Matlab r2019b

The production of organic acids by L. plantarum was described by this common equation (see e.g., [18 (link),19 (link)]): $$\frac{dP}{dt}=Y_p \frac{dN}{dt}+m_{P}N$$
where P is the concentration of the organic acid, Y_p (mM/kg/cell or µM/kg/cell) is the organic acid concentration produced by cellular division by time unit and m_p (mM/kg/cell.h or µM/kg/cell.h) is the organic acid concentration produced by a cell by time unit.
First, the growth curves of L. plantarum were fitted with the model of Baranyi and Roberts [45 (link)] using non-linear regression. Then, the growth-associated coefficient (Y_p), and non-growth-associated coefficient (m_p) were estimated from product formation models by minimizing the sum of the squared errors between the observed and simulated concentrations of the organic acid. Note that the parameter m_p was set to 0 for OH-PLA as its production was only observed during the growth phase (and not the stationary phase). The system of equations for bacterial growth and end-product formation was solved numerically by the Runge–Kutta method (ODE23, MATLAB R2019b, The MathWorks, Portola Valley, CA, USA). The estimation of the model parameters was performed using a non-linear fitting module (NLINFIT, MATLAB R2019b, The MathWorks).

To compare the experimental results of the PWM-VLC with those of the PDM-VLC, we calculated the theoretical results using the LTspice (LTspice, Analog Devices, Inc., U.S.A.).
When the frequency of waves was 8.728 Hz, we simulated the input and output signals on the lowpass filter as a digital-to-analog conversion component.
Furthermore, when the frequency of the sine wave was 8.728 Hz in both the PWM-VLC and the PDM-VLC, we obtained the DMD switching frequency dependence of the total harmonic distortion (THD), which was calculated by the fundamental wave and five higher harmonic waves using MATLAB (MATLAB R2019b, The MathWorks, U.S.A.).

Data were preprocessed using MATLAB R2019b software (MathWorks, Natick, MA) and the CONN 19c toolbox for functional connectivity analysis (26 (link)). The data processing included functional realignment and unwarp, slice-timing correction, outlier identification, direct segmentation, and normalization into standard MNI space. Functional smoothing was performed using spatial convolution with a Gaussian kernel of 8 mm full width half maximum. The default denoising pipeline combines two general steps: linear regression of potential confounding effects in the blood-oxygen-level-dependent imaging signal (BOLD) based on an anatomical component-based noise correction procedure–“aCompCor” and temporal band-pass filtering. Temporal frequencies below 0.008 Hz or above 0.09 Hz are removed from the BOLD signal to focus on low-frequency fluctuations while minimizing the influence of physiological, head-motion, and other noise sources. All the data were processed on a single MacBook (OS Catalina 10.15.5 software).

Morphometric analysis was developed on full-thickness specimens, as previously described (8 (link), 22 (link)). Briefly, 10 μm thick sections (three consecutive slices/sample), stained with H&E, were recorded with a high-resolution digital camera (DC 200, Leica Microsystems). With a data processing software (Matlab R2019b, MathWorks Inc., Natick, MS, USA), the adipocytes were selected, and the images were converted to 8-bit binary images. The perimeter (i.e., the distance around the boundary of the selected region) and the area of the internal selected region were determined for each adipocyte. Hence, the equivalent diameter (i.e., the diameter of a circle with the same area as the region) was determined, and the equivalent volume was calculated. Considering the adipocytes morphometry, the adipocytes were then automatically approximated to ellipses prior to calculate major and minor axes and eccentricity (23 (link), 24 (link)). For each section, three different fields were analyzed.

We used the Art toolbox (http://web.mit.edu/swg/software.htm) to detect motion and susceptibility artifacts. In total, 0.41% of all scans were outliers (head motion above 2 mm and/or changes in mean signal intensity above 9). The highest percentage of outlier scans for any participant was 7.23%. No participant was excluded after the quality check.
We used SPM12 (Statistical Parametric Mapping, Welcome Trust Centre for Neuroimaging, London, UK) on MATLAB R2019b (Mathworks, Natick, MA, USA) to perform preprocessing and all of our analyses. Preprocessing steps included slice timing correction (the first slice was used as the reference slice), realignment and unwarping with fieldmap correction (with reslicing), coregistration (with reslicing), segmentation, normalization (using forward deformation obtained from segmented images based on tissue probability maps as templates) and smoothing using a 4 mm full-width at half-maximum Gaussian kernel.

Before the EEG data analysis, we accounted for a constant delay of 102 ms between the EEG data and the event marker stream, which in turn contained the onsets of each 10-min block. All analysis steps were performed in EEGLAB v13.6.5b (Delorme and Makeig, 2004 (link)) and implemented in MATLAB R2019b (The MathWorks, Natick, MA, United States). MATLAB code used to compute the results presented in the current study can be found on GitHub¹. For artifact correction, data were first low-pass filtered with a pass-band edge of 40 Hz and then high-pass filtered with a pass-band edge of 2 Hz (pop_eegfiltnew). Data were then epoched into consecutive 1-s segments. Segments containing atypical artifacts were rejected using the build-in EEGLAB function pop_jointprob (local and global threshold: 2 SDs). Subsequently, data were decomposed, running an independent component analysis (ICA), and components containing stereotypical artifacts (e.g., eye blinks, heartbeat, etc.) were identified by visual inspection. The computed ICA weights were then applied to the unfiltered raw data and all but the artifactual components were back-projected. On average, per participant 7.78% of all components were identified as artifactual, ranging from 2 out of 49 components in the best case to 6 out of 49 components in the worst case.

Brain structural images (three-dimensional T1-weighted Magnetization Prepared—RApid Gradient Echo (MPRAGE) MRI) were collected using a 3-tesla Siemens Skyra scanner. As the first step, the raw DICOM scans were converted into the Neuroimaging Informatics Technology Initiative format, using MRIcroGL software (www.nitrc.org/projects/mricrogl). T1-weighted images were then processed and analyzed with the voxel-based morphometry (VBM) pipeline implemented in the Computational Anatomy Toolbox (CAT12 v.1742) (www.neuro.uni-jena.de/cat) for Statistical Parametric Mapping (SPM12, v.7219) (www.fil.ion.ucl.ac.uk/spm/software/spm12) running on MATLAB R2019b (the MathWorks, Inc., Natick, Massachusetts, United States). The VBM pipeline consists of several stages (tissue segmentation, spatial normalization to a standard Montreal National Institute [MNI] template, modulation, and smoothing), as previously described (Kurth et al., 2015 (link)). CAT12 potentially provided more robust and accurate performances compared to other VBM pipelines (Farokhian et al., 2017 (link)) in the calculation of gray matter volume (GMV). The normalized and modulated gray matter images were then smoothed with 10-mm full width at half-maximum Gaussian kernel.