Effective algebraic degeneracy

On degeneracy of lower envelopes of algebraic surfaces

We analyze degeneracy of lower envelopes of algebraic surfaces. We focus on the cases omitted in the existing complexity analysis of lower envelopes [Halperin and Sharir 1993], and re-define the degeneracy from the viewpoint of the adjacency structure and the number of connected components. We also define badness of degeneracy from such viewpoint and show how bad the degeneracy can be. This res...

Effective Algebraic Power Series

The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series.

Effective Hamiltonian for the pyrochlore antiferromagnet: Semiclassical derivation and degeneracy

In the classical pyrochlore lattice Heisenberg antiferromagnet, there is a macroscopic continuous groundstate degeneracy. We study the semiclassical limit of large spin length S, keeping only the lowest-order in 1 /S correction to the classical Hamiltonian. We perform a detailed analysis of the spin-wave modes, and using a real-space loop expansion, we produce an effective Hamiltonian, in which...

Conformational degeneracy restricts the effective information content of heparan sulfate.

The linear, sulfated polysaccharide heparan sulfate occupies a pivotal position in intercellular signalling events, interacting with numerous proteins on the cell surface and in the extracellular matrix. Its complex sequences suggest high potential information content but, despite extensive efforts, a clear relationship between its substitution pattern and biological activity remains elusive. T...

Effective Algebraic Analysis in Linear Control Theory