequency bands (7–13 Hz and 15–25 Hz). While ffDTF and ffPDC were based on the VAR model, logarithmic BP was calculated directly from the time signals to serve as a baseline. Finally, we trained a shrinkage linear discriminant analysis (sLDA) classifier on the time segment where classes were best discriminated for each feature type.
We tested the procedure on the run that was previously withheld from initialization. First, we decomposed the EEG into the same components as in the initialization step by spatially filtering the test set with the unmixing matrix obtained during initialization. For each time segment, we subsequently fitted regularized VAR models individually on every trial, extracted the ffDTF, ffPDC, and BP features, and applied the classifier. This resulted in a confusion matrix for each time segment. We calculated Cohen's kappa κ for each segment during the MI phase. The κ metric is preferable over classification accuray because it takes class distribution into account (Billinger et al., 2013b). From all segments, we took the 0.9 quantile of κ as classification performance, which is less sensitive to outliers than peak performance. This measure of classification performance was obtained for each subject and session.
Classification performance is significantly higher with CSPVARICA than with MVARICA (Figure 6). Thus, CSPVARICA seems to be preferable over MVARICA for MI classification. It is also reasonable to assume that CSPVARICA is useful for studying connectivity under varying conditions or tasks.
Figure 6. Classification performance (0.9 quantile of Cohen's kappa) for PCA-based dimensionality reduction (MVARICA) and CSP-based dimensionality reduction (CSPVARICA). The standard error of mean classification performance is indicated on top of the bars.
Furthermore, we demonstrate the effects of regularization on classification performance. In Figure 7, we compare per-subject optimization of the regularization parameter with no regularization and with applying over-regularization by setting the parameter to a high value. Optimal regularization was determined in the initialization phase of the cross-validation for each time segment individually, resulting in κ = 0.62 ± 0.18. Clearly, no regularization performs worst with κ = 0.38 ± 0.11. For over-regularization, we chose λ roughly an order of magnitude higher than the average optimal value, which slightly decreased classification performance to κ = 0.57 ± 0.15. However, the impact of too much regularization is difficult to quantify.
Figure 7. Classification performance (0.9 quantile of Cohen's kappa) for different regularization approaches. Regularization was optimized for individual subjects (λopt), set to zero (λ0), and to a high value (λ300). The standard error of mean classification performance is indicated on top of the bars.
5. Discussion
In this article, we introduced SCoT, the Python toolbox for source connectivity estimation. It provides tools for ICA-based source decomposition, VAR model fitting, and extraction of connectivity measures.
Widely used neuroscience software packages2 (Hanke and Halchenko, 2011) such as EEGLAB (Delorme and Makeig, 2004), Fieldtrip (Oostenveld et al., 2011), and Biosig (Schlögl and Brunner, 2008) support connectivity analysis. Particularly, the SIFT toolobx (Delorme et al., 2011) includes routines for adaptive and segmented VAR model fitting with various smooth and sparse regularization techniques. Furthermore, SIFT supports SCSA (Haufe et al., 2010) for jointly estimating sources and connectivity. These packages are released under open source licenses and are available for MATLAB3. In contrast, the MNE software package4 supports model-based source reconstruction and exposes functionality for calculating several non-parametric connectivity measures in a Python API. With SCoT, we attempt to provide reusable and modular routines, which can help application developers avoid re-implementing the wheel in future projects based on Python.
For the first time, we presented our new CSPVARICA method and demonstrated that it is a useful source decomposition approach for data that contains different labeled conditions. Currently, our implementation supports only two conditions, but generalization to an arbitrary number of conditions is planned for a future release. Our BCI simulations showed that CSPVARICA outperforms MVARICA in terms of classification performance. This is not surprising since CSPVARICA favors sources that contain highly discriminative signals. However, MVARICA might be less susceptible to noise because it retains high-variance components. Whether or not one of these methods yields physiologically more meaningful results is an open question.
Although we conceived CSPVARICA mainly for application in BCIs, it is likely to be useful for other disciplines of neuroscience as well. Therefore, we encourage researchers to consider using CSPVARICA when analyzing differences between conditions.
SCoT relies on MVARICA or CSPVARICA for source decomposition. Alternative joint source/connectivity estimation techniques such as SCSA (Haufe et al., 2010) have not been implemented yet in SCoT. Furthermore, model-based source reconstruction is not included, because source localization is not within the scope of SCoT. However, SCoT can work with source decompositions obtained from such approaches by utilizing unmixing matrices obtained from other software packages.
VAR model fitting in SCoT is performed with regularized least squares optimization in general. Routines for ridge regression are built in, and other approaches such as Lasso, Elastic Net, LARS, or Bayesian regression are available through scikit-learn. Our simulations show an improvement in classification performance from κ = 0.38 without regularization to κ = 0.62 when applying ridge regression, which underscores the importance of regularization in single-trial connectivity. Support for more VAR fitting and regularization strategies is planned. A noteworthy approach is the group LASSO (Vidaurre et al., 2013), which promotes sparse connectivity. This could prove useful for the visualization of large networks, as it limits the number of non-zero connections.
Time-varying connectivity analysis is possible in SCoT by employing a sliding window. An alternative could be adaptive VAR models. However, adaptive models can be more difficult to handle due to their inherent exponential window. Furthermore, such models need to be updated for every single sample, while sliding windows can skip an arbitrary number of samples.
Our default implementation of ICA uses an external Linux binary to perform Infomax ICA. On other platforms, the FastICA implementation from scikit-learn may be used instead. Furthermore, the flexible backend mechanism should make it easy to include other ICA implementations such as CUDAICA (Raimondo et al., 2012) or the ICAs shipped with MDP (Zito et al., 2009).
In summary, SCoT provides tools required for estimating connectivity on EEG data to the free and open Python platform. It is designed to tightly integrate with popular scientific computation and visualization modules in order to be accessible to researchers familiar with Python.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This work was supported by the FP7 Framework EU Research Project ABC (No. 287774) and the Austrian Science Foundation FWF Project 'Coupling Measures for BCIs' (P20848-N15).
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Keywords: electroencephalogram, connectivity, Python, single-trial, brain-computer interface
Citation: Billinger M, Brunner C and Müller-Putz GR (2014) SCoT: a Python toolbox for EEG source connectivity. Front. Neuroinform. 8:22. doi: 10.3389/fninf.2014.00022
Received: 30 October 2013; Accepted: 20 February 2014;
Published online: 11 March 2014.
Edited by:Yaroslav O. Halchenko, Dartmouth College, USA
Reviewed by:Thorsten O. Zander, Berlin Institute of Technology, Germany
Timothy Mullen, University of California, San Diego, USA
Nick N. Oosterhof, University of Trento, Italy
Copyright © 2014 Billinger, Brunner and Müller-Putz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Clemens Brunner, Institute for Knowledge Discovery, Graz University of Technology, Inffeldgasse 13/IV, Graz 8010, Austria e-mail: firstname.lastname@example.com


text:
Around 54 million tonnes of carbon is lost from the Amazon every year due to selective logging and wildfires, making up 40% of the global yearly carbon loss from deforestation.
The findings come from Lancaster University, which conducted landmark research calculating the carbon loss from logging and fires in the tropics. It examined samples of trees, soil, litter and dead wood from 225 sites in the eastern Brazilian Amazon.
The findings highlight the impact that the forest degradation due to logging has on emissions. Logging has altered the forest canopy making it less able to store carbon and more prone to wildfire.
This post was amended on June 3, 2014, to correct the figure to 54 million tonnes of carbon, not 54 billion as erroneously reported in the media release. The original research is available here.Read more at Lancaster University

subset: commoncrawl


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Stay tuned for the new single, "Wild West Girl" add JenRO on Spotify for the latest! Have you seen the latest music video "Diamond Girl"?
Watch "Planet Z" new music vid below! New music in the "MUSIC SHOP" here! See her latest feature in SFWeekly Vaga Magazine! The video for the single "Ride it" can be seen here: "Ride it Video"!


text:
Monday, March 2, 2009
Not too much...
Ok, now that you've been warned, I will continue with my awesomely boring post.
First off, I CANNOT believe it's March! Seriously, where did February go? Hmm...not that I'm sad or anything, but that was just crazy fast! Second, HAPPY BIRTHDAY OLIVIA (my niece who is turning 3, going on 30!)!! I tried to get all excited and tell her yesterday that her birthday was in ONE day, but then I was quickly hushed by her momma (something about they don't want her getting too excited about it, because she's not having a party till later...can't really remember why). So, I wanted to tell her happy birthday, but decided that this was the safest way, considering she probably won't be reading this!:)
Now, onto our family news. BIGGEST NEWS OF ALL: We are moving to the Phoenix area! Yeah, that's a big change. Eric's uncle has bought a number of properties down there that need to be fixed up and then rented out. So, off we go to a new adventure! We are excited about doing something new, and meeting new people, but we are sad to leave our families (most important), and our ward and friends. But, we hope to be up here often to visit, or have many visitors down there! How about we come up here in the summer, and you all come visit us in the winter. Plan? I get more and more excited about moving down there each time Eric leaves again to go work down there. It will just be nice to not be a single mom 1/2 of the time. We will leave as soon as we get a house down there.
NEXT BIGGEST NEWS: Tay is taking steps. Like lots of steps. Well, the highest so far is 8. Some days she's really into it, and other days she gets all nervous and makes funny sounds out of her throat. It is too cute. We don't have it on video yet, but when we do, I'll try and get it up here.
Also, Tay now has two bottom teath. It is adorable. And, her hair is coming in so super fast. It is so fun. Sometimes I put a cutie little clip in it, which will stay with lots of hairspray for about an hour! ha. She eats like crazy. She will chew anything up with those little baby teeth. It seems like her favorite thing so far is fetuchini alfredo, and ANY form of potato. Looks like she's taking after her mom. Or maybe she has no other choice, because I just feel her all the carbs I love to eat. Oh wait, she also LOVES cake and ice cream, but who doesn't?
She has turned into such a good sleeper. She is taking two naps for about 1.5 hours each, and sleeping about 12 hours at night. Ohhhh heaven! It is amazing. She is really cute when I put her down for naps and bed time, because she'll play in her bed for about 15 minutes before she goes to sleep, and she usually doesn't cry. What a doll face. I SO wish I had some pictures to put up, but that just means I need to do another post later.
I got to go to a couple of concerts this past week which were way fun. Last Sunday I went with my sis-in-law to the Celine Dion concert. She was awesome. We tried to get the best seats ever on the second row, but dumb guy showed up like an hour into the concert (before Celine had even come out), and we got kicked out. Dang. Then, Eric and I and Eric's parents all went to the Brian Reagan concert. He was sooo funny. It was a great night. I just love him, because he is a clean comedian. If you've never heard his stuff, you should check it out!
When Eric was home last week he started painting the outside of the house. It is going to look great!! It already looks like 100 times better, because it just looks so much cleaner! Love it. Thanks babe.
Well, Tay is awake from her nap, so I will stop here. I swear I'll get some pictures up when Eric gets back.
11 comments:
- Alex and Katie said...
Bree, you're moving to Phoenix! We can hang out! Except we are moving to Oregon in early August, so get here soon!
- March 2, 2009 at 11:08 AM
- -KJ said...
Hahaha! Thanks for being the only one to officially wish Olivia a happy birthday! My concern was more that Spencer would be disappointed that we weren't doing anything. We aren't doing anything yet because Kev is out of town today and tomorrow. I think we may try Wednesday. We shall see.
I am so excited for this crazy adventure. Big changes, but I think you were meant to be a desert rat!!!
I love that little gal of yours. She is getting so big! LOVE HER! Thanks for playing with my kiddos last night. Dang, I was so tired and ornery! You are da baste!
- March 2, 2009 at 11:24 AM
- Saren Atkisson said...
Well well look who posted! Just kidding with or without pictures you have an interesting life!
- March 2, 2009 at 8:57 PM
- Seth said...
- March 2, 2009 at 9:49 PM
- Erica said...
Pheonix!? Well, I bet you will love it down there! It is hard to be a single mom, huh!? Even when you don't have to work. I don't know how some people do it!
Please give your super-cute babe a hug for me. I still cannot believe she is walking! That is so much fun. I would love to come visit you before you leave, but I know you are probably super busy! Let me know! Take care!
- March 2, 2009 at 11:11 PM
- Karalee said...
I can't believe your are moving to Phoenix! I bet your mom is about as happy about you moving as my mom is about me moving. You will love the warm weather though. I am jealous about the naps. Joshua will usually go down fine, but he never stays down very long. Oh well. I am excited for you to put pictures up, Taylor sounds cuter than ever.
- March 3, 2009 at 4:58 AM
- Erica said...
Well, I learned something last night . . . Phoenix. Whoops!
- March 3, 2009 at 3:34 PM
- The Carlsens said...
Are you planning on keeping your house here or are you going to sell it?
- March 4, 2009 at 10:22 AM
- Bree :--) said...
We are selling our house.
- March 5, 2009 at 11:20 AM
- Jake and Nicole said...
Wow you're moving! That is so exciting! Change is so fun espically if you've been somewhere for a looooong period of time! :) Arizona is one place I wouldn't mind moving! Gald we can keep in touch this way!
- March 5, 2009 at 2:21 PM
we are very happy for you forward to seeing you in the winters there and Summers here. We will just have to stay more connected in other ways. Love, dad
- March 10, 2009 at 10:35 AM


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In my opinion, there's not a better time to be an outdoors person each calendar year than right now. The mid November to early December time frame features not only awesome bass fishing, but also deer hunting and the start of waterfowl season — which I've treasured since I was a kid hunting "diver ducks" on Kentucky Lake with my dad.
Dad is a hard-working, Carhartt-wearing, aluminum siding contractor, and he's wise enough to know that where we live in central Kentucky is not exactly a waterfowl mecca. So I'm forever grateful he took time to drive us over to Kentucky Lake where he knew I'd have plenty of ducks to hold my attention as a young hunter.
As I got a little older, dad and I would hunt an open-water blind at legendary Reelfoot Lake in Northwest Tennessee, right off the Mississippi River. We shot a ton of mallards there over the years, and a lot of other species too.
These days, I spend a lot of time running all over the region with a bunch of guys my age that are passionate waterfowlers like me. It's not uncommon for us to drive 100 miles from one day to the next to stay dialed-in to the best hunting spots.
But as you might expect, autumn isn't all about ducks and geese — it's also my absolute favorite time of the year to fish for bass. And from right now until March I never go fishing without an Alabama rig, and what a lot of us simply call the "little brown jig."
The big key is to find areas close to deep water with shad present. It could be a point, or it might be a place where the original creek or river channel swings close to the bank. Both areas usually prove productive, and if there's a laydown tree near that point or on that channel swing bank, that's even better.
A lot of guys throw their Alabama rigs on braided line, but I like the feel and performance of 20-pound monofilament a whole lot better. And while I have five lures on my umbrella rig like most people, I fish a slightly smaller version of an Alabama Rig and present it more like a heavy spinnerbait. It's physically easier to cast all day long, and it allows me to fish it a little more methodically.
When it comes to the "little brown jig," I like a 5/16-ounce with a fairly compact skirt and trailer. My favorite color is one Cumberland Pro Lures makes called green pumpkin/barbed wire. I tie it to 17-pound fluorocarbon line.
I think I'll spend the next couple days scouting a place where we can shoot a limit of ducks by 9 a.m. on opening day, and then go set the hook on a limit of bass by sunset later the same day. Again, man, I just love this time of year.


text: https://www.trumbulltimes.com/news/schools/article/Trumbull-High-School-Golden-Eagle-Marching-Band-13932800.php Trumbull High School Golden Eagle Marching Band places third Julie Miller Published 2:53 pm EST, Thursday, November 8, 2018 Image 1 of / 1 Caption Close Image 1 of 1 Trumbull High School Golden Eagle Marching Band places third 1 / 1 Back to Gallery The Trumbull High School Golden Eagle Marching Band traveled to Danbury on Saturday, Nov. 3, for the USBands New England Regional championships, where they placed third in their class, earning a score of 95.7875, and capturing the award for best color guard. The band concludes their season next weekend at the USBands National Championships at MetLife Stadium in East Rutherford, N.J. and thanks "Every 1" for all of their support this season. View Comments © 2020 Hearst Communications, Inc.


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KENNESAW, Ga.–(BUSINESS WIRE)–Inc. Magazine today ranked commerce platform LendingPoint No. 17 on its 37th annual Inc. 5000, the most prestigious ranking of the nation's fastest-growing private companies. LendingPoint joins companies such as Microsoft, Dell, Pandora, Timberland, LinkedIn, Yelp, Zillow, and many other well-known names who gained their first national exposure as honorees on the Inc. 5000. LendingPoint has hit successive funding records year-over-year and is on pace to reach $100 million per month in loan originations by the end of 2019.
LendingPoint is excited to announce that CEO and founder Tom Burnside was selected as a finalist for EY's Entrepreneur of the Year Southeast.
While its more enjoyable to travel, go on adventures or relax during Summer, it is also a good time to plan for your future and revisit your finances on the slower days of summer.
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We've decided to highlight some of our women leaders who help make LendingPoint shine. Here's a list of some of our fintech LendingPoint Ladies.
The rate of borrowers using loans for debt management drops; growing proportion of borrowers use loans for new purchases
Most people who take out personal loans do so to help manage their pre-existing debt. That is true of all borrowers, no matter the lender involved. LendingPoint is no exception.
LendingPoint will hire 100 new team members in atlanta headquarters, increasing local headcount to nearly 300
Staffing expansion comes after online lender posted its most successful year to date
Take advantage of Spring cleaning to start getting out of debt!
Stay on top of your finances to avoid this worst-case scenario.
Here are a few ways in which you can save some money on insurance this year.
On St. Patrick's Day, a few questions you should be asking yourself about your personal stash of green.
Take a look at some of the wildest wedding venues of 2019.
Realizing your check engine light is on is a moment every driver should dread.
Pay off credit card debt and achieve financial freedom in less time.
Here are the factors that affect your auto loan interest rate and how to prepare when shopping around for a used car.


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Tips, thoughts, tools, techniques and practices to increase success rates with software demonstrations
Monday, February 25, 2008
Do the Last Thing First!
Welcome to our new blog - tips, thoughts, tools, and techniques for demonstrating software.
Posted by Peter E. Cohan at 12:11 PM
3 comments:
- Sean Murphy said...
Peter, it's great to see you blogging. I will have to add you to my blogroll.
- February 25, 2008 at 1:59 PM
- John Kreisa said...
Yeah Peter!
I'm also glad to see you blogging and we look forward to your demo insights!
- February 25, 2008 at 7:52 PM
- Rachael O'Meara said...
hi Peter - good stuff ! I like the 10 word exercise.
- February 27, 2008 at 8:28 PM
Subscribe to: Post Comments (Atom)


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We woke up to a rain and winds and this was the day we were to take the ferry to Mallaig to get the Harry Potter train. Unfortunately it was too windy and the smaller ferry that we were to take was cancelled. Our amazing bus chauffeur, Simon said he would drive us there to get the train. Awesome! I admit that I would be rather disappointed if we didn't make the train.
We made it with time to spare and even with enough to grab some hot soup!
I must thank Google photos for their fabulous shot. It was too rainy for me to get any pictures that would be anything close to this.
We were riding the Jacobite Steam Train from Mallaig to Fort William. I was immersed in the history of Harry Potter while in Scotland and I must admit that I never read a book or saw one of the movies! I did buy a t-shirt that says 9 3/4 and I get so many comments on it. Maybe I should ask Santa for a Harry Potter book?!
Beautiful scenery! I was sitting on the wrong side of the train to really get the best views.
My sistah Meredith Willett, my seat mate was taking pictures! It was a very fun ride and I would do it again in a heartbeat!
It was over all too quickly and soon Simon would whisk us away in our coach as we head for our last stay at the Perle Oban, home of Oban Scotch Whiskey.
When in Oban, I of course ordered an Oban Scotch, neat!
There was no stitching today! Tomorrow would be another exciting day as we tour the Dunollie Castle and view the original slips of embroidery that inspired our pieces.
There are only 3 nights left in this beautiful country of Scotland. I can't believe how fast it's gone by! I am going to try and finish up by Thanksgiving, or maybe not?! The kids are napping right now, so they gave me a chance to write. No guarantees what the next nights will bring.
Miss Meow loves jumping up on my shoulder and sitting there or even across the back of my shoulders as she is here. It is challenging to get a picture of them together unless they're curled up!


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The Golden Apple
I know the traditional harvest decorations are corn and pumpkins but what about apples. Specifically golden apples. Ever heard of the goose that laid the golden apple? Yeah, this tutorial is kinda like that, but I'm not laying anything and we are making an golden apple… With letters… So basically not the same at all… … Read more


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SlimmerTime vs Glucomannan
SlimmerTime vs Glucomannan: Although you can read both SlimmerTime forum and Glucomannan forum and try to choose one of these weight loss pills, you can use this page and directly compare SlimmerTime and Glucomannan.
What is better, SlimmerTime or Glucomannan? We suggest you should read both SlimmerTime review and Glucomannan review, find the differences between these two popular products, see how real people rated these weight loss pills and make your choice based on real results and user reviews from our Weight Loss Forum.
What is better, SlimmerTime or Glucomannan?
14 days
The number one goal of SlimmerTime is to make you feel full for longer. The ingredients used in the supplement use the water in your body to make you stomach feel full. Furthermore, SlimmerTime speeds up your metabolism, reduces appetite, and effectively eliminates toxins in the body as it burns fat.
It is for those reasons, and more besides, why so many men and women are making SlimmerTime their slimming pill of choice.
Since SlimmerTime is a natural supplement, you will not experience any side effects. Documentation can be provided to show how safe it is to use, and you will also find many positive recommendations for SlimmerTime from the medical community.
SlimmerTime should be taken no more than twice daily. For best results, take 1 capsule about 20 minutes before a meal. Drink plenty of water with the capsule, and never exceed the recommended daily dosage.
Listed below are just some of the incredibly effective ingredients used to create SlimmerTime:
30 Days
If you have ever tried losing weight before or have gone on a diet, you know the issues that you have to deal with when you try to lose weight the normal way. Oftentimes you are going to be hungry, cranky, and feel as though you want to eat everything in your path.
When you use Glucomannan Plus, you are using a water-soluble dietary fiber that is going to create bulk in your stomach. This is going to grow to a bulky fiber in your stomach after you consume it. That means that you are going to feel full whenever you eat much smaller portions. Because it promotes satiety, you are far less likely to snack when you use Glucomannan Plus.
If you look at the overall properties of Glucomannan Plus, it might be interesting to note that it can garner upwards of 50 times its natural weight. This means that you are going to have to take relatively little Glucomannan Plus in order to feel much fuller. If you want to lose weight, without any risky side effects and without the frustration of constantly going hungry, you owe it to yourself to try Glucomannan Plus at least once.
|More information SlimmerTime Forum
|More information Glucomannan Forum
SlimmerTime vs Glucomannan
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There's more than a 3-in-4 chance that your blood sugar is too high, and this can lead to a number of chronic health issues, even shorten your life. Learn how to measure and fix your blood sugar. The Apple Watch, FitBit Ionic and Epic Health lead the way.Continue reading
Three medical doctors reveal nine anti-aging lifestyle habits that work. Take a peek and see which you're willing to do.Continue reading
Dr. Brett Osborn is a stud and a neurosurgeon, and he wants to share his top 10 supplements to help you live a long and strong life.Continue reading
A new study on deep biomarkers found five that can predict your biological age with 81.5% certainty. See what they are and what to do to make them slow down your aging rate and decrease your biological age.Continue reading


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Photos from Cheruvally, Kerala.
Pygmy Dartlet or Midget Wisp Damselfly (Male)
Photos from Cheruvally, Kerala.
As always, a visual treat! Amazing.
superb captures!!
Very delicate, fragile. Great pictures!
Carpe Diem
Great shots!
You did well to capture this minute damselfly.It's very pretty!
your shots are beautiful! i can imagine how tiny it is!
A nice damselfly, I love its smallness, thanks.
I love damselflies! I found one the other day on my walk – not this small, though! This one is beautiful!
Beautiful shots of damselfly…
amazing pics !!!
Hi, Magnificent shot, i love this shot.
Amazing shots.
buddy, your photos are always so amazing and inspiring…
Są malutkie, ale śliczne i mają świetne zdjęcia. Pozdrawiam.
They are tiny, but beautiful and have great pictures. Yours.
A very interesting catch. 😀
Very nice post and beautiful photographs Abhinav..:-)..Thanks for the visit and add..I'm already following you..:-)
Keep up the good talent..:-)
Hi Abhinav
First visit here,introduced by Ranjana. You have a lovely photoblog here. Your damselfly pics are magical and mesmerizing. Pl do visit my blog at your convenience.
Regards Ram
Very interesting!
Fabulous. I love the green look of your blog.
Love the photos,
This is for you
Stupende fotografie! buona giornata…ciao
Oh…this is such a delicate darling :)) Great shot…
Loved your space and shots :))
wow… lovely captures Abhinav. Your photos are so vibrant. 🙂
This one brought back my childhood nursery school (home and wooded homestead) memories at my village in Konkan. Beauty!!!
My nursery school was nothing but paddy fields and wooded area around home: no walls, no teachers, no books… and variety of colorful birds, insects, reptiles. Thanks again!


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Shabbat Shalom, friends! I trust you are having a relaxing and delightful Sabbath. After a busy week of cleaning yachts here in Kemah, Texas, I am delighted for it to be Sabbath!
What's In A Name?
In this week's Torah portion, we start a new book: Exodus and are studying Exodus 1:1-6:1. As always, much could be discussed in this Torah portion, but today I want to focus on clarity and courage, something Abba has been personally teaching me in everyday life. Inevitably, life will present many precarious scenarios that we will need clarification on and then much courage to pursue whatever it is we needed help discerning. Moreover, what does our names and more importantly God's Name have to do with clarification and courage?
Early on in the Book of Exodus, we see two midwives, Shiphrah and Puah, who ancient Jewish sages have speculated may actually be the names of Moses' mother and sister, but we don't know for certain. Since the assigned title of this week's Torah portion is "Shemot", which means "names" in Hebrew, it may be worth mentioning the potential meaning of Shiphrah as "beauty, harmony" and "Puah", means something similar "splendid, radiant". Both these ladies were commissioned to kill the Hebrew baby boys at birth, but instead these women bravely saved them. Consequently, the Lord viewed their obedience as beautiful, in harmony with His will, and splendid so He blessed them accordingly (Exodus 1:20-21). In order to have that amount of courage, Shiphrah and Puah must have had much clarity and motivation for rebelling against Pharaoh by saving the Hebrew babies. Some historians have said this was the first act of recorded civil disobedience.
One such Hebrew baby Shiphrah and Puah saved was Moses, who was named by Pharaoh's daughter upon finding him in a tiny ark at the banks of the river. She named him "Moses" because it means "pulled out of the water" or "drew out" or "delivered out of the water". Fascinatingly enough, Moses' entrance into Pharaoh's realm was the same as his exodus being delivered by water. After all, we know in later chapters of Exodus, Moses and all those who followed him, were indeed delivered out of the water many years later in the crossing the Red Sea incident. Through it all, the God of Abraham, Isaac, and Jacob not only reveals Himself to Moses, but He shares His Name, and gave Moses clarification on how God wants to use him to save not just Hebrew babies, but all the Hebrews dwelling in Egypt at that time. Unlike Shiphrah and Puah though, Moses is not willing to challenge Pharaoh. He often attempts to persuade God he is not the guy for the job. However, God specializes in selecting unlikely candidates to fulfill God's "to-do-list". God's plan was to use a man named "delivered out of water" to deliver His people through water.
Names are significant and can be prophetic. For example, when living in Myrtle Beach, South Carolina, a couple of years ago, I was on a God "to-do-list" assignment looking for a specific individual, at a specific event (Carolina Country Music Fest), to give a specific word. In the process of waiting for that divine encounter, Jerry, my husband, and I met a man name Luke meandering outside a bar listening to the country music being blasted from a stage nearby. While Jerry was being his typical jovial self, my eyes continually scanned the crowd looking for the gal I was supposed to find and give a word to. But while my eyes were scanning the people around us, my ears were surprisingly tuning into a word for Luke. The Holy Spirit was reminding me of Luke in the Bible, who was a doctor by profession and clearly an author or writer (to have written that book of the Gospel). I sensed the Spirit wanted me to encourage the Luke in my presence to write the book he's been afraid to write for it will heal people. So despite the loud music and drunken obnoxious people partying in our midst, I said what I was implored to say to dear Luke. Upon saying such things, Luke began to tear up wondering how I knew that he had been fearful about writing his idea for an book. All of which allowed for me to share with him (while Jerry was there) the love God has for Luke and God's plan for him. All Luke needed was divine clarification and courage. I guess God could check that one off His list that night.
Similarly, all Moses needed was clarification and courage even after he stepped out of his comfort zone and attempted to confront Pharaoh. In Exodus 5:22-23, Moses goes back to God to essentially say, "Yeah, this crazy assignment of Yours isn't looking the way I think it should, so why are we doing this again?" Sound familiar? I confess I have had similar rebuttals with God. And yet, God reminds Moses of His plan of making His Name known to the Hebrews in it all (Exodus 6:3). Why is it important to know God's identity, His Name? Because as His people, we are called to bear God's Name as His representatives bringing heaven to earth. How do we bear God's Name? By obeying Him. So whether you are instructed to save Hebrew babies or lead people out of captivity or simply compelled to rest on the Sabbath, you are bearing God's Name to a confused, lost world. By obeying God in His written instructions and personal specific instructions for your life, you are bringing others into clarification and courage as well as being delivered in the process.
Could your name be a prophetic clue as to how you can best share God's Name here and now? Does your new name given after overcoming this world reflect how well you beared God's Name over your lifetime or represent how you will serve Him in the world to come (Revelation 3:17)? In other words, is your name giving His Name shame or does it represent His latter rain? Something to pray about and ponder this Shabbat.


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Introduction: How to Build and Use a Prototype Solderless Breadboard
In a previous video, I had built my own solderless breadboard from cheap ebay parts. This turned out to be a terrible idea since those cheap ebay parts turned out to be crappy and unusable. Aside from two of these small protoboards I bought from Olimex, the rest were garbage.
If you want to know precisely why these fake ebay breadboards are useless, check out Julian Ilett's video on the subject. He goes into depth as to why the suck. So I am disassembling my old breadboard, keeping the two genuine Olimex pieces and throwing the rest out.
Step 1: Removing Old Parts
I began by unsticking the bits of breadboard from the PVC sheet they were stuck to using a screwdriver. With that done, I recovered the binding posts to reuse in other projects.
Step 2: Wisher WB 106 Proto Board
I bought this solderless breadboard made by Wisher Enterprises called the WB 106. It has 1920 nickel plated contact points, made of phosphor bronze. And it was only 20 euros. What you will notice is that it is screwed to a piece of aluminium backing and the feet are already installed. I also got a new back of wire jumpers also from Wisher.
The first step was to insert the new binding posts into the holes. I then inserted permanent jumper wires at the halfway point of the boards since there is a gap in the ground and power rails that needed to be bridged.
Step 3: Adding Colour to the Power / Ground Rails
Since this model board is pure white, I decided to use a permanent marker to draw lines corresponding to the ground and power rails. I like to have the visual confirmation which sets the ground and power rails apart.
Step 4: Bridging the Power / Ground Rails With Jumper Wires
I then bridged all of the ground and power rails together using various sizes of jumper wires. With that finished, I branded the top with the Made 2 Hack logo.
The way solderless breadboards work is very simple. You have the ground and power rails that are positioned vertically. On this model of breadboard, there is also an extra ground and power rail that is horizontal towards the top.
Step 5: How Breadboards Work
If you look at the bare board, you will see the ground and power rails and how they are connected by the same piece of metal. And you can also see the gap at the mid point of the breadboard and the reason I used jumper wires to bridge the gap.
The components are inserted in the signal holes that are connected horizontally. Each of the pins on one row are connected to each other as you can see. Anything you plug into that row will make electrical contact with everything else plugged into that row. The horizontal signal rows also have a gap. Therefore, the pins on this 16 pin ic chip are isolated from each other by inserting the IC in such a way that it bridges the gap between two columns of signal rows.
Check out Sparkfun's tutorial on breadboards.
In order to supply voltage and ground to the IC, it is a simple matter of connecting jumper wires to the respective rails or a component directly as in the case of the resistor going to ground. You can also use components to bridge both sides of the IC such as in the diode that is inserted. And you can use jumper wires to connect components farther away on the breadboard to each other as in the case of the two wires going to the potentiometer.
I hope this video helped you understand solderless prototype breadboards and why they are an essential tool in electronics.
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5 Discussions
I saw Julian Ilett's video. Do you have an opinion yet of the quality of the new breadboards vs your previous ones?
Hi mikeeve,
I can tell you right away the difference is Huge! All of the holes are the same size and they are properly stamped. All of the leads fit right in even the very thin ones from resistors and tiny capacitors. The finish is excellent. My only annoyance is that I wasted so much time using my crappy breadboard.
But you live and learn.
Thanks. You sold me! Here in the US, couldn't find the Wisher at Amazon.com, but I did find it for $25 at Diligent.com (outrageous shipping, though), or the same item at mouser.com (with reasonable shipping):
Mouser Part #:
There is also K&H (I think also from Taiwan) that makes good breadboards. And of course 3M, the Rolls Royce of breadboards, but they are way too expensive in my opinion.
Oops. I meant Digilent.com not Diligent.com


text: Bioware Developer Forum Posts #2 Maintenance: 12 January 2016 Print Email Details Category: Developer Forum Posts Published: Monday, January 11th, 2016 Originally Posted by TaitWatson ( Original Post ) | 11.01.2016 11:25AM Quote: Originally Posted by Aeristash It's the 11th, where are those patch notes posted? On the Patch Notes page About the Author View the discussion thread. back to top Prev Next


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Recording Microphone Accessories
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In today's fast pace world, every once in a while we see random acts of kindness that make us stop, reflect, and even make a tear roll down our cheeks. Some people share this kindness with others In The Athletic Mindset – Three tools for success, "Gratitude" as the third tool and is truly one of the key tools for any success. You cannot always take from others without giving back. Call it the Ying and Yang, or the balance of nature. This universal law of balance rewards those who give back. On the other hand, those who hurt people, bully, or continuously take from others often find that positive rewards are few and far between. One high school football star could have taken the ball into the end zone capturing all the glory for himself, but instead ran out of bound at the one yard line, saving the glory for his team mate who had just lost his father. This young teammate grieving over the loss of a loved one and the football star came together, as well as all of his teammates to achieve great joy, humbleness, and gratitue. This moving story was shown on National TV, and went viral thru social media so others could witness this great story and experience compassion. With today's ability to share great stories through social media, we can see amazing acts of kindness even from strangers all over the world. How lucky are we to be able to share such wonderful stories, and perhaps tip the scales of humanity for the greater good. This football star exemplified The Athletic Mindset through his gracious and humble act, which in turn was truly… the winning touchdown! Read the article and watch the VIDEO that allowed Logan to score his first touchdown. http://bit.ly/SVOMcA
Not all people are showing kindness to other people. Logan is a hero because he played in such a time too.
I agree with this sentence of the whole article much,
"You cannot always take from others without giving back."
Many people don't teach others, but to learn from others, Many people don't work hard for the team, but to get benefits from the team. So Logan is a great guy.
Tony Anderson.