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Loan behavior modeling is crucial in financial engineering. In particular, predicting loan prepayment based on large-scale historical time series data of massive customers is challenging. Existing approaches, such as logistic regression or nonparametric regression, could only model the direct relationship between the features and the prepayments. Motivated by extracting the hidden states of loan behavior, we propose the smoothing spline state space (QuadS) model based on a hidden Markov model with varying transition and emission matrices modeled by smoothing splines. In contrast to existing methods, our method benefits from capturing the loans’ unobserved state transitions, which not only increases prediction performances but also provides more interpretability. The overall model is learned by EM algorithm iterations, and within each iteration, smoothing splines are fitted with penalized least squares. Simulation studies demonstrate the effectiveness of the proposed method. Furthermore, a real-world case study using loan data from the Federal National Mortgage Association illustrates the practical applicability of our model. The QuadS model not only provides reliable predictions but also uncovers meaningful, hidden behavior patterns that can offer valuable insights for the financial industry. 

Tandem catalysis couples multiple reactions and promises to improve chemical processing, but precise spatiotemporal control over reactive intermediates remains elusive. We used atomic layer deposition to grow In₂O₃over Pt/Al₂O₃, and this nanostructure kinetically couples the domains through surface hydrogen atom transfer, resulting in propane dehydrogenation (PDH) to propylene by platinum, then selective hydrogen combustion by In₂O₃, without excessive hydrocarbon combustion. Other nanostructures, including platinum on In₂O₃or platinum mixed with In₂O₃, favor propane combustion because they cannot organize the reactions sequentially. The net effect is rapid and stable oxidative dehydrogenation of propane at high per-pass yields exceeding the PDH equilibrium. Tandem catalysis using this nanoscale overcoating geometry is validated as an opportunity for highly selective catalytic performance in a grand challenge reaction.