8 Matching Annotations
1. Mar 2023
2. mathbabe.org mathbabe.org
1. What tensor products taught me about living my life<br /> by Cathy O'Neil aka mathbabe

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3. May 2022
4. en.wikipedia.org en.wikipedia.org
1. Some individuals can voluntarily produce this rumbling sound by contracting the tensor tympani muscle of the middle ear. The rumbling sound can also be heard when the neck or jaw muscles are highly tensed as when yawning deeply. This phenomenon has been known since (at least) 1884.

Yes, I can do this.

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5. Apr 2022
6. cs.stanford.edu cs.stanford.edu
1. input (32x32x3)max activation: 0.5, min: -0.5max gradient: 1.08696, min: -1.53051Activations:Activation Gradients:Weights:Weight Gradients:conv (32x32x16)filter size 5x5x3, stride 1max activation: 3.75919, min: -4.48241max gradient: 0.36571, min: -0.33032parameters: 16x5x5x3+16 = 1216

The dimensions of these first two layers are explained here

7. May 2021

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9. sitiobigdata.com sitiobigdata.com

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10. May 2017
11. arxiv.org arxiv.org
1. the 2-tensorE(k)is defined byE(k)ij:=−12k+1gliδli1i2···i2k−1i2kjj1j2···j2k−1i2kRi1i2j1j2···Ri2k−1i2kj2k−1j2k.Here the generalized Kronecker delta is defined byδj1j2...jri1i2...ir= detδj1i1δj2i1···δjri1δj1i2δj2i2···δjri2............δj1irδj2ir···δjrir.As a convention we setE(0)= 1. It is clear to see thatE(1)is the Einstein tensor. The tensorE(k)ijis a very natural generalization of the Einstein tensor. We callE(k)thek-th Lovelockcurvature

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12. arxiv.org arxiv.org
1. Pstjl(k)=12δi1i2···i2k−3i2k−2stj1j2···j2k−3j2k−2j2k−1j2khj1i1hj2i2···hj2k−2i2k−2gj2k−1jgj2kl,which implies by (2.20) that(4.10)2ePstjl(k)hsj= (2k−1)! (T(2k−1))tpgpl

Esse resultado faz uso apenas do fato de que o ambiente tem curvatura seccional constante, da fórmula de Gauss (vide nota anterior) e das definições do tensor de curvatura $$\tilde{P}_{(k)}$$ e do tensor de Newton, respectivamente.

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13. terrytao.wordpress.com terrytao.wordpress.com
1. variation formula for the Ricci tensor (13) where is the trace, and the Lichnerowicz Laplacian (or Hodge-de Rham Laplacian) on symmetric rank (0,2) tensors is defined by the formula (14) and is the usual connection Laplacian.