Permitted and Forbidden Sets in Symmetric Threshold-Linear Networks

Permitted and Forbidden Sets in Symmetric Threshold-Linear Networks

The richness and complexity of recurrent cortical circuits is an inexhaustible source of inspiration for thinking about high-level biological computation. In past theoretical studies, constraints on the synaptic connection patterns of threshold-linear networks were found that guaranteed bounded network dynamics, convergence to attractive fixed points, and multistability, all fundamental aspects...

Pattern Completion in Symmetric Threshold-Linear Networks

Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable candidates for memory encoding and retrieval. In this work, we characterize stable fixed points of general threshold-linear networks with consta...

Permitted trigonometric thin sets and infinite combinatorics

We investigate properties of permitted trigonometric thin sets and construct uncountable permitted sets under some set-theoretical assumptions.

A Family of Permitted Trigonometric Thin Sets

We introduce the notion of perfectly measure zero sets and prove that every perfectly measure zero set is permitted for the families of all pseudoDirichlet sets, N0-sets, A-sets and N-sets. In particular this means that these families of trigonometric thin sets are closed under adding sets of cardinality less than the additivity of Lebesgue measure. §0. Introduction Let F be a family of sets of...

Linear Algebra and Forbidden Configurations