Rigidity of valuative trees under henselization

Skeletal Rigidity of Phylogenetic Trees

Motivated by geometric origami and the straight skeleton construction, we outline a map between spaces of phylogenetic trees and spaces of planar polygons. The limitations of this map is studied through explicit examples, culminating in proving a structural rigidity result. 1. Motivation There has been tremendous interest recently in mathematical biology, namely in the field of phylogenetics. T...

Valuative Arf Characteristic of Singularities

The proof by Hironaka [5] of resolution of singularities of algebraic varieties over fields of characteristic zero raised the problem of classifying singularities by looking at the resolution process. Thus, equisingularity of plane curve singularities was introduced and developed by Zariski in [15] by showing that the combinatorics of the resolution processes is equivalent data to Puiseux invar...

The Valuative Theory of Foliations

Valuative invariants for polymatroids

Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-JiaReiner quasi-symmetric function, and the invariant G introduced by the first author, are valuative. In this paper we construct the Z-modules of all Z-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the Z-modules of valuat...

GABAergic circuits underpin valuative processing

Affect is the fundamental neuropsychological state combining valueand arousal-related processes underpinning emotion and mood. A major goal of the emerging field of affective science is to explain the mechanisms of valuation within the brain. A core network of brain activity is seen across mammals in response to appetitive or aversive stimuli, and appears to be largely independent of stimulus m...