Matlab version r2020a

Viral load data utilized for this study were digitized from previously published clinical studies [38 (link),60 (link)]. Data from infected individuals with at least three measurements above detection limits within 20 days of symptom onset were included in our analysis. Thus, we had 8 patients with mild symptoms [38 (link)] and 14 patients with severe symptoms [60 (link)]. In the former cohort, all individuals were young and had no comorbidities. In the latter, 80% were hospitalized with symptoms of severe disease. They had different comorbidities, such as diabetes, hypertension and obesity, and 7 were above 65 years of age. The clinical measurements were digitized using a custom script in the MATLAB (version R2020a) image analysis toolbox (www.mathworks.com).

The raw, three-dimensional COM acceleration signal recorded over the duration of the study period was downloaded from each accelerometer for analysis. The resultant (vector magnitude) of the acceleration signal was calculated using the Euclidean norm and was used for all subsequent analyses. For each recorded run, a custom activity recognition algorithm developed in MATLAB version R2020a (The MathWorks Inc, Natick, MA, USA) was used to identify and extract periods of non-running data from the running time-series data (Davis IV et al., 2019 ). For example, if a participant briefly stopped (e.g., tie a shoe) or walked during his/her run, this non-running time was isolated and removed from the time series. Data identified as “running” with this algorithm had to last 30 s or more for it to remain in the time series. All periods identified as running were appended together and treated as a single continuous run. The total duration of the analyzed time series from each individual running session was between 17,900 and 665,500 data points (i.e., 2.98–110.92 min).

Signals were first examined visually using LabChart Pro (AD Instruments) to segment data into specific recording periods. Files were further analysed using custom scripts for Matlab Version R2020a (Mathworks; Natick, MA) and processed using Origin Pro (Microcal Software Inc.; Northampton, MA).
Spectral analysis was accomplished using a series of 6-second long, Hanning-windowed samples with a 2-second overlap using Welch’s periodogram method. For spectrograms, a sliding window approach was used to analyze the data segment, wherein 30-second windows were moved across the data segment in 6-second increments. State changes could most reliably be characterized by large fluctuations in the power at 1Hz. Period analysis of these alternations was conducted by determining the saddle point of the bimodal distribution characterizing these power fluctuations, and this power value was used as a threshold for determining deactivated (>threshold) versus activated (Heart rate and breathing rate were analyzed using spectral time windows 20-seconds in duration, with a frequency resolution of 0.05 Hz. Peak frequencies were extracted and plotted across time for spectrographic analysis. Heart and breathing rate were compared both across and within states for any temporal variations throughout the duration of the experiment.
Summary reports of data across experiments and conditions were reported as arithmetic means together with standard error of the mean (SEM). Statistical comparisons were performed using paired t-tests, with a significance level of 0.05. Period length, ratio of activated to deactivated time, average heart rate, and average breathing rate were plotted as a function of time. Linear regressions were calculated using Prism 8 (GraphPad Prism Software Inc, San Diego, CA). The arithmetic means and standard deviations of breathing rate were calculated for each state over 1 minute in duration, and a coefficient of variation (standard deviation divided by arithmetic mean) was calculated from these values.

Four columns with various stationary phase ligands were evaluated
in terms of chromatographic resolution. The tested columns were Torus
1-AA (1-aminoanthracene), Torus 2-PIC (2-picolylamine), Torus DIOL
(high-density diol), and Torus DEA (diethylamine) (see Supporting
Information Figure S1). All columns were
purchased from Waters (Milford, MA, USA) with a length, inner diameter,
and particle size of 100 mm, 3 mm, and 1.7 μm, respectively.
Gradient programs (see Supporting Information Figure S2) were further developed to improve the resolution
with the best performing column before fine-tuning by the experimental
design.
A Box–Behnken experimental design^{32 (link)} was applied to fine-tune chromatography in order
to maximize the chromatographic resolution between close eluting peaks.
The flow rate of the mobile phase was varied between 1.2 and 1.6 mL/min,
the column temperature was varied between 30 and 60 °C, and the
backpressure of the system was varied between 100 and 130 bar. Furthermore,
different solvents such as methanol, isopropanol, heptane, and THF
were evaluated as alternative sample diluents, independently from
the experimental design. MODDE (Umetrics, Umeå, Sweden) software
was used to design, evaluate, and use a Box–Behnken experimental
design for method optimization. Post-processing of chromatographic
data was carried out using MATLAB Version R2020a (MathWorks Inc.).

Scatterplots were used to assess the correlation between CFR and POS%, and expCFR and POS%. Analyses were performed using MINITAB 19 and MATLAB version R2020a (The MathWorks, Inc., Natick, MA).