The audio and visual weights are considered fixed parameters of the system, restricted to sum up to one and optimized for speech recognition on the evaluation dataset.
A systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of C*-algebras.
Finally the pullback and pushout constructions are applied to the class of noncommutative CW complexes defined by (S. Eilers, T. A Loring, and G. K. Pedersen J. Reine Angew. Math., 1998, 499, 101 143) to show that this category is stable under tensor products and under restricted direct sums.
However, by restricting the sum of each event to a solitary page, Davies risks a charge of promoting form over content.
By the definition of (P_{2m}), we can restrict the sum in (3.21) to vectors (kinmathbb{X}^{m+1}) with mathbb{X}^{m+1}equivbigl{ kinmathbb {Z}^{2L_{m+1}}:0< vert k vert < M_{m+1}bigr}.
To solve this problem, we follow Gardeazabal and Ugidos (2004) and Yun (2005) and restrict the sum of the estimated coefficients of each set of dichotomous variables to zero in performing the decomposition (8).
Then g = ∑ g i 1 ⋯ i n, and g = ⨁ g i 1 ⋯ i n if we restrict the sum to those n –tuples ( i 1, ⋯, i n ) for which 0 ≤ i j < m j, where m j is the order of σ j.
By restricting the sum in Eq. (19) to some window W, a small in amplitude but potentially long tail is neglected.
Here ∑ ∥ restricts the sum to opposite links on each plaquette, B □ ≡ S i j + S k j − S k ℓ + S i ℓ − + H.c., and the coupling constants are given by J = − 4 μ 2 Ω − 4 η 2 Ω − ω, V = − 2 β 2 ω.
An efficient way to reduce complexities and power in the implementation of digital finite impulse response (FIR) filters is to design the filters with coefficients restricted to the sum of signed powers-of-two (SPoT) terms.
