Universal manifold pairings and positivity

Universal Manifold Pairings and Positivity

Gluing two manifolds M1 and M2 with a common boundary S yields a closed manifold M . Extending to formal linear combinations x = ΣaiMi yields a sesquilinear pairing p = 〈 , 〉 with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p onto a finite dimensional quotient pairing q with values in C which in physically...

Human language reveals a universal positivity bias

Using human evaluation of 100,000 words spread across 24 corpora in 10 languages diverse in origin and culture, we present evidence of a deep imprint of human sociality in language, observing that (i) the words of natural human language possess a universal positivity bias, (ii) the estimated emotional content of words is consistent between languages under translation, and (iii) this positivity ...

Centroidal Voronoi tessellation in universal covering space of manifold surfaces

The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization, etc. In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework – the CVT in universal covering space. The novel spherical and hyperbolic CVT energy funct...

Mani and shapur a universal faith for e universal kingdom

On the relationship between squared pairings and plain pairings

In this paper, we investigate the relationship between the squared Weil/Tate pairing and the plain Weil/Tate pairing. Along these lines, we first show that the squared pairing for arbitrary chosen point can be transformed into a plain pairing for the trace zero point which has a special form to compute them more efficiently. This transformation requires only a cost of some Frobenius actions. Ad...