Mathias Fuchs

Self-employed

A thermal bridge is a component of a building that is characterized by a higher thermal loss compared with its surroundings. Their accurate modeling is a key step in energy performance analysis due to the increased awareness of the importance of sustainable design. Thermal modeling in architecture and engineering is often not carried out volumetric...

U-statistics enjoy good properties such as asymptotic normality, unbiasedness and minimal variance among unbiased estimators. The estimation of their variance is often of interest, for instance to derive asymptotic tests. It is well-known that an unbiased estimator of the variance of a U-statistic can be formulated explicitly as a U-statistic itsel...

Agent-based semiology is a powerful simulation and prediction environment for pedestrian simulation that allows for accurate balancing of complexity. Here, we describe a framework to simulate increasing behavioural interactivity between agents via agent-based modeling, together with a statistical approach to make the results amenable to a quantitat...

This research paper explores the use of 3D-printing technologies in prototyping of Topology Optimization (TO) driven design. The paper describes the integration of TO into an early design work-flow and highlights the difficulties thereof. Due to the high computation times of TO, we outline the use of statistical learning to approximate TO material...

As modern biotechnologies advance, it has become increasingly frequent that different modalities of high-dimensional molecular data (termed “omics” data in this paper), such as gene expression, methylation, and copy number, are collected from the same patient cohort to predict the clinical outcome. While prediction based on omics data has been wide...

We consider the mean prediction error of a classification or regression procedure as well as its cross-validation estimates, and investigate the variance of this estimate as a function of an arbitrary cross-validation design. We decompose this variance into a scalar product of coefficients and certain covariance expressions, such that the coefficie...

We compute the equivariant K-homology of the groups PSL2 of imaginary quadratic integers with trivial and nontrivial class group. This was done before only for cases of class number one. We rely on reduction theory in the form of the Γ-CW-complex defined by Flöge. We show that the difficulty arising from the nonproper action of Γ on this complex c...

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally distributed. Moreover, there is a...

In modern molecular biology, high-throughput experiments allow the simultaneous study of expression levels of thousands of biopolymers such as mRNAs, miRNAs or proteins. A typical goal of such experiments is to find molecular signatures that can distinguish between different types of tissue or that can predict a therapy outcome. While research typi...

We compute the equivariant K-homology of the groups PSL_2 of imaginary quadratic integers with trivial and non-trivial class-group. This was done before only for cases of trivial class number. We rely on reduction theory in the form of the $\Gamma$-CW-complex defined by Fl\"oge. We show that the difficulty arising from the non-proper action of $\Ga...

Data collection (compressed). This zip-file contains the networks and the background data. Further information is given in a README file. The TRANSPATH derived signaling network's adjacency list is excluded due to license agreements.

Summary of the pathway over-representation analysis (compressed). For each pathway analysis, the corresponding Fisher's exact p- and q-values are included. GSEA was performed on the pure expression data set as well as those subsets of the gene identifier which could be mapped to the reference networks' or the filtered networks' vertices. Further in...

Code collection (compressed). This zip-file contains the code for all pathway over-representation tests. Further information is given in a README file.

Reconstruction of protein-protein interaction or metabolic networks based on expression data often involves in silico predictions, while on the other hand, there are unspecific networks of in vivo interactions derived from knowledge bases.We analyze networks designed to come as close as possible to data measured in vivo, both with respect to the se...

Formation of the mammalian primitive streak appears to rely on cell proliferation to a minor extent only, but compensating cell movements have not yet been directly observed. This study analyses individual cell migration and proliferation simultaneously, using multiphoton and differential interference contrast time-lapse microscopy of late pregastr...

We show that a cellular complex defined by Flöge allows us to determine the integral homology of the Bianchi groups PSL2(O-m), where O-m is the ring of integers of an imaginary quadratic number field Q[-m] for a square-free natural number m. In the cases of nontrivial class group, we handle the difficulties arising from the cusps associated to the...

We give a new proof of the absence of non-trivial idempotents in the group ring of torsion-free cocompact lattices in SL(n,C). It is based on the following procedure. We lift the class of the trace in the cyclic cohomology of the group ring to the crossed product of the smooth functions on the Furstenberg boundary of SL(n,C) with the lattice. We th...

We calculate the integral homology of the non-Euclidean Bianchi groups $PSL_2$ of the ring of integers of the number field $Q[\sqrt{-m}]$ for $m=5,6,10,13$, making essential use of an equivariant cellular decomposition of a retract of hyperbolic three-space due to Floege.