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Diagram of a restricted Boltzmann machine with three visible units and four hidden units (no bias units) A restricted Boltzmann machine (RBM) (also called a restricted Sherrington–Kirkpatrick model with external field or restricted stochastic Ising–Lenz–Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs.
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A graphical representation of a Boltzmann machine with a few weights labeled. Each undirected edge represents dependency and is weighted with weight . In this example there are 3 hidden units (blue) and 4 visible units (white). This is not a restricted Boltzmann machine.
In statistical mechanics, multiplicity (also called statistical weight) refers to the number of microstates corresponding to a particular macrostate of a thermodynamic system. [1]
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The elements of the spatial weight matrix are determined by setting = for all connected pairs of nodes with all the other elements set to 0. This makes the spatial weight matrix equivalent to the adjacency matrix of the corresponding network. It is common [2] to row-normalize the matrix ,
The Lattice Boltzmann methods for solids (LBMS) are a set of methods for solving partial differential equations (PDE) in solid mechanics. The methods use a discretization of the Boltzmann equation(BM), and their use is known as the lattice Boltzmann methods for solids. LBMS methods are categorized by their reliance on: Vectorial distributions [1]
(B) (,) of weight = and minimal order exist if is a prime power and such a circulant weighing matrix can be obtained by signing the complement of a finite projective plane. Since all C W ( n , k ) {\displaystyle CW(n,k)} for k ≤ 25 {\displaystyle k\leq 25} have been classified, the first open case is C W ( 105 , 36 ) {\displaystyle CW(105,36)} .