For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.

Citation: The PLOS ONE Staff (2014) Correction: Global Genetic Response in a Cancer Cell: Self-Organized Coherent Expression Dynamics. PLoS ONE 9(8): e105491. doi:10.1371/journal.pone.0105491 Published August 8, 2014 Copyright: 2014 The PLOS ONE Staff. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribu...

Probability forecasts in complex environments can benefit from combining the estimates of large groups of forecasters (“judges”). But aggregating multiple opinions faces several challenges. First, human judges are notoriously incoherent when their forecasts involve logically complex events. Second, individual judges may have specialized knowledge, so different judges may produce forecasts for d...

Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting structures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they con...

An algebra A is uniform if for each θ ∈ ConA, every two classes of θ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.

The states |α,m〉, defined as â†m|α〉 up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f(n̂,m)â where f(n̂,m) is a nonlinear function of the number operator n̂. The explicit form of f(n̂,m) is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of th...

This paper presents a new approach to the problem of gap bridging and junction detection. Perceptual groupings and evidence from existing boundaries are combined to produce joins which are consistent with the initial image structure. In particular, a new definition of co-curvilinearity, which distinguishes between true and false co-curvilinearity, is given. Structural quantities are computed fo...