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.

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).

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.

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.