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The Geometry of the Word Problem for Finitely Generated Groups

Noel Brady Tim Riley Hamish Short

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

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Tipo de recurso:

libros

ISBN impreso

978-3-7643-7949-0

ISBN electrónico

978-3-7643-7950-6

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Birkhäuser Verlag 2007

Cobertura temática

Tabla de contenidos

The Isoperimetric Spectrum

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part I - Dehn Functions and Non-Positive Curvature | Pp. 5-27

Dehn Functions of Subgroups of CAT(0) Groups

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part I - Dehn Functions and Non-Positive Curvature | Pp. 29-76

Filling Functions

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part II - Filling Functions | Pp. 89-108

Relationships Between Filling Functions

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part II - Filling Functions | Pp. 109-121

Example: Nilpotent Groups

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part II - Filling Functions | Pp. 123-127

Asymptotic Cones

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part II - Filling Functions | Pp. 129-143

Dehn’s Problems and Cayley Graphs

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part III - Diagrams and Groups | Pp. 157-162

Van Kampen Diagrams and Pictures

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part III - Diagrams and Groups | Pp. 163-177

Small Cancellation Conditions

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part III - Diagrams and Groups | Pp. 179-185

Isoperimetric Inequalities and Quasi-Isometries

Noel Brady; Tim Riley; Hamish Short

This paper deals with the lead optimization phase of pharmaceutical research where a number of leads (molecules as a basis for potential drugs) are processed by different departments in order to optimize their biochemical characteristics. We depict each lead as a project and model the problem as a static multi-project selection and scheduling problem under resource constraints with the objective to maximize the weighted work performed. For solving the problem we propose two heuristics. We assess their performance in a computational study and we point out one dominant method. Furthermore we show the impact of problem parameters such as the extend to which projects can be crashed.

Part III - Diagrams and Groups | Pp. 187-196