for example, the differentiation, or derivative, captures rate of change of a system with respect to the change of some causes. so the operation of differentiation produce a wholly different kind(type) of object, which is used to act on the some quantity(object) in the original system to ...
这种优化将一些算子(例如 transpose)下沉到其它算子(例如 batch normalization,ReLU,sigmoid 和 channel shuffle)之下。通过这种优化,许多相似的操作会靠得更近,使得我们有更多的机会进行代数简化。 4.3.3 Dataflow-level optimizations. Common sub-expression elimination (CSE). 公共子表达式消除。 Dead code elimination...
The first time derivative \({\dot{w}}_{i}\left(t\right)\) in the logistic model accounts only for properties of this change in an infinitely small neighborhood of the considered time t. However, the change of the amount of waste in a given country at t depends on the changes of inp...
Whole-brain models have proven to be useful to understand the emergence of collective activity among neural populations or brain regions. These models combine connectivity matrices, or connectomes, with local node dynamics, noise, and, eventually, transm
1. Unified definition of the derivative It is necessary to define derivatives of functions y=f(x) where x and y are matrices (and their special cases, that is, numbers, row vectors, column vectors) or symmetric matrices. To begin with, the differential df(x) of a function f:X→Y at...
Using the CB rule (1), one can obtain:(6)a2(i,j)=A(i,j)·(I+2E)·A(i,j)where the Lagrangian strain E=12(FT·F-I) with I the second order identity tensor, and FT is the transpose of F. A centrosymmetric (simple Bravais) lattice is one that has pairs of bonds in opposite...
transpose(m) Returns the transpose of the matrix m. If the source is dimension mrows× mcolumns, the result is dimension mcolumns× mrowsTexture Sampling IntrinsicsThere are sixteen texture sampling intrinsics used for sampling texture data into a shader. There are four types of textures (1D,...
We study the neural field equations introduced by Chossat and Faugeras to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure tensor, intrinsically lives in a
We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches t
Here, material derivative (), pressure () and body forces (). The material moduli must meet the given relationship of the Maxwell fluid model ab above. The velocity field and matrix transposeis presented as The energy equations for nanofluid is ...