Here I write down some ideas existing long time in my mind, I really appreciate every discussion and cooperation, even someone can use any idea from here without a notification to me.

- Times Series Analysis of Music
- Thinking in Universal Language
- Three Representations for Epidemics
- A Funny Way to Show the Spirit of Renormalization Group Theory in Statistical Physics
- Software Developer: Scientific Project Manager

- Introduction to Econophysics
- Note papers
- Wavelet Analysis
- fda method

Now let's turn to the human language. Many different languages are used and we can understand each other. In mathematical language means a mapping between any two languages can be found and constructed. Let's take one sentence S for example. It can be expressed in English originally as Se, and then it can be translated into Chinese Sc, French Sf and any other languages as Si. Using the mathematical languages usually for Quantum Mechanics, Si is the presentation of the abstract S. Although presentation form has to be used to express, like we usually use the position presentation grad for abstract momentum operator P, the abstract form S is independent on any language forms.

OK, now think about the thinking process. When we think in our mind, we have to use a specific language, most time the native language. So for you, maybe usually thinking in English, for me, sometimes English, sometimes Chinese. Also use the sentence S for example, in your mind it's Se, for me Sc, and Si for all others. Since we can understand each other, a common meaning of Si must exist. Actually the common meaning is the abstract S. But unfortunately, no one can think in abstract form, we have to use language to help us to think, although thinking should be a process independent of language.

Now, let's ask the same question for computer. Can computer think in abstract form or a common language? Actually, the compilers give us the answer. What the most compilers do is translate program written in all high level languages into low level ones as bite code. Therefor, although bite code is also a specific language not a abstract form, it is the most common language being understood by most computers. However, bite code is machine dependent, so it's not a good choice for abstract language. We want to get a universal language which has the same form in every machine. So maybe interpreter language is a good choice. In fact, we can find more properties required as an abstract language and try to realize them in a specific language. For Computer Science, I think, Java is a good candidate. Although we know that any specific languages is only an approximation realization of the universal language, but a good approximation will definitely help the communication and development.

Hehe, we are too far from the mark. OK, let's come back to thinking and human language. Just like the common language and universal language for computer, can we find or construct a universal language for human? What's the necessary properties of the universal language? First, the universal language is designed for thinking process, so maybe in some kinds it looks like mathematical language and it should develop itself along the research progress in thinking process. Second, the universal language is designed for communication, so it must have the same form for every one and easily to be translated into any other languages. Like the C-like grammar in Java, our universal language must be constructed on the basis of the most common language. If we can define all the properties required for a universal language, we also can construct an approximate specific language. If it's possible to accomplish it, Oh, I can't image what will happen to our world.

Another reason for the mapping between different language and the reason we can understand each other, besides the common thinking process, it's the materials world. Since we have the same materials all over our world, we can understand each other every time by refer the sentence to the materials object. So here this object replaces the position of abstract form. However, not all representation form can be referred to such materials object. So we have to say that the reason for that we can understand each other is that we have the same thinking process. So if we can construct a specific representation directly related with thinking, everyone will be able to think in a universal language.

However, sometimes a mixture mistake happens in such application[5]. And also because of their different characters and convenience, here we want to discuss the relation and the difference.

(1) |

in which is the total capacity, we can use rate equation to describe the same model as

Another set of variables can be constructed to use for Master equation. Consider an ensemble of such systems, in which every system independently develops as the same birth process. The population in every system can be looked as a random variable. We define the fraction of systems with specific population as

(4) |

(5) |

(6) |

The first order of this equation is

(8) |

and no one can guarantee that the second order is much less than the first order unless

The master equation presentation looks much more complex than the other two. However, after all we have the differential equation for the distribution function and it's the most general one. In fact the former two equation can be regarded as the mean value equation and deduced from master equation. It's also worth noticing that and is related as

which can be found from comparison of the corresponding solution and for equation (2) and (3). Another example is pure infection process, in which

and the rate equation is

The relation between probability and rate is

One can get this relation by substituting , the solution of equation (13) into equation (12). And following the same analysis procedure, we can get the master equation as bellow,

Similarly, when condition (10) holds, we can use the first order master equation,

In fact, sometimes another difference equation is used instead of equation (12) as in [4] as,

which also can be written down as

when . This equation is based on different assumption with equation (12) about the contacting frequency. In this equation, during every time step, every healthy individual contacts with every infected individual, while in the former case, every healthy individual only contact with one of all other individuals, so the probability to encounter an infected individual is . In this paper, we use the constant contacting frequency as in equation (12) other than the sufficient contacting frequency in equation (17).

- James H. Matis, Thomas R. Kiffe,
*Stochastic population models : a compartmental perspective*, Lecture notes in statistics (New York, Springer-Verlag, 2000) v.145; - R. Pastor-Satorras and A. Vespignani, Epidemic dynamics and endemic states
in complex networks, Phys. Rev. E
**63**, 066117(2001). - G. Ghoshal, L. M. Sander, I. M. Sokolov, SIS epidemics with household structure: the self-consistent field method, e-print cond-mat/0304301.
- M. E. J. Newman, Spread of epidemic disease on
networks, Phys. Rev. E
**66**, 016128(2002). - Rinaldo B. Schinazi, On the Role of Social Clusters in the Transmission of Infectious
Diseases, Theoretical Population Biology
**61**, 163-169(2002).

- Introduction
- Phenomenological fundamental of Renormalization
- Transformation and invariants
- Existence of such transformation and the relation with critical exponents
- Examples
- Summary
- Bibliography

So if we rescale the size of the system as , then the characteristic length will change along with as . Applying this result to equation (1), we will have an induced transformation,

(2) |

Induced Transformation:

(5) |

(6) |

- Value of total free energy

- Function form of free energy density

and substitute (8) into equation above,

Then, put the induced transformation in,

This equation is the requirement of induced transformation as . Now we suppose is the fixed point. We have and . Expand them at ,

(10) |

(11) |

let , then

Therefor,

Similarly, from , we can get

let , then

Therefor,

At last,

(14) |

(15) |

(16) |

(17) |

(18) |

(19) |

(20) |

(21) |

Using the transformation as shown in figure (2).

We have invariants as

(22) |

(23) |

- 1
- Rachel,
*A Moden Course of Statistical Physics*(xxxx). - 2
- Henk W.J. Blöte,
*Renormalization Theory of Phase Transitions*(Electrical lecture manuscript, Sept. 2001). - 3
- Ma Shang-Keng,
*Modern Theory of Critical Phenomena*(W.A.Benjamin Inc. Advanced Book Program Reading, Massachusetts, 1976).

This document was generated using the LaTeX2HTML translator Version 2002 (1.62)

Copyright © 1993, 1994, 1995, 1996, Nikos Drakos, Computer Based Learning Unit, University of Leeds.

Copyright © 1997, 1998, 1999, Ross Moore, Mathematics Department, Macquarie University, Sydney.

The most important character of this software should be free and open source. So everyone can use it and improve it. It should be developed as a tool for scientists and by scientists. The second principle of this software is readable and compatible. Everything can be read by text editors and the whole structure of saving files, like the tree-like directory also can be read by human eyes. And the if the database has to be used here, a convertor for readable text file also should be distributed together with the software.

Next part is my function analysis of this software.

- Project Management
- Reference Management
- Data Management
- Personnel Management
- Report Producer
- Saving Place Synchronizer
- Pool Information and Temp File

As Dirac, one genius in Physics, said Mathematics is the thing you create when you need, Knuth is the equivalent giant in Computer Science, I think, because when he decided to write down a great and huge book, he designed TeX system first. ^_^, therefore, after some initial research experience, I find maybe I should develop a project manager system when I have free time. Of course, if someone else want to create it first for all scientists, I really appreciate she/he just use this idea and structure. Only thing she/he need to do is drop me an email to let me know someone else try to do it. All my analysis is following the similar format and idea of the reference listed below.

- The TeXbook, Donald E. Knuth, Reading, Massachusetts: Addison-Wesley, 1984
- LaTeX: A Document Preparation System, Leslie Lamport, Addison-Wesley, 2nd edition, 1994, ISBN 0-201-52983-1.
- Reference Manager, http://www.refman.com/, ISI ResearchSoft
- EndNote, http://www.endnote.com/, ISI ResearchSoft
- Microsoft Office Enterprise Project Management (EPM) Solution, http://www.microsoft.com/canada/epm/default.mspx, Microsoft Corporation