We associate to each row-finite directed graph E a universal Cuntz-Krieger C - algebra C (E), and study how the distribution of loops in E affects the structure of C (E). We prove that C (E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which

, then Amdahl’s law says that speedup is given by Speedup = (s + p)/(s + p/N) = l/b + p/N), where we have set total time s + p = 1 for algebraic simphcity. For N = 1024 this is an unforgivingly steep function of s near s = 0 (see Figure 1). The steepness of the graph near s = 0 (approximately-N’) implies

In recent years the theory of structured ring spectra (formerly known as A # - and E # -ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect

; adjacency matrix; graph; algebraic spectrum. I.

We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides real-time exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over

of rank up to some arbitrary large cardinal together with the graphs of the polymorphic functions definable mathematical concepts. The interpretation is constructed by defining “names ” or “representatives ” for the sets in the domain of discourse by transfinite inductive definition in the context of a

We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s

For almost all graphs the answer to the question in the title is still unknown. Here we survey the cases for which the answer is known. Not only the adjacency matrix, but also other types of matrices, such as the Laplacian matrix, are considered.

Abstract. In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator

, we will show that both approaches are essentially correct if one considers the appropriate matrices. We will prove that (under certain mild conditions) the eigenvalues of the (normalized) Laplacian of a random power law graph follow the semi-circle law while the spectrum of the adjacency matrix of a