### Our Approach

#### From Business Goals to Mathematical Models

Due to our long-standing experience in scientific research the development and implementation of mathematical and physical models is one of our strengths. Our work is tailored to the requirements and demands of your company so that you can rely on predictions and forecasts of the corresponding simulation results for future decisions and choose the best option.

The basic idea behind the mathematical modelling of business questions is to calculate predictions for your company, which show the outcome of certain decisions, processes or manufacturing steps and help to forecast certain trends. We apply diverse algorithms, scientific laws of nature, statistics, neuronal networks, machine learning and much more. Examples for typical questions that can be treated with such methods are:

- What will be the result/consequence of a certain decision?
- What output will be generated by machine X in the future?
- What should we do next?
- How should we proceed to exploit probabilities in our favour?

The application of mathematical models is of big avail especially for cost-intensive decisions, because serious consequences can usually be determined beforehand with relatively low efforts.

### Approach and Models

We clarify in a personal discussion which model suits your problem best. The possible solution relies heavily on the available data - if one knows, how a system is working, usually physical laws based on classical models can be applied. Is this not the case or if only partial information is available, models based on data are the method of choice.

A very efficient method is deep learning - this is the general term for learning algorithms and optimisation methods of neuronal networks, which nowadays are very successfully employed in automotive cars, photo and image recognition, in the financial world for risk or stock price forecasting, in biology and medicine or for the recognition of anomalies in the IT sector.

Use our enthusiasm for such possibilities in mathematics and physics to get the best out of your company and to be able to make decisions based on mathematical facts!

### Final Product

How the mathematical models are integrated into your infrastructure in the end depends heavily on your requirements and condition. A few possible examples are listet here:

- MXnet for deep learning algorithms
- Fortran code with executables and trained machine learning algorithms
- Standalone Matlab or Octave application
- Interactive CDF Mathematica-files with graphical user interface
- Cloud APIs

### Big Data Example

A simple example for the business-related information that can be extracted from a given amount of data are the taxis in New York. Every month the collected taxi data (time and place of pickup, distance, fare, number of guests, etc.) ist published on a website. The data volume of one year is quickly more than 20 GB and it is not possible to simply open or process such an amount of data in Excel or another conventional office program (catchword Big Data). Nevertheless, with the appropriate tools such gigantic amounts of data can still be processed easily and already simple statistical models allow to make important strategic company decisions. In the following animation the result of a Matlab simulation is depicted, where the taxi data of one day has been evaluated.

Already with this first and simple result we can draw conclusions at which particular time a taxi company will need the most drivers and at which place they should be positioned. If we apply further statistical analysis we learn for example that at 19:00 the tips are highest, which driving distance is most common or at which time of the day the most group taxis will be needed. The next step would be to apply corresponding forecast models, so that the right taxis can be placed at the right position and time with the calculated probabilities - this optimisation could be a crucial advantage compared to other competitors.