We developed a novel mathematical approach that allows streak and time lines to be described using ordinary differential equations therewith overcoming the drawbacks of former complex algorithms.
Olga Kalinina combines genomic-, modeling-, and biophysics-based methods to assess the mutations observed in given sequences of viral proteins and infer their potential influence on the function of the protein. This enables suggestions for drug treatment of viral diseases.
We could improve the bounds of numerical steps needed to find an exact solution for polynomial systems by multiple orders of magnitude. Given present knowledge, they are nearly optimal.
The interrelation between supply and demand is easily described as long as you have just one good. For the complicated calculations in an economy with many goods, many suppliers, and many buyers Ran Duan and Kurt Mehlhorn found a relatively simple combinatorial algorithm.
Processing "Big Data" poses new challenges to computer science. At the Max Plack Institute for Informatics, we are investigating algorithms and systems to mine useful information from large, complex data sources efficiently and effectively.
Capturing motion pictures and representing them as 3d objects could until now only be efficiently performed by utilizing marker-based camera systems. Using new algorithms developed by Professor Theobalt and co-workers actors are no longer constricted by marker suits.
Finding and following people is a key technology for many applications such as robotics and automotive safety, human-computer interaction scenarios, or for indexing images and videos from the web or surveillance cameras. At the same time it is one of the most challenging problems in computer vision and remains a scientific challenge for realistic scenes.
Human mathematicians prove a theorem by combining individual computation steps. This is a rather trivial task for a computer program once the necessary steps are known. For automatized processes, however, choosing which steps to execute is similar to looking for a needle in an infinitely large haystack. The research group "Automation of Logic" is one of the world leaders in developing efficient automated theorem provers.
