In the MSSM the quasi-infra-red fixed point for the top-quark Yukawa coupling
gives rise to specific predictions for the soft-breaking parameters. We discuss
the extent to which these predictions are modified by the introduction of
additional ``non-holomorphic'' soft-breaking terms. We also show that in a
specific class of theories there exists an RG-invariant trajectory for the
``non-holomorphic'' terms, which can be understood using a holomorphic spurion
term.Comment: 24 pages, TeX, two figures. Uses Harvmac (big) and epsf. Minor errors
  corrected, and the RG trajectory explained in terms of a holomorphic spurion
  ter

B. Lu

B.D. Dent

J. Krozel

J. Mitchell

M. Brazil

O. Aichholzer

S. Ramnath

S. Rao

T.A. Slocum

W. Shi

W. Tobler

English

arXiv

Kevin Buchin

Bettina Speckmann

Kevin Verbeek

CiteSeerX

Angle-restricted Steiner Arborescences for Flow Map Layout

Flow maps visualize the movement of objects between places. One or more sources are connected to several targets by arcs whose thickness corresponds to the amount of flow between a source and a target. Flow maps reduce visual clutter by merging (bundling) lines smoothly and by avoiding self-intersections. We present algorithms that compute crossing-free flows of high visual quality. To this end we introduce a new variant of the geometric Steiner arborescence problem. The goal is to connect the targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle they form with the source. Such an angle-restricted Steiner arborescence, or simply ow tree, naturally induces a clustering on the targets and smoothly bundles arcs. We study the properties of optimal flow trees and show that they consist of logarithmic spirals and straight lines. Computing optimal flow trees is NP-hard. Hence we consider a variant of flow trees which uses only logarithmic spirals, so called spiral trees. Spiral trees approximate flow trees within a factor depending on the angle restriction. Computing optimal spiral trees remains NP-hard. We present an efficient 2-approximation for spiral trees, which can be extended to avoid certain types of obstacles

Buchin, K.

Speckmann, B.

Verbeek, K.A.B.

NARCIS 

Angle-restricted Steiner arborescences for flow map layout

Pure OAI Repository

In the MSSM the quasi-infrared fixed point for the top-quark Yukawa coupling gives rise to specific predictions for the soft-breaking parameters. We discuss the extent to which these predictions are modified by the introduction of additional “nonholomorphic” soft-breaking terms. We also show that in a specific class of theories, there exists an RG-invariant trajectory for the “nonholomorphic” terms, which can be understood using a holomorphic spurion term. © 2000 The American Physical Society

Jack, I

Jones, DRT

University of Liverpool Repository

Quasi-infrared fixed points and renormalization group invariant trajectories for nonholomorphic soft supersymmetry breaking

Flow maps visualize the movement of objects between places. One or more sources are connected to several targets by arcs whose thickness corresponds to the amount of flow between a source and a target. Flow maps reduce visual clutter by merging (bundling) lines smoothly and by avoiding self-intersections.
We present algorithms that compute crossing-free flows of high visual quality. To this end we introduce a new variant of the geometric Steiner arborescence problem. The goal is to connect the targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle they form with the source. Such an angle-restricted Steiner arborescence, or simply 
ow tree, naturally induces a clustering on the targets and smoothly bundles arcs.
We study the properties of optimal flow trees and show that they consist of logarithmic spirals and straight lines. Computing optimal flow trees is NP-hard. Hence we consider a variant of flow trees which uses only logarithmic spirals, so called spiral trees. Spiral trees approximate flow trees within a factor depending on the angle restriction. Computing optimal spiral trees remains NP-hard. We present an efficient 2-approximation for spiral trees, which can be extended to avoid certain types of obstacles

Buchin, KA Kevin

Speckmann, B Bettina

Verbeek, KAB Kevin

Repository TU/e

We introduce a new variant of the geometric Steiner arborescence problem, motivated by the layout of flow maps. Flow maps show the movement of objects between places. They reduce visual clutter by bundling lines smoothly and avoiding self-intersections. To capture these properties, our angle-restricted Steiner arborescences, or flux trees, connect several targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle they form with the source.
We study the properties of optimal flux trees and show that they are planar and consist of logarithmic spirals and straight lines. Flux trees have the shallow-light property. Computing optimal flux trees is NP-hard. Hence we consider a variant of flux trees which uses only logarithmic spirals. Spiral trees approximate flux trees within a factor depending on the angle restriction. Computing optimal spiral trees remains NP-hard, but we present an efficient 2-approximation, which can be extended to avoid  positive monotone  obstacles

We introduce a new variant of the geometric Steiner arborescence problem, motivated by the layout of flow maps. Flow maps show the movement of objects between places. They reduce visual clutter by bundling lines smoothly and avoiding self-intersections. To capture these properties, our angle-restricted Steiner arborescences, or flux trees, connect several targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle they form with the source. We study the properties of optimal flux trees and show that they are planar and consist of logarithmic spirals and straight lines. Flux trees have the shallow-light property. Computing optimal flux trees is NP-hard. Hence we consider a variant of flux trees which uses only logarithmic spirals. Spiral trees approximate flux trees within a factor depending on the angle restriction. Computing optimal spiral trees remains NP-hard, but we present an efficient 2-approximation, which can be extended to avoid "positive monotone" obstacles

Crossref

Angle-Restricted Steiner Arborescences for Flow Map Layout