Universality of geometry

Scaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp

We develop a new approach to combinatorial games (e.g., chess, Go, checkers, Chomp, Nim) that unveils connections between such games and nonlinear phenomena commonly seen in nature: scaling behaviors, complex dynamics and chaos, growth and aggregation processes. Using the game of Chomp (as well as variants of the game of Nim) as prototypes, we discover that the game possesses an underlying geom...

Geometry, scaling, and universality in the mass distributions in heavy ion collisions.

Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate the mass yields and the distribution of cluster sizes. Simple Malthusian dynamics and nonlinear Verhulst dynamics are used to illustrate the approach. Nucle...

Weak alg-universality and Q-universality of semigroup quasivarieties

In an earlier paper, the authors showed that standard semigroups M1, M2 andM3 play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by M2 and M3 are neither relatively alg-universal nor Q-universal, while there do exist finite semigroups S2 and S3 generating the same semigroup variety as M2 and ...

Universality of Nash Equilibria

Universality of beamsplitters

We consider the problem of building an arbitrary N × N real orthogonal operator using a finite set, S, of elementary quantum optics gates operating on m ≤ N modes the problem of universality of S on N modes. In particular, we focus on the universality problem of an m-mode beamsplitter. Using methods of control theory and some properties of rotations in three dimensions, we prove that any nontri...