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The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle.
The Radial Unit Hypothesis (RUH) is a conceptual theory of cerebral cortex development, first described by Pasko Rakic. It states that the cerebral cortex develops during embryogenesis as an array of interacting cortical columns , or 'radial units', each of which originates from a transient stem cell layer called the ventricular zone , which ...
A marginal likelihood is a likelihood function that has been integrated over the parameter space.In Bayesian statistics, it represents the probability of generating the observed sample for all possible values of the parameters; it can be understood as the probability of the model itself and is therefore often referred to as model evidence or simply evidence.
The physics of the system will be described by a certain formula, say the Hamiltonian H(T, J). Now proceed to divide the solid into blocks of 2×2 squares; we attempt to describe the system in terms of block variables , i.e., variables which describe the average behavior of the block.
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary).
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". A theory that includes the principle of locality is said to be a "local theory".
The marginal zone, along with the cortical zone, make up the 6 layers that form the cortex. This zone is the predecessor for layer I of the cortex. Astrocytes form an outer limiting membrane to interact with the pia. In humans it has been found that the cells here also form a subpial layer. [1]
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