This is the **private** homepage of Jürgen Will (Chemist, born 1962). My
topics of **private** interest are among others:

Algebra,

Air Ships (e.g. Air Ship with Dolphin form and Wave Propeller)

Artficial Intelligence (Neural Networks, Learning from Graphs and other Non-Vectors, Conceptual Analysis, Decision Trees)

Combinatorial Pólya Enumeration (Bibliography on Combinatorial
Pólya-Redfield-De Bruijn Enumeration Theory)

- J.Will, B.Adler, G.Biess, S.Dobers: "Combinatorial Enumeration of Topological Indices";
in D. Ziessow (Ed.): Software-Entwicklung in der Chemie 7; Gesellschaft Deutscher Chemiker,
Frankfurt/Main, 1993

Summary:

Methods of combinatonal enumeration [1] are used in chemistry to calculate numbers of
positional, skeletal, configurational and stereo isomers, isomers of nonrigid molecules,
isomerizations, and other reactions. They serve to derive reaction probabilities, spectroscopic
signals, quantum chemical parameters, virial coefficients and other features [2] - [4]. The
Pólya theorem allows one to calculate not only the total number of representatives of a
class of compounds but also to subdivide them into groups with predefined properties of their
molecular graphs.

Graphs can be enumerated by simple properties like vertex number, edge number, and vertex
degree [5]. These values can be already interpreted as trivial topological indices. A method is
discussed which allows the formation of new properties by combination of substructural properties.
This is an extension of commonly used enumeration techniques. Thus, the molecular graphs of
classes of acyclic compounds can be enumerated by topological indices such as number of paths of
a defined length, connectivity indices and characteristic polynomial. The enumeration of path
lengths in the molecular graphs of alkanes is demonstrated by example. Possible applications in
the simulation of quantitative structure-property relations are discussed. A computer program
allowing Pólya insertion in polynomials with several variables is under development.

- J.Will, B.Adler, G.Biess, S.Dobers: "Kombinatorische Abzählung Topologischer Indizes";
Match 30 (1994) 275-288

Zusammenfassung:

Angenommen, uns interessieren die Molekülgraphen mit bestimmten Eigenschaften. Durch
systematische Konstruktion aller entsprechenden Graphen läßt sich die gewünschte
Information erhalten. Oft ist dieses Vorgehen jedoch nicht praktikabel. Die Kombinatorische
Abzählungstheorie ermöglicht dann neben der Bestimmung der Gesamtzahl von
Molekülgraphen vorgegebener Stoffklasse eine Aufteilung dieser Stoffklasse in Klassen von
Graphen mit bestimmten Eigenschaften. Durch diese Klassifikation läßt sich eine
genauere Übersicht über die betrachtete Stoffklasse erreichen. In der vorliegenden
Arbeit wird gezeigt, wie die Bildung neuer Eigenschaftsparameter bei der Kombination von
Eigenschaftsparametern im Abzählungsverfahren berücksichtigt werden kann. Damit lassen
sich etwa über das Pólya-Verfahren Topologische Indizes, z.B.
Konnektivitäts-Indizes und Charakteristisches Polynom, für Klassen
nichtzyklischer Verbindungen ermitteln. Dies stellt eine Erweiterung bisher üblicher
Abzählungsverfahren dar. Der Artikel gibt eine kurze Einführung in die Anwendung der
gewichteten Form des Satzes von Pólya und beschreibt die rekursive Abzählung von
Bäumen und Wurzelbäumen. Am Beispiel der Abzählung von Knotenzahl,
Knotengrad und Spektrum aller Weglängen der Alkane wird das Rechenverfahren vorgestellt.
Mögliche Anwendungen in der Quantitativen Struktur-Eigenschafts-Simulation (QSPR) werden
kurz angedeutet.

Computer Algebra (Symbolic Integration, Symbolic Summation)

Computer Chemistry (Nonclassical QSAR, Unique Structure Codification)

Data Analysis (Multivariate Analysis, Data Mining, New Regression and Interpolation Methods,

Global Optimization)

Emulsions of technical fats and oils

Free Energy (Bibliography Free Energy)

Graph Theory (Nondirected Graphs, Unique Codification of Graphs)

Living Water

Mathematics with Power Series (Formal Power Series, Summation)

Petri Nets for Simulation of Biopathways

- J.Will, M.Heiner: Petri Nets in Biology, Chemistry,
and Medicine. Bibliography; Brandenburg University of Technology Cottbus, Computer Science
Reports 04/02, 2002; ISSN 1437-7969
- hierarchies,
- colour

as well as for quantitative modelling and simulation: - time dependency: discrete, continuous, hybrid,
- stochastics,
- self-modification, in different variations, and
- fuzzy Petri nets.

Preliminary Remarks:

This bibliography has been gathered during a practical training period at the
Brandenburg University of Technology at Cottbus. Special emphasis has been laid on Petri nets
applications in biochemistry for modelling, analysis, and simulation.

To the best of our knowledge, it was 1993 that Reddy et al. introduced
Petri nets for the qualitative modelling of biochemical networks. Since that time, just a few
papers appeared every year with similar approaches in order to model and/or analyse biochemical
pathways, dealing with metabolism, gene regulation, or signal transduction, respectively. Only
recently, there seems to be an increasing interest in that research topic, at least as far we
can tell from the total number of published papers.

A quick search through the papers found reveals a quite large variety of Petri net extension, for qualitative modelling:

In chemistry, applications seem to be restricted to the control and regulation of process technologies and installations. Just Kuroda et al. used Petri nets for modelling more complex reaction dynamics.

Also, many applications are conceivable in the field of stuff and energy flows, ecological systems, population dynamics and evolution. Suzuki introduces spatial hybrid Petri nets for that purpose.

In medicine, the majority of the published applications come from the field of management processes, for instance the passing on of patients, diagnosis preparation, display preparation, and therapy. But, there are also a few applications, modelling the development of some diseases.

A central topic of almost all investigated publications is the demonstration of a methodology how to use Petri nets for the chosen application area, often associated with the presentation of related software tools. Accordingly, almost all published applications seem to rely on demonstration examples only. Therefore, a major break through of a Petri net based technology for modelling and analysis in applications related to biology, chemistry, or medicine can´t be reported yet.

A quick search through the papers found reveals a quite large variety of Petri net extension, for qualitative modelling:

In chemistry, applications seem to be restricted to the control and regulation of process technologies and installations. Just Kuroda et al. used Petri nets for modelling more complex reaction dynamics.

Also, many applications are conceivable in the field of stuff and energy flows, ecological systems, population dynamics and evolution. Suzuki introduces spatial hybrid Petri nets for that purpose.

In medicine, the majority of the published applications come from the field of management processes, for instance the passing on of patients, diagnosis preparation, display preparation, and therapy. But, there are also a few applications, modelling the development of some diseases.

A central topic of almost all investigated publications is the demonstration of a methodology how to use Petri nets for the chosen application area, often associated with the presentation of related software tools. Accordingly, almost all published applications seem to rely on demonstration examples only. Therefore, a major break through of a Petri net based technology for modelling and analysis in applications related to biology, chemistry, or medicine can´t be reported yet.

- M. Heiner, I. Koch, J. Will: Model Validation of Biological Pathways Using
Petri Nets - Demonstrated for Apoptosis"; in Priami, Corrado (ed.): Computational Methods in
Systems Biology (CMSB 2003), Lect. Notes Comput. Sci. 2602 (2003) 173 und BioSystems 75 (2004)
15 -28

Abstract:

This paper demonstrates the first steps of a new integrating methodology
to develop and analyse models of biological pathways in a systematic manner using well
established Petri net technologies. The whole approach comprises step-wise modelling, animation,
model validation as well as qualitative and quantitative analysis for behaviour prediction. In
this paper, the first phase is addressed - how to develop and validate a qualitative model, which
might be extended afterwards to a quantitative model.

The example used in this paper is devoted to apoptosis, the genetically programmed cell death. Apoptosis is an essential part of normal physiology for most metazoan species. Disturbances in the apoptotic process could lead to several diseases. The signal transduction pathway of apoptosis includes highly complex mechanisms to control and execute programmed cell death. This paper explains how to model and validate this pathway using qualitative Petri nets. The results provide a mathematically unique and valid model enabling the confirmation of known properties as well as new insights in this pathway.

The example used in this paper is devoted to apoptosis, the genetically programmed cell death. Apoptosis is an essential part of normal physiology for most metazoan species. Disturbances in the apoptotic process could lead to several diseases. The signal transduction pathway of apoptosis includes highly complex mechanisms to control and execute programmed cell death. This paper explains how to model and validate this pathway using qualitative Petri nets. The results provide a mathematically unique and valid model enabling the confirmation of known properties as well as new insights in this pathway.

________________________________________________________________________________________________

Theses:

- A single computer programming language should be possible, which combines all known universal

programming languages.

- A computer programming language should be possible, which allows to describe mathematical

algorithms as by formulas and short texts in a book.

- Higher speeds of computing would be possible with novel __analog__ computers that work with for example

electrical, magnetical or optical fields.

- Reflect on winning a thunderstorm's lightning energy by creating the lightning.

- Reflect on creating a locally restricted wind vortex like tornado vortices to winning wind energy.

(I don't mean the Yen tornado tower.)

- Reflect on hanging up a very long funnel tube at a high mountain to increase an upwind power

plant's efficiency.

- Is there a spray for self-defense possible which has an awfully nasty smell (like butyric acid or

mercaptanes)?

- Would an everywhere portable little camera protect someone against criminal attack?

- Protection against remote ignition of a bomb could be possible by
using a Faraday cage.

- Try to make photos (at a stand) from an aircraft's model.

- Would it be possible to change the form of a thing (car, aircraft, air foil or so) continuously?

- Could catching fishes be possible by attracting them with sound?