Additionally, discriminating C+A- (in a red context) or A+C(in a yellow context) would be combinatorially
As such, they need not be 100% accurate to have adaptive utility--especially when used combinatorially
(see Gigerenzer & Brighton, 2009).
and geometrically, natural constraints often cause data to cluster along low-dimensional structures, such as unions-of-subspaces or manifolds, having a few degrees of freedom relative to their size.
Although stated combinatorially
, the only proof we know is algebraic.
5] shows that every arrangement of spheres (and hence every central arrangemen of hyperplanes) is combinatorially
equivalent to some convex polytope,  proved that there is a relation between the number of lattice point on a sphere and the volume of it.
For both conventional phase diagrams and the combinatorially
constructed phase diagrams discussed below, it should be noted that in principle it is desirable to demonstrate reversibility of each equilibrium represented.
Frequency of rare combinations of inputs has been studied combinatorially
is called a combinatorially
Riemannian manifold, denoted by ([?
Due to their typical structure, it has been proved that the information conveyed by a 1-dimensional size function can be combinatorially
stored in a formal series of points and lines (Frosini and Landi, 2001).
Subsequent test procedures examined the derivation of mutually and combinatorially
The topics include the isotopy of links, most knots are wild, infinite cyclic coverings, some curious involutions of spheres, two complexes that are homeomorphic but combinatorially
distinct, uses of the fundamental group, and a unique decomposition theorem for three-manifolds.
Furthermore, participants will now also select C given A and A given C in accordance with derived transitive and equivalence, or combinatorially
entailed, stimulus relations without further training.