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The SSReflect/Math Components Library

SSReflect (4-color)

Feit-Thompson

Math Components

Feit-Thompson

𝑣1, 𝑣2, 𝑣3, 𝑣4 ∈ 𝑹2

𝑢 = (1,0)

Q(𝑢) = 𝑢, 𝑣12 + 𝑢, 𝑣2

2 + 𝑢, 𝑣32 + 𝑢, 𝑣4

2

=1 + 0 + ¼ + ¼

=1.5

Q(𝑢) = 𝑢, 𝑣12 + 𝑢, 𝑣2

2 + 𝑢, 𝑣32 + 𝑢, 𝑣4

2

=0 + 1 + ¾ + ¾

=2.5

𝑢 = (1,0)

Main Theorem. Suppose 𝑣1, … , 𝑣𝑚 ∈ 𝑹𝑛 are vectors ||𝑣𝑖|| ≤ .01 and

energy one in each direction:

∀||𝑢|| = 1 𝑢, 𝑣𝑖2 = 1

𝑖

Then there is a partition 𝑇1 ∪ 𝑇2 such that each part has energy close to half in each direction:

∀||𝑢|| = 1 𝑢, 𝑣𝑖2 =1

2± 0.05

𝑖∈𝑇𝑗

…

…

97.5% Human

93.3% Tom vs Pete

92.4% Joint Bayesian

85.3% Attribute & Simile

88.0% CSML+ MkNN

89.0% Combined multishot

91.2.0% face.com

88.1% Brain-Inspired Features

80.7% NReLU

90.5.0% Associate-Predict

84.5% Multiple LE + comp

multi-scale

sampling dense

landmarks

Bhatnager, Sinha, Samdaria, Gupta, Batra, Bhardwaj, and Thies, Int’l Conf. on Persuasive Technology, June 2012