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Heuristics on pairing-friendly elliptic curves
Elliptic curves finite fields pairing-based cryptography
2011/8/23
Abstract: We present a heuristic asymptotic formula as $x\to \infty$ for the number of pairing-friendly elliptic curves with fixed embedding degree $k\geq 3$, with fixed discriminant, with rho-value b...
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts.Firstly as field theories on noncommutat...
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts.Firstly as field theories on noncommutat...
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
fractional Brownian motion stochastic integrals rough paths
2011/2/22
Let B = (B1(t), . . . ,Bd(t)) be a d-dimensional fractional Brownian motion with Hurst index ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly...
A survey of the Poincaré Center Problem in degree 3 using finite field heuristics
survey Poincaré Center Problem degree 3
2011/2/21
We compare a heuristic count of components of the center variety in degree 3 with the equivalent count obtained from known families.From this comparison we conjecture that more than 100 unknown compon...