Mathias is a Mathematician by training, with experience in a number of applied fields:
Numerical Mathematics, Bioinformatics, Medical Statistics, Mathematical Statistics, and Architectural Geometry.
He has been a postdoc, a freelancing consultant and an employee.
Currently, he works for Zaha Hadid Architects, London, as a Senior Researcher. Freelancing consultant coming soon.
shape recognitionof a 2D office layout by the straight skeleton
Company 
Location 
Job title 
Format 
Years 
Karamba3d.com 
Vienna 
Mathematical Consultant and Programmer 
Freelance 
ongoing 
Zaha Hadid Architects 
London 
Senior Researcher 

2016  present 
Ludwig Maximilian University 
Munich 
Postdoctoral Researcher 

2013 – 2016 
TNG Technology Consulting GmbH 
Munich 
Statistical Consultant 
Freelance 
2014 
Georg August University 
Goettingen 
Postdoctoral Researcher 

2009  2012 
Georg August University, Institute Numerical and Applied Mathematics 
Goettingen 
Visiting Professor 

2008 
Georg August University 
Goettingen 
Postdoctoral Researcher 

2007 – 2008 
AixMarseille University 
Marseille 
Doctorate Researcher at Graduate School 

2003  2007 
We show that that the error rate of a supervised learning algorithm can be estimated without bias as long as the test set is at least twice as large as the learning set.
We show a way to make the results of pedestrian simulation availabe to the designer. It relies on a spatial regression of the simulated density on distance fields and other architectural features.
My first architectural paper. We described outputs of a finite element software in terms of geometrical features, by a linear regression. This was fun and interesting, but the most important part was finding out that the surface normal's z component was an important explanatory variable in that linear regression. We found out about that by investigating the Airy approach to structural mechanics more closely.
Here, we took a look at the problem of integrating different group of covariables, the prototypical situation being when mRNA and miRNA are to be integrated. We pursue a fairly immediate line of thought: to apply different lasso penalizations to each of them. The details, however, are quite nittygritty. We show how penalized regression generalises naturally to multiple data sources, by penalising each modality differently. This sounds easy and straightforward, but it's the details which make it hard. Took a long time to publish  not catchy enough.
Yet another topic: theoretical statistics. This is my second favorite paper on this side. We identified and computed certain covariances between evaluations of error estimators. Furthermore, we identified Ustatistics to show how these covariances can be estimated.
Back to pure Mathematics. This paper is in spirit not too far away from that of my PhD thesis. I think this paper is the one I am most proud of.
Yet another topic: a general overview of data combination strategies. In retrospect, there are better ones out there, though, than the ones we looked at.
Once again, a completely different topic: biology, and in particular developmental biology. The primitive streak is the first morphogenic feature in the nascent mammalian embryo. We applied circular statistics to show that cell divisions prefer certain directions.
My first nonmathematical paper: Some work on biological databases, of a rather algebraic/nonquantitative flavor. Biological databases ... nothing I really worked on before or after anytime again ....
The title says it all: we compute the group homology of a certain class of groups acting on hyperbolic threespace. Was (mostly) fun. I learned a lot about homological algebra, and about fundamental sets of actions.
ThesisPhD thesis: M. Fuchs, "Cohomologie cyclique des produits croises associes aux groupes de Lie". Written at the Institut de Mathematiques de Luminy under the direction of Michael Puschnigg at the Universite de la Mediterranee AixMarseile,
https://arxiv.org/abs/math/0612023
I give a completely new proof of the fact that the group ring of torsionfree discrete cocompact subgroups of SL(n, C) satisfies the KadisonKaplansky conjecture: it is free of nontrivial idempotents. Unfortunately, I never came back to that topic later.
Technical ReportsA simulation study on supervised learning is when the following process is carried out repeatedly, with independent repetitions: One draws a learning sample from a distribution. The size of the learning sample, i.e., the number of observations it is comprised of, is to be kept the same throughout. Each observation consists of predictors or (covariables), and an outcome or value of response variable, for instance, a binary prediction target. Furthermore, one evaluates the performance of the predictive model thus achieved, by evaluating it on a test set. Averageing out across all independent iterations is guaranteed to converge towards the true expectated value of the error estimator  the true error. It might seem a little unintuitive that the latter statement holds true regardless of the size of the test set. The reason is that the mentioned expected value is unaffected by the size of the test set. Therefore, it is just a matter of computational convenience to choose it carefully. It is the goal of this paper to perform that choice in an educated way, as a function of the machine computation execution speed.
We show a bunch of things about the errror estimator of a machine learning algorithm, on a real data sample of fxed size (typically denoted by n in statistics). Among several statements, we show that the studentized error estimator is asymptotically normally distributed. This is a new contribution.