We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis, by a comprehensive evaluation using different model selection criteria over three typical data types--a resting state, an event-related design, and a block design data set--with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback's IC (KIC) based on Kullback's symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve VAR model selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts, which suffer from overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly from small, specific networks such as the resting-state default mode network and the task-related motor networks, whereas low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks.
This study investigated the influence of chitosan (CH) and hydroxypropyl methylcellulose (H), along with ultrasound power, on the physicochemical properties, antifungal activity, and stability of oil-in-water (O/W) nanoemulsions containing thymol and cinnamaldehyde in a 7:3 (v/v) ratio. Eight O/W formulations were prepared using CH, H, and a 1:1 (v/v) blend of CH and H, both with and without ultrasonication (U). Compared to untreated samples, U-treated nanoemulsions had lower droplet sizes (433-301 nm), polydispersity index (0.42-0.47), and zeta potential (-0.42-0.77 mV). The U treatment decreased L* and b* values, increased a* color attribute values, and increased apparent viscosity (0.26-2.17) at the same shear rate. After 28 days, microbiological testing of nanoemulsions treated with U showed counts below the detection limits (< 2 log CFU mL-1). The U-treated nanoemulsions exhibited stronger antifungal effects against R. stolonifer, with the NE/CH-U and NE/CH-H-U formulations demonstrating the lowest minimum inhibitory and fungicidal concentrations, measured at 0.12 and 0.24 μL/mL, respectively. On day 28, U-treated nanoemulsions demonstrated higher ionic, thermal, and physical stability than untreated samples. These findings suggest that the stability and antifungal efficacy of polysaccharide-based nanoemulsions may be improved by ultrasonic treatment. This study paves the way for innovative, highly stable nanoemulsions.