Deformations

This is the last conjecture of Stephen Hawking. You need the singularity to exceed his theory. This is the the holographic no-boundary wave function.

(hij, φ) is the wave function, and S is the usual surface terms. Z is the Euclidean AdS/CFT.

The black birds move to the infinite on the surface without directions. Moreover, this is like a cylinder. Euclidean AdS/CFT generalized to complex relevant deformations implies an approximate realisation.

This is the mass deformed free model partition function, and m^2 is supergravity theories which typically contain scalars of mass.

This is the action of the free O(N) model, and O(N) is the partition function of supersymmetry breaking deformations.

You plot two one-dimensional slices of the distribution for two different values of ~m^2.

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①

~m^2=0

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②

~m^2=0.05i

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This conjecture strengthens the intuition that holographic cosmology implies a significant reduction of the multiverse to a much more limited set of possible universes.

1+2+3+4+・・・

This is irrational because this must increase infinitely basically.

This is like a black hole.

Srinivasa Aiyangar Ramanujan solved it.

2F=1

∴

F=1/2

∴

A=1/4

∴

S=-1/12

This is tricky in infinity because he moves the series.

You can also use the Zeta Function.

This is A=1-2+3-4+・・=1/4

This is the Abel's summability method.

This is F=1-1+1-1+・・・=1/2

∴

ζ(-1)=1+2+3+4+・・・=-1/12

Whole Genome Shotgun Sequencing

This is the Hamiltonian path problem, which is closed.

V(G)={a,b,c,d,e,f,g,h}

This is the graph of each dot.

E(G)={ab,bc,cd,de,ef,fg,gh,ha}

This is the graph of the Hamiltonian path.

Then you see the Whole Genome Shotgun Sequencing.

This isn't closed, but there is the Hamiltonian path.

S4→S2→S1→S3→S5

You cut the chain of your DNA, and you reorganize it.

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S1→ACCTG

S2→CGACC

S3→CTGAG

S4→CGTCG

S5→AGTAC

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∴

S4→CGTCG

S2→XXXCGACC

S1→XXXXXACCTG

S3→XXXXXXXCTGAG

S5→XXXXXXXXXXAGTAC

You connect the pattern.

CGTCGACCTGAGTAC