What Topological Dynamics stand for?
We use methods from well-established branches of mathematics not yet explored in data analysis. The methods of dynamical systems are widespread in all applied sciences since its beginnings at the end of the 19th century. The development of dynamics is based on the analytic approach. On the other hand, the ease of acquiring gigabytes of data from experiments or numerical simulations stimulates the need for obtaining the results without building an analytic model. It is natural to expect that these methods might be adapted to the data-driven problems where the analytic model is poorly understood or not known.
Our technology is based on strong theoretical foundations derived from the analytical approach to dynamical systems, however, it is data-driven and does not require to create an analytic model manually. To analyze the data we combine traditional computer science tools, e.g. graph-theory, together with modern machine learning methods, e.g. neural networks, NLP, classifiers.
The approach may give a new perspective on the collected information and improve current methods. We are looking for cooperation with an industrial partner open to use and improve new technologies. In particular, our approach may be helpful in the analysis of collected data from sensors, especially advanced velocimetry instruments used for stress sensitivity measurement.
What are the advantages?
The technology is based on more than 20 years of research experience in computational mathematics. The team behind the technology has successful international research cooperation, but also an experience in professional software development. Our research was founded by top grants awarded by national and EU research agencies.
We bring a unique technology based on established theory and modern technology which is already verified as a practical research tool. We implement the solutions using industrial standards and we verify the implementations for small as well as big data sets processed on a cluster. All these factors may provide a first-mover advantage for our industrial partner. Our methods may be useful as complementary tools to traditional statistical methods. But, they may also provide a break-through insight into the dataset global geometric structure, not discoverable by statistical methods. We are open to new ideas and willing to discuss details.