Based on prevailing numerical forecasting models (Community Multiscale Air Quality [CMAQ] model , Comprehensive Air Quality Model with Extensions, and Nested Air Quality Prediction Modeling System) and observations from monitoring stations in Hong Kong, we employ a set of autoregressive integrated moving average (ARIMA) models with numerical forecasts (ARIMAX) to improve the forecast of air pollutants including PM2.5, NO2, and O3. The results show significant improvements in multiple evaluation metrics for daily (1–3 days) and hourly (1–72 hr) forecast. Forecasts on daily 1‐hr and 8‐hr maximum O3 are also improved. For instance, compared with CMAQ, applying CMAQ‐ARIMA reduces average root‐mean‐square errors (RMSEs) at all stations for daily average PM2.5, NO2, and O3 in the next 3 days by 14.3–21.0%, 41.2–46.3%, and 47.8–49.7%, respectively. For hourly forecasts in the next 72 hr, reductions in RMSEs brought by ARIMAX using CMAQ are 18.2% for PM2.5, 32.1% for NO2, and 36.7% for O3. Large improvements in RMSEs are achieved for nonrural PM2.5 and rural NO2 using ARIMAX with three numerical models. Dynamic hourly forecast shows that ARIMAX can be applied for forecast of 7‐ to 72‐hr PM2.5, 4‐ to 72‐hr NO2, and 4‐ to 6‐hr O3. Besides applying ARIMAX for NO2, we recommend a mixed forecast strategy to ARIMAX for normal values of PM2.5 and O3 and employ numerical models for outputs above 75th percentile of historical observations. Our hybrid ARIMAX method can combine the advantage of ARIMA and numerical modeling to assist real‐time air quality forecasting efficiently and consistently.

Biological motor control is versatile and efficient. Muscles are flexible and undergo continuous changes requiring distributed adaptive control mechanisms. How proprioception solves this problem in the brain is unknown. Here we pursue a task-driven modeling approach that has provided important insights into other sensory systems. However, unlike for vision and audition where large annotated datasets of raw images or sound are readily available, data of relevant proprioceptive stimuli are not. We generated a large-scale dataset of human arm trajectories as the hand is tracing the alphabet in 3D space, then using a musculoskeletal model derived the spindle firing rates during these movements. We propose an action recognition task that allows training of hierarchical models to classify the character identity from the spindle firing patterns. Artificial neural networks could robustly solve this task, and the networks' units show directional movement tuning akin to neurons in the primate somatosensory cortex. The same architectures with random weights also show similar kinematic feature tuning but do not reproduce the diversity of preferred directional tuning nor do they have invariant tuning across 3D space. Taken together our model is the first to link tuning properties in the proprioceptive system to the behavioral level. Proprioception | Goal-driven modeling | Handwritten character recognition | Deep neural networks | Musculoskeletal models | Somatosensory cortex | S1 | Cuneate NucleusHighlights:• We provide a normative approach to derive neural tuning of proprioceptive features from behaviorallydefined objectives.

Biological motor control is versatile, efficient, and depends on proprioceptive feedback. Muscles are flexible and undergo continuous changes, requiring distributed adaptive control mechanisms that continuously account for the body's state. The canonical role of proprioception is representing the body state. We hypothesize that the proprioceptive system could also be critical for high-level tasks such as action recognition. To test this theory, we pursued a task-driven modeling approach, which allowed us to isolate the study of proprioception. We generated a large synthetic dataset of human arm trajectories tracing characters of the Latin alphabet in 3D space, together with muscle activities obtained from a musculoskeletal model and model-based muscle spindle activity. Next, we compared two classes of tasks: trajectory decoding and action recognition, which allowed us to train hierarchical models to decode either the position and velocity of the end-effector of one's posture or the character (action) identity from the spindle firing patterns. We found that artificial neural networks could robustly solve both tasks, and the networks'units show tuning properties similar to neurons in the primate somatosensory cortex and the brainstem. Remarkably, we found uniformly distributed directional selective units only with the action-recognition-trained models and not the trajectory-decoding-trained models. This suggests that proprioceptive encoding is additionally associated with higher-level functions such as action recognition and therefore provides new, experimentally testable hypotheses of how proprioception aids in adaptive motor control.

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