Mathematics-Lab is an organization specialized in the Scientific Computing.
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A B O U T   U S

Goals

We would like to propose you in the most pleasant way we could, models we have found about Nature (η φυσις). We will study the structures and their transformations, and we will develop libraries working on data and their relations. If we achieve to motivate a critical mass of concerned people, then we will deploy a collaborative tool allowing an efficient spread of the scientific knowledge.

Projects

The site is organized on three main axes: (1) the platform section proposes powerful solutions based on the open-source offers. They have the advantage to be not expansive and tailorizable; (2) the research section is the place where notes and papers related to sciences are published. Their content is the responsibility and the ownership of the writers; and (3) the development section provides source code on mathematics computation. An open source license will be proposed.

Currently, the site is a simple display case without any processes to handle the content. The notes and the source codes accumulated during the past 25 years have no pretension of originality. We are only hoping they motivate the young generations in the way of the scientific thinking.

Little by little, some functionalities will be progressively added to handle the exactness of the site content (content management) and to retrieve information (data mining).

Further, the site should become a complete collaborative workspace for scientists. In the same way as the open source paradigm had allowed to some computer scientists around the world to work and gain professional competencies, we believe that it is possible to achieve the same result with the scientific knowledge.

When some valuated people will spend time to our ideas, it will be time to develop processes to take care of the content (coherency, correctness and up-to-dateness). Tools will be deployed to achieve this goal. By examples, tools allowing the referees to consult each others about submitted texts, and tools allowing watching on the scientific literature and on internet. When there are enough people to guarantee the content quality, and there are enough people interested by the open research, it will be time to deploy an ad-hoc environment to organize scientific "open labs" (e.g., scientific computing lab, neurocomputing lab). Finally, when there are enough people to spread the knowledge, "open academies" will be created.

Current Topics

  • Memory Joggers on Mathematics. Collection of notes useful to recall mathematics knowledge, college level in a first time. They content a minimum of explanation without exercises.

  • Automata Theory. Synthesis on the different kinds of automata: finite state automata, pushdown automata, semi-Thue systems, L-systems, kinetic logic, cellular automata, neural networks, Markov chains, etc. In addition to the definitions and the main properties, major theorems should be proved and illustrated with examples.

  • Complex Systems. Synthesis on the different models with their strengths and weaknesses. Numerical libraries allowing exploitation of such systems should be provided.

Resources

Federation

Mathematics-Lab is the research part of the Argonauts-IT group. The Argonauts-IT group is an organization providing software engineering services mainly in the open source developments and more specifically in the e-business fields. We think that the ability to think in terms of abstract concepts is the key to build complex systems. The business objects becoming more and more complex, we need more and more sophisticated tools to model businesses and to provide high quality products and services.

People

The founder (Didier Willame) is currently working as a senior methodologist for a Belgian IT company. In a few words, he had worked as software engineer for international companies like Gec-Alstom (Belgium), Eurocontrol (The Netherlands) and Ericsson (Canada). He has a double education. First, he was graduated in Medicine, and he is familiar with the bio-medical processes (from chemistry to social sciences, including physiology, anatomy, pathology, pharmacology, psychology, etc.). After many years of physician practice, he went back to the University, and he was graduated in Mathematics, major in Computer Sciences. His master thesis concerned the Image Restoration by Simulated Annealing. This is a mix of pure mathematics (Markov Chains) and applied mathematics (Signal Processing). Thus, he is skilled in pure sciences, applied sciences, and human sciences.

The Didier's previous interests are (1) the complex systems (kinetic logic, non-linear thermodynamics, chaos, cellular automata, fractals, catastrophe theory, auto-organization, synchronization, stochastic systems, time series), and (2) mathematics (p-adics analysis, knots theory, Collatz problem, voting theory, optimization). His current interests are the automata theory and the related fields (e.g., recursive functions, computability, algorithmics, programming languages, protocols, testing).

Development Plan

  1. Deploy a news system.
  2. Write the legal page.
  3. Write the map page.
  4. Write the contact us page.
  5. Write the support page with the basic processes (e.g., how to write a memory jogger? how to develop source code? what is required to be published? how to get an ISSN and ISBN codes? how to do marketing?).
  6. Write papers (e.g., Memory Joggers on Mathematics) and deliver software's (e.g., avalanche simulator) on the platforms, researches and developments pages.
  7. Use news groups to promote the site (e.g., sci.math.research, sci.math, alt.math, alt.math.undergrad, alt.math.recreational and fr.sci.maths).
  8. Deploy a content management system and a data mining system (search icon)
  9. Deploy a collaborative system (login icon, cf. wiki).
  10. Deploy a mailing list system.
  11. Do marketing to recruit associates.