Mathematica 9

The position of a worm in a bundle was often impossible to measure because the worms in the bundle were too crowded. Therefore, a few head neurons of worms were marked by expressing the fluorescent protein TagRFP (Fig. 3b). The sparse TagRFP expression made it easy to locate individual worms. Images of worms on a plastic surface were taken by a Leica MZ10F fluorescence microscope equipped with a Plan apochromatic objective lens (×1.0, NA = 0.125; Leica Microsystems) at 15 frames s⁻¹. The movement directions of 39 worms in a bundle for 10 s were manually identified based on the positions of the fluorescence. The pie chart in Fig. 3c was created by analysing all movement directions with Mathematica 9.0 (Wolfram).

For the numeric computation of condensate vectors c, a finite threshold δ>0 was introduced into the inequalities (5): Ac≤0 and c–Ac≥δ>0. Its value was set to δ=1 by rescaling of c. Numerical solution of the inequalities was performed by using the IBM ILOG CPLEX Optimization Studio 12.5 and its interface to the C++ language. The software Mathematica 9.0 from Wolfram Research was also found to be applicable. Further information on the calibration of the linear programming algorithm and a simplified Mathematica algorithm are provided in Supplementary Note 3.

All statistical analyses were performed with the program Mathematica 9.0 (Wolfram Research). When calculating the statistical significance of the differences between two series of data, the Location-Test function was used to choose the most appropriate test for the comparison, which in all cases, except for the comparison of the size of the lysis plaques produced by different viruses, was the t-test (Function T-Test).

ANOVA statistical tests were conducted individually for each of the four experiments to test for differences between mean DNA copy numbers. A two-sided t-test was used to test differences in the average amount of DNA recovered from fresh CTAB and Longmire's extractions within the ‘filter preservation experiment’. Technical replicates were averaged for the analysis, residuals from the ANOVAs and t-test were checked for normality using normal Q–Q plots, and pairwise comparisons in the ANOVA were performed using Tukey's post hoc test. All statistics and plots were conducted and created in Mathematica 9.0.1.0 (Wolfram Research, Inc., Version 9.0.1.0, Champaign, IL 2013). All tests conformed to the normality assumptions unless otherwise indicated.

Video data were calibrated and digitized using Matlab (MathWorks, Natik, USA) Digitizing Tools DLTcal5 and DLTdv5 [34 (link)]. The digitization process produced three-dimensional coordinates defining the position of each marker, in each frame, in the capture volume. These coordinates were then loaded into Mathematica 9.0.1.0 (Wolfram Research, Champaign, USA) where all further data processing and analysis was conducted. The X, Y and Z coordinates were filtered using a second-order reverse Butterworth filter with a cut-off frequency of 30 Hz. A dynamic stick figure model for each trial was produced using the marker coordinates for each trial. Straight lines connecting the digitized marker points were used to represent the limb segments.
Walking speed was calculated from the position of the head marker, in metres per second (m s⁻¹), between the start of stance and the end of the limb cycle. Stride length was calculated as the Euclidean distance between the position of the foot at the start of stance phase and the position of the same foot at the end of the limb cycle, using the longest digit of the right hindlimb for reference. Stride frequency was calculated as one over stride duration (seconds). Hindlimb motion was then characterized using two methods: the three-dimensional vector angle method and the polar coordinate angle method.