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This paper develops iterative learning control strategies for discrete-time linear systems. An explicit state-space formula for the inverse-model-based ILC algorithm is derived under general conditions, which simplifies further when matrices B and C are invertible, providing a foundation for MIMO non-square systems. Building upon this formulation, a class of composite inverse-model algorithms is proposed, ensuring zero tracking error after a finite number of iterations while maintaining approximately minimal transient errors, and serving as a flexible framework to integrate optimization or greedy strategies. Robustness analysis is conducted for the multi-iteration inverse-model algorithms under model uncertainties, demonstrating uniform convergence properties. Furthermore, the framework is extended to systems with uncertain initial conditions, achieving zero-error convergence without requiring the initial state to converge to a fixed value, overcoming limitations in existing literature. Numerical simulations validate the effectiveness and practicality of the proposed methods.

Optically pumped magnetometers (OPMs) are new, room-temperature alternatives to superconducting quantum interference devices (SQUIDs) for measuring the brain’s magnetic fields. The most used OPM in MagnetoEncephaloGraphy (MEG) are based on alkali atoms operating in the spin-exchange relaxation-free (SERF) regime. These sensors do not require cooling but have to be heated. Another kind of OPM, based on the parametric resonance of 4He atoms are operated at room temperature, suppressing the heat dissipation issue. They also have an advantageous bandwidth and dynamic range more suitable for MEG recordings. We quantitatively assessed the improvement (relative to a SQUID magnetometers array) in recording the magnetic field with a wearable 4He OPM-MEG system through data simulations. The OPM array and magnetoencephalography forward models were based on anatomical MRI data from an adult, a nine-year-old child, and 10 infants aged between one month and two years. Our simulations showed that a 4He OPMs array offers markedly better spatial specificity than a SQUID magnetometers array in various key performance areas (e.g., signal power, information content, and spatial resolution). Our results are also discussed regarding previous simulation results obtained for alkali OPM.

This paper posits that the brain evolved for the control of action rather than for the development of cognition per se. We note that the terms commonly used to describe brain–behavior relationships define, and in many ways limit, how we conceptualize and investigate them and may therefore constrain the questions we ask and the utility of the “answers” we generate. Many constructs are so nonspecific and over-inclusive as to be scientifically meaningless. “Executive function” is one such term in common usage. As the construct is increasingly focal in neuroscience research, defining it clearly is critical. We propose a definition that places executive function within a model of continuous sensorimotor interaction with the environment. We posit that control of behavior is the essence of “executive function,” and we explore the evolutionary advantage conferred by being able to anticipate and control behavior with both implicit and explicit mechanisms. We focus on the cerebellum's critical role in these control processes. We then hypothesize about the ways in which procedural (skill) learning contributes to the acquisition of declarative (semantic) knowledge. We hypothesize how these systems might interact in the process of grounding knowledge in sensorimotor anticipation, thereby directly linking movement to thought and “embodied cognition.” We close with a discussion of ways in which the cerebellum instructs frontal systems how to think ahead by providing anticipatory control mechanisms, and we briefly review this model's potential applications.

Previous studies have demonstrated that signals originating from the South Pacific can improve the El Niño‐Southern Oscillation (ENSO) prediction at various lead times. In this study, it is found that sea surface height anomalies in the off‐equatorial South Pacific (SP SSH), potentially improves ENSO prediction with lead times exceeding 9 months. Using linear inverse models, we find that SP SSH anomalies and the associated accumulation of warm water result from continuous easterly winds over the tropical central Pacific that force downwelling Rossby waves in the off‐equatorial South Pacific. These downwelling Rossby waves reflect into equatorial downwelling Kelvin waves that propagate into the central and eastern Pacific, ultimately leading to an El Niño event in the following winter.

Dissolved organic phosphorus (DOP) has been identified as a key phosphorus source that supports primary production and microbial nitrogen (N2) fixation. However, the specific contribution and spatial distribution of DOP utilization remain poorly understood due to limited in‐situ measurements. In this study, we explored the role of DOP in supporting N2 fixation using a modified inverse biogeochemical ocean model. Our findings reveal that DOP utilization primarily occurs in subtropical gyres, where it serves as a critical phosphorus source. Direct DOP assimilation reduces phosphorus limitation in nutrient‐depleted gyres, thereby stimulating global N2 fixation, the global distribution of which is re‐estimated. The new estimate shows a significant increase in N2 fixation rates in the North Atlantic compared to the previous estimate because DOP utilization reduces the severe phosphorus limitation in that region. Neglecting DOP utilization would result in an approximately 9% underestimation of the global N2 fixation rate. Plain Language Summary Dissolved organic phosphorus plays a crucial role in providing phosphorus, which is essential for primary production and microbial nitrogen (N2) fixation. However, due to limited in‐situ measurements, the extent and pattern of DOP use in the ocean are not well understood. In this study, we used a modified ocean model to investigate how DOP supports N2 fixation. Our results show that DOP is mainly used in subtropical gyres, where it helps reduce phosphorus shortages, thereby boosting N2 fixation globally. We found that N2 fixation rates, especially in the North Atlantic, are much higher than previously thought due to the mitigating effect of DOP on phosphorus limitation. Ignoring the role of DOP would lead to an underestimation of global N2 fixation by about 9%. Key Points Autotrophic dissolved organic phosphorus (DOP) uptake supports 15% of marine net primary production (NPP), with nearly 60% from the subtropical gyres of the North Pacific and North Atlantic DOP utilization leads to a 9% increase in global N2 fixation compared to the model without direct DOP utilization DOP utilization boosts the contribution of N2 fixation to export production by 20%–40% in subtropical gyres

In performing skillful movement, humans use predictions from internal models formed by repetition learning. However, the computational organization of internal models in the brain remains unknown. Here, we demonstrate that a computational architecture employing a tandem configuration of forward and inverse internal models enables efficient motor learning in the cerebellum. The model predicted learning adaptations observed in hand-reaching experiments in humans wearing a prism lens and explained the kinetic components of these behavioral adaptations. The tandem system also predicted a form of subliminal motor learning that was experimentally validated after training intentional misses of hand targets. Patients with cerebellar degeneration disease showed behavioral impairments consistent with tandemly arranged internal models. These findings validate computational tandemization of internal models in motor control and its potential uses in more complex forms of learning and cognition.

Understanding and forecasting Tropical Pacific Decadal‐scale Variability (TPDV) strongly rely on climate model simulations. Using a Linear Inverse Modeling (LIM) diagnostic approach, we reveal Coupled Model Intercomparison Project Phase 6 models have significant challenges in reproducing the spatial structure and dominant mechanisms of TPDV. Specifically, while the models' ensemble mean pattern of TPDV resembles that of observations, the spread across models is very large and most models show significant differences from observations. In observations, removing the coupling between extratropics and tropics reduces TPDV by ∼60%–70%, and removing the tropical thermocline variability makes the central tropical Pacific a key center of action for TPDV and El Niño Southern Oscillation variability. These characteristics are only confirmed in a subset of models. Differences between observations and simulations are outside the range of natural internal TPDV noise and pose important questions regarding our ability to model the impacts of natural internal low‐frequency variability superimposed on long‐term climate change. Plain Language Summary Tropical Pacific Decadal‐scale Variability (TPDV) has been shown to impact global‐scale climate fluctuations, weather regimes, and temperature trends such as the 1998–2012 global warming hiatus. Understanding and predicting TPDV's impacts strongly rely on climate model simulations and projections. However, the models show key deficiencies in reproducing the observed structure of TPDV. Although the arithmetic mean of TPDV's spatial pattern in each individual model is similar to observations, there is a large spread among models, and most models show significant differences from observations. Using an empirical dynamical model to decompose the mechanisms of the climate models reveals that more than 50% of the models fail to reproduce the roles of extratropics‐tropics coupling and the tropical thermocline variability play in TPDV. These differences show significant challenges exist across the models for modeling the decadal‐scale climate variability in the tropical Pacific. Improving the simulation of TPDV in climate models is vital for understanding the impacts of natural internal low‐frequency variability alongside long‐term climate change. Key Points A Linear Inverse Model is used to decompose and compare tropical Pacific decadal variability dynamics in observations and climate models Coupled Model Intercomparison Project Phase 6 models have significant challenges in reproducing the observed dynamics and spatial pattern of tropical Pacific decadal variability Many models (>50%) cannot reproduce the roles of extratropics‐tropics coupling and thermocline variability in tropical Pacific variability

The impacts of tropical interbasin interaction (TBI) on the characteristics and predictability of sea surface temperature (SST) in the tropics are assessed with a linear inverse modelling (LIM) framework that uses SST and sea surface height anomalies in the tropical Pacific (PO), Atlantic (AO), and Indian Ocean (IO). The TBI pathways are shown to be successfully isolated in stochastically-forced simulations that modify off-diagonal elements of the linear operators. The removal of TBI leads to a substantial increase in the amplitude of El Niño-Southern Oscillation (ENSO) and related variability. Partial decoupling experiments that eliminate specific coupling components reveal that PO-IO interaction is the dominant contributor, whereas PO-AO and AO-IO interactions play a minor role. A series of retrospective forecast experiments with different operators shows that decoupling leads to a substantial decrease in ENSO prediction skill especially at longer lead times. The relative contributions of individual pathways to forecast skill are generally consistent with the results from the stochastically-forced experiments. Qualitatively similar results are obtained from an additional set of forecast experiments that partially apply initial conditions over specific basins, but several important differences were also found due to differences in the representations of each TBI pathway. Finally, the cause of contrasting SST anomalies over the AO after the extreme 1982/83 and 1997/98 El Niño events is explored using LIM forecast experiments to demonstrate the strength and flexibility of our LIM-based approach.

Observational and modeling studies have elucidated the influential role played by the southern and northern extratropical Pacific (SEP and NEP) forcing in shaping dynamics of tropical Pacific climate variability. However, the relative importance of the NEP and SEP and the timescale on which they impact the tropics remain unclear. Using a linear inverse model (LIM) that selectively incorporates or excludes tropical‐extratropical coupling, we find a reduction in tropical interannual variability (∼40%) and low‐frequency (sub‐decadal to decadal) variability in the southeastern tropical Pacific region (∼70%) in the absence of SEP. Conversely, the absence of NEP yields no significant impact on tropical interannual variability but markedly diminishes low‐frequency variability in the central tropical Pacific region (∼70%). LIM and statistic diagnostics on CMIP6 models show the low‐frequency to total variability ratio in the tropical Pacific depending on their NEP and SEP representation. Models with more (less) low‐frequency power tend to show stronger NEP (SEP) dynamics. Plain Language Summary The tropical Pacific climate variability exerts a strong impact on global climate, regional weather, and marine ecosystems. The tropical and extratropical Pacific are closely coupled with each other through oceanic and atmospheric processes. Previous studies have shown that the southern and northern extratropical Pacific (SEP and NEP) forcing greatly impact the tropical Pacific climate variability. To understand and predict tropical Pacific variability, it is necessary to study the relative importance and the timescale on which the SEP and NEP exert their influence. In this study, we use an empirical dynamical model to exclude the impacts of SEP or NEP on the tropical Pacific based on the observational data. We find that the absence of SEP leads to a significant reduction of interannual variance (∼40%) and the low‐frequency (sub‐decadal to decadal) variance in the southeastern tropical Pacific region (∼70%), while the absence of the NEP does not change the interannual variance but significantly reduces the low‐frequency variance in the central tropical Pacific region (∼70%). In observations, the ratio of low‐frequency to total tropical variability is 0.36, while CMIP6 models exhibit a wider range, with enhanced low (high) frequency power associated with stronger NEP (SEP) dynamics. Key Points The SEP dynamics contribute ∼40% of the tropical interannual variance and ∼70% of the southeastern tropical low‐frequency variance The NEP dynamics do not impact the tropical interannual variance but lead to ∼70% of the central tropical low‐frequency variability CMIP6 models show stronger NEP (SEP) dynamics tend to manifest ENSO with more (less) low‐frequency (>6 years) power

The Interdecadal Pacific Oscillation (IPO) and Atlantic Multidecadal Variability (AMV) substantially affect global climate system. Model studies suggested a fast interaction between the IPO and AMV through atmospheric teleconnections, but observations exhibit a weak IPO–AMV contemporaneous correlation. To address this paradox, we apply linear inverse model (LIM) in observations to decode the interaction. We reveal that a cancel effect of the interaction lowers the observed IPO–AMV contemporaneous correlation. When only retaining the one‐way modulation (the IPO forces the AMV or the reversed one) in the observational LIM, their correlation peaks nearly simultaneously, consistent with the fast IPO–AMV interaction in model experiments. We further demonstrate that the fast interaction is associated with both tropical and extratropical processes. Our study reconciles the discrepancy between observations and models on the IPO–AMV interaction. Plain Language Summary Many decadal‐to‐multidecadal climate and biological variations could be attributed to two climate modes, the Interdecadal Pacific Oscillation (IPO) and Atlantic Multidecadal Variability (AMV). In model simulations, the two modes interact via fast atmospheric teleconnections, implying a high contemporaneous correlation between them. However, in observations, the IPO–AMV contemporaneous correlation is weak. Here, by using observations and model simulations, we show that the weak contemporaneous correlation results from the competition between the IPO‐forced positive correlation and the AMV‐forced negative correlation. Our study confirms a fast interaction between the IPO and AMV in observations, which has broad implications for improving climate simulation and decadal climate prediction. Key Points The Interdecadal Pacific Oscillation–Atlantic Multidecadal Variability interaction lowers their contemporaneous correlation Both observational linear inverse model and general circulation model experiments support the cancel effect of the interaction The commonly used correlation analysis in climate science may lead to misunderstanding in a coupled system