Separable representations of a $W\sp{\ast} $ algebra

Succinct Representations of Separable Graphs

We consider the problem of highly space-efficient representation of separable graphs while supporting queries in constant time in the RAM with logarithmic word size. In particular, we show constanttime support for adjacency, degree and neighborhood queries. For any monotone class of separable graphs, the storage requirement of the representation is optimal to within lower order terms. Separable...

Linear Algebra Approach to Separable Bayesian Networks

Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node’s parents, instead of the joint distributions. We describe the connection between an arbitrary Conditional Probability Table (CPT) and separable systems using linear algebra. We give an a...

Estimation of Separable Representations in Psychophysical Experiments

Studying how individuals compare two given quantitative stimuli, say d1 and d2, is a fundamental problem. One very common way to address it is through ratio magnitude estimation, that is to ask individuals not to give values to d1 and d2 but rather to give their estimates of the ratio p = d1/d2. Several psychophysical theories (the most known being Stevens’ power-law) claim that this ratio cann...

8 Integral representations of separable states

We study a separability problem suggested by mathematical description of bipartite quantum systems. We consider Hermitian 2-forms on the tensor product H = K ⊗ L, where K, L are finite dimensional complex spaces. Inspired by quantum mechanical terminology we call such a form separable if it is a convex combination of hermitian tensor products σ * p ⊙ σ p of 1-forms σ p on H that are product for...

The Algebra of Fibonacci Representations