Background signal level was derived from the values for that feature among placebos, as the placebo mean plus one standard deviation .

Finally, the vaccinee values for the feature were scaled and centered to a mean of 0 and a standard deviation of 1, with values truncated to 60.

Nonetheless, even with a rigorous 200-replicate fivefold cross-validation, a mean AUC of 0.83 ( standard deviation of 0.10) was observed, indicating that antibody features are highly and robustly predictive of high vs. low ADCP activity.

Despite the reduction in data considered, Fig 3C and 3D shows that the resulting performance with the filtered feature set is comparable to that with the complete feature set, with a mean AUC of 0.84 ( standard deviation 0.10).

We found that on average an AUC of 0.79 was obtained, with a range from 0.67 to 0.87 and a standard deviation of 0.04 (recall that the PCC-based approach obtained 0.84).

The models are clearly predictive of ADCP, obtaining a mean Pearson correlation coefficient PCC = 0.64 ( standard deviation 0.15) over the 200-replicate fivefold.

Models learned from the filtered features from Fig 2B maintain about the same accuracy (mean PCC = 0.61 with standard deviation 0.15 for the 200-replicate fivefold (Fig 4D); an example LOOCV scatterplot is illustrated in Fig 4C).

Similarly, PCA-based models attain mean PCC of 0.61 With standard deviation 0.15 (Fig 4E and 4F), based largely on PC2 (1gG2/4 vs. 1/3) and someWhat on PCS (IgG4 vs. others), as can be seen in Fig 41.

The actual reward earned on an individual trial was given by a sample from a Gaussian distribution with the current mean, and a standard deviation of 4.

In addition, when the discount parameter is larger (7 = 0.90 vs 7 = 0.99) the algorithm samples more often, consistent with the larger difference in utility for a given standard deviation for larger discount parameters (Fig.

Standard deviation option 1

Utility as a function of mean of option 1 and mean of option 2, with standard deviation of both options set to 4 and discount rate, v = 0.90.

Utility as a function of standard deviation for 2 discount values when mean is 50 for both options and standard deviation is 4 for option 2.

For the non-stationary two-armed bandit, the means were fit with a 3rd order B-spline, and the standard deviations were fit with a 2nd order piecewise polynomial.

The node locations for the standard deviations were given by 0.25, 1, 3, 5, and 15.

The standard deviations were evaluated at 0.5, 1, 2, 3, 4, 5, 7 and 14.

Therefore the information space for this POMDP, equivalent to the state space for the MDP, can be compactly represented: bt = ([11, 61, [12, 62) as the estimated mean and standard deviation (or variance) of each bandit.

This integral was calculated numerically by discretizing y over +/- 2 standard deviations , and sampling 10 points.

To understand the limits of the COOP parameter, we constructed a series of cases With different organizations by truncation of Gaussian distributions With specified standard deViations (Fig.

For example, the standard deviation is not an appropriate metric for quantifying orientation distribution of Z-lines as they are not distributed normally.

To calculate the average angle between the constructs ((60)) and the standard deviation of those angles (060) across multiple conver-slips, it is essential to keep in mind that the angle period is 71.

The (90) and 090 are the average and standard deviation of 90,,- for all cover-silps.

For example, some assume that the parameter can be described as the standard deviation of a truncated Gaussian, or normal, distribution [12].

Assuming OOPp and OOPQ are normally distributed with the standard deviation UOOPP and O'OOPQ, respectively, and OOPP and OOPQ are independent, then the variance: and the standard deviation:

formulated the estimate for the the standard deviation of COOPC:

For (AD) schematic of the construct is on the left, and the orientation distribution With the GOP and standard deviation is on the right.

3) contained 108 random numbers (MATLAB function normrnd) that were normally distributed With the specified mean and standard deviation .

For our test cases, we find that using 10,000 time steps for each evolution stage (with and then without prescribed node states) is enough to preserve the first three digits of the estimated probabilities p Am of reaching the attractor of interest, consistent with what is expected from the standard deviation of the estimated probability p Am.

For our test cases, we find that 100,000 initial conditions are enough to estimate the probabilities p Am of reaching the attractor of interest with an error ( standard deviation of the estimated probability p Am) of 3' 10'3 [p Attr(1—p Attr)] 1/ 2.

The number of time steps we use is enough to show no changes in p Am beyond what is expected from the standard deviation of the estimated probability p Am, and is also found to be enough for the initial conditions to reach the attractors when no interventions are applied.

The percentages are significant in the digits shown and have an estimated absolute error ( standard deviation of the mean) of 3'10_3[%

The percentages are significant in the digits shown and have an estimated absolute error ( standard deviation of the mean) of 3-10—3[%pAttr(1OO%—%pAttr)] “2 %, Where %pAttr is the percentage shown (e.g.

The percentages are significant in the digits shown and have an estimated absolute error ( standard deviation of the mean) of 6- 10_3[%pAttr(100%—% pAttr)]1/2 %, Where %pAm is the percentage shown (e.g.

Bayesian evidence values and model parameter estimates (and their standard deviations ) are computed using nested sampling for all signatures for each time series.

CAGE clusters are assigned to one of the exponential kinetic signatures if log Z for that signature is greater than 10 times log Z for the linear model and log Z minus its standard deviation (sd) is greater than log Z plus the estimated sd for any other eXponential signature (nested sampling computes log Z for parameters mapped to O..1 and we used the resulting log Z for the unit cube for model comparison).

A cluster was assigned to a ‘no decision’ category if the values of log Z (and the associated standard deviations ) computed for each model did not permit a clear assignment.

CAGE TPM values are plotted as circles (median value is filled), predictions of the kinetic signature models using parameter means are shown in blue and the vertical green lines indicate the mean t5 (or th in the case of the decay signature) and one standard deviation above and below.

CAGE TPM values are plotted as circles (median value is filled), predictions of the kinetic signature models using parameter means are shown in blue and the vertical green lines indicate the mean ts and one standard deviation above and below.

CAGE TPM values are plotted as circles (median value is filled), predictions of the kinetic signature models using parameter means are shown in blue and the vertical green lines indicate the mean ts and one standard deviation above and below.

CAGE TPM values are plotted as circles (median value is filled), predictions of the kinetic signature models using parameter means are shown in blue and the vertical green lines indicate the mean ts and one standard deviation above and below.

Expression values are plotted as circles (median value is filled), predictions of the model using parameter means are shown in blue and the vertical green lines indicate the mean th (or ts) and one standard deviation above and below.

For both models, the natural frequencies of the oscillators in our simulation are given as a Gaussian distribution to simulate alpha with mean at 10 Hz and standard deviation 1, making wj around 10211 rad/ s. Time delay is (a) given an identical value between 2ms and 50 ms for all edges (for model networks as well as Gong et al.’s and Hagmann et al.’s human brain networks), or (b) given proportional to the physical distances for each edges with propagation speed of between 5 to 10m/ s (for Gong et al.’s human brain network) [60, 61].

For all simulations, we also added a Gaussian white noise @(t) of vanishing mean and standard deviation of 2 to each oscillator's equation to test the robustness of our results against random fluctuations.

The natural frequency of each node was randomly drawn from a Gaussian distribution with the mean at 10 Hz and standard deviation of 1 Hz, simulating the alpha bandwidth (8-13HZ) of human EEG, and we systematically varied the coupling strength 8 from 0 to 50.

Fig 2A shows the mean phase coherence (measure of how synchronized the oscillators are; see Materials and Methods for details) [42] for two groups of nodes in the network: 1) hub nodes, here defined as nodes with a degree above the group standard deviation (green triangles, 8 out of 78 nodes); and 2) peripheral nodes, here defined as nodes with a degree of 1 (yellow circles, 33 out of 78 nodes).

Each plot shows distinct local dynamics for hub nodes (darker green diamond: defined as nodes With degree above the group standard deviation), and peripheral nodes (lighter green square: defined as nodes With degree 1 for scale-free network, and as nodes With degree below the group standard deviation for other networks) as coupling strength S is varied.

Nodes are indexed in decreasing order of their degree; the degree distribution graph is red if the node degree is less than the average degree of the network, green if it is more than the average, and blue if it is higher than one standard deviation from the average.

Instead, we found that the best approach was to convert the values in each time series to Z-scores—i.e., for each gene in each dataset, we subtract its mean eXpression level and divide by its standard deviation .

To prevent the need to recalculate the null distribution for every pattern of NAs in the data for empirical ITK_CYCLE (there were 5005 unique NA permutations in the data), the NAs were replaced by random noise drawn from a Gaussian distribution with mean and standard deviation that match those of the data on the whole.

3A we generated 10,000 time series with uniformly distributed random phase shifts (always with a 24 h period) and added Gaussian noise to each point with a standard deviation of 25% or 50% of the total waveform amplitude, examples of which can be seen in Fig.

(B) Cosine in black, with Gaussian noise with standard deviation of 25% (blue) or 50% (green) of amplitude.

We added Gaussian noise with a standard deviation of either 25% or 50% of the amplitude of the time series, as previously described.

AUROCs for simulated data with 25% noise ( standard deviation of Gaussian noise as a percent of amplitude).

When the standard deviation is increased upto 50% of the mean value of the ACTX, both pre-DTT and post-DTT areas decreased only by 20% (Supplementary Sl Fig).

The instantaneous input rate was choosen from a low pass filtered noise (time constant 2 5 msec) and standard deviation of :05 around the mean.

The mean of the input rate was varied every 500 msec while the standard deviation remained fixed.

D1 MSNs received additional input with a mean of 1 HZ and standard deviation 0 — A — ctxl.

We injected into layer 2/3 pyramidal cells current consisting of three components: simulated, artificial excitatory postsynaptic current (aEPSC) from a single presynaptic neuron, fluctuating noise with standard deviation 0, and a DC offset (Fig.

After this adjustment, the overall standard deviation of the scaled fluctuating current awas between 70 and 110pA.

Current for injection in this first set of experiments was composed of 1) a fluctuating component 017(t), where 17(t) is a standardized (zero mean, unit variance) Ornstein-Uhlenbeck (OU) process with a correlation time of T = 5ms rescaled to have standard deviation 0, 2) artificial EPSCs of several different amplitudes: 0.1, 0.2, 0.25, 0.3, 0.5, 1.0 and 1.5 of the noise standard deviation 0, and 3) a DC component tuned to maintain a desired firing rate, around ~ 5 Hz.

Error bars denote standard deviation across cells.

Error bands denote standard deviation across cells.

We recalculated the standard deviation (0) from the cvar and the mean, such that a = y-cvar/ 100.

The thick dark blue line indicates the average cell size in the population and the light-blue area the range of one standard deviation (SD).

The thick dark blue line indicates the average cell size in the population and the light-blue area the range of one standard deviation (SD).

Numbers and error bars indicate average i standard deviation .

The figures give the squared coefficient of variation ( standard deviation normalized to the mean) for each conductance/flux parameter during the optimization process, averaged for the 10 GA runs.

Running the optimization with the combined objective does indeed lead to improved accuracy of the parameter estimation, with all nine current parameters being recovered to within one standard deviation (orange symbols, Fig 4B).

In addition Gaussian fit of the resulting delay histograms for values 0.85 g VC 3 0.95 did not show significant differences either in the standard deviation or the 95% confidence interval from a Gaussian fit of Fig.

Breakdown of the original spatio-temporal data into the individual and paired flight trajectories together with mean and standard deviation values of the temporal and spatial length as well as speed of all flights.

Computing the mean and standard deviations we obtain 349.4° and 169.4°, (i33.1°), for the individual flying bats and 348.0° and 168.0°, (i36.7°), for the paired flying bats.

The “Global Z-score” (G2) is obtained by running the predictions of all drugs present in DrugBank against all targets, obtaining a global mean (1m) and a global standard deviation (CG) to Z-score a specific predicted pair.

The “Local Z-score” (L2), is similarly calculated by running the predictions of all drugs present in DrugBank retrieving the mean (1,4 L) and the standard deviation (CL) of the score for a specific target.

Mean values and standard deviation after 10-fold cross-validation.

The standard deviation of the Gaussian blob was only 3.5 mm (0.37 deg) on the screen in order to provide visually very reliable feedback.

Black circles and error bars indicate the mean and standard deviation across participants.

The yellow line and shaded area show the Mixture-of-Kalman-Filters Model mean and standard deviation across participants.