Author Correction: Cerebellar state estimation enables resilient coupling across behavioural domains

Sensory impulses related to touch, pressure, vibration, and proprioception from various body parts, such as the limbs, trunk, neck, and posterior head, travel to the cerebral cortex through the posterior column-medial lemniscus pathway. The pathway’s name derives from the two white-matter tracts that convey the impulses: the spinal cord's posterior column and the brainstem's medial lemniscus. First-order sensory neurons extend their axons into the spinal cord, forming the...

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...

The cerebellum, while traditionally associated with motor control, also plays a crucial role in memory, particularly in procedural memory, which involves learning motor tasks that become automatic through repetition. For example, studies have shown that when the cerebellum is damaged, individuals or animals lose the ability to learn conditioned motor responses, such as the conditioned eye-blink response in classical conditioning experiments with rabbits. This study demonstrates the...

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

A rigid body is in static equilibrium when the net force and the net torque acting on the system are equal to zero.
Consider two children sitting on a seesaw, which has negligible mass. The first child has a mass (m1) of 26 kg and sits at point A, which is 1.6 meters (r1) from the pivot point B; the second child has a mass (m2) of 32 kg and sits at point C. How far from the pivot point B should the second child sit (r2) to balance the seesaw?