Jean Bourgain, problem solver

Domain Problem Solver Layer Domain Problem Solver

Corrections and Additions to “entropy of Quantum Limits” Jean Bourgain and Elon Lindenstrauss

This theorem implies that every ergodic component of a quantum limit μ under the flow a(t) has entropy ≥ κ′. In a later paper [2], the second named author has been able to use Theorem 1 in conjunction with a partial classification of measures on X invariant under the geodesic flow that satisfy a recurrence property under the Hecke correspondence to prove that the only arithmetic quantum limit i...

Toward a Unified Theory of Sparse Dimensionality Reduction in Euclidean Space Jean Bourgain and Jelani Nelson

Let Φ ∈ Rm×n be a sparse Johnson-Lindenstrauss transform [KN] with s non-zeroes per column. For T a subset of the unit sphere, ε ∈ (0, 1/2) given, we study settings for m, s required to ensure E Φ sup x∈T ∣∣‖Φx‖22 − 1∣∣ < ε, i.e. so that Φ preserves the norm of every x ∈ T simultaneously and multiplicatively up to 1 + ε. In particular, our most general theorem shows that it suffices to set m = ...

Problem Solver

The contract net protocol has been developed to specify problem-solving communication and control for nodes in a distributed problem solver. Task distribution is'affected by a negotiation process, a discussion carried on between nodes with tasks to be executed and nodes that may be able to execute those tasks. We present the specification of the protocol and demonstrate its use in the solution ...

Optimal Ordered Problem Solver