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Abstract In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data. 

The thermoresponsive properties of poloxamine (tetra-branch PEO-PPO block copolymer) hydrogels are related to several variables. Of particular interest to this study were the molecular weight of the polymer, the molar ratio between PEO and PPO blocks, and the concentration of the aqueous solution. Accurately controlling the thermoresponsive behaviors of the polymer is critical to the application of such materials; therefore, the structure–property relationship of tetra-branch PEO-PPO block copolymer was studied by synthesis via anionic ring-opening polymerization (AROP). The structure–property relationships were studied by measuring the thermoresponsive behavior via differential scanning calorimetry (DSC) and developing an empirical model which statistically fit the collected data. This empirical model was then used for designing poloxamines that have critical micellization temperatures (CMT) between room temperature and physiological temperature. The model was validated with three polymers that targeted a CMT of 308 K (35°C). The empirical model showed great success in guiding the synthesis of poloxamines showing a temperature difference of less than 3 K between the predicted and the observed CMTs. This study showed a great potential of using an empirical model to set synthesis parameters to control the properties of the polymer products.