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Andreas Weber

Publications and source records attributed to Andreas Weber.

34 records · Page 2Linked to original sources
arXiv2016

On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

math.AP↗
arXiv2016

Gene networks accelerate evolution by fitness landscape learning

We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. We propose a new model of gene regulation, where gene expression is controlled by a gene network with a threshold mechanism and there is a feedback between that threshold and gene expression. We show that this regulation is very powerful: depending on parameters we can obtain any functional connection between thresholds and genes. Under general assumptions on fitness we prove that such model organisms are capable, to some extent, to recognize the fitness landscape. That fitness landscape learning sharply reduces the number of mutations necessary for adaptation and thus accelerates of evolution. Moreover, this learning increases phenotype robustness with respect to mutations. However, this acceleration leads to an additional risk since learning procedure can produce errors. Finally evolution acceleration reminds races on a rugged highway: when you speed up, you have more chances to crash. These results explain recent experimental data on anticipation of environment changes by some organisms.

q-bio.PE↗
arXiv2016

A Dual-Source Approach for 3D Pose Estimation from a Single Image

One major challenge for 3D pose estimation from a single RGB image is the acquisition of sufficient training data. In particular, collecting large amounts of training data that contain unconstrained images and are annotated with accurate 3D poses is infeasible. We therefore propose to use two independent training sources. The first source consists of images with annotated 2D poses and the second source consists of accurate 3D motion capture data. To integrate both sources, we propose a dual-source approach that combines 2D pose estimation with efficient and robust 3D pose retrieval. In our experiments, we show that our approach achieves state-of-the-art results and is even competitive when the skeleton structure of the two sources differ substantially.

cs.CV↗
arXiv2015

Geometric analysis of pathways dynamics: application to versatility of TGF-β receptors

We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is much slower compared to the rest of the phase space. Given the network topology and the orders of magnitude of kinetic parameters, the number of such metastable regimes is finite. The dynamics of the network can be described as a sequence of jumps from one metastable regime to another. We show that a geometrically computed connectivity graph restricts the set of possible jumps. We also provide finite state machine (Markov chain) models for such dynamic changes. Applied to signal transduction models, our approach unravels dynamical and functional capacities of signaling pathways, as well as parameters responsible for specificity of the pathway response. In particular, for a model of TGF$β$ signalling, we find that the ratio of TGFBR1 to TGFBR2 concentrations can be used to discriminate between metastable regimes. Using expression data from the NCI60 panel of human tumor cell lines, we show that aggressive and non-aggressive tumour cell lines function in different metastable regimes and can be distinguished by measuring the relative concentrations of receptors of the two types.

q-bio.MN↗
arXiv2015

A geometric method for model reduction of biochemical networks with polynomial rate functions

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.

q-bio.MN↗
arXiv2015

Efficient Unsupervised Temporal Segmentation of Motion Data

We introduce a method for automated temporal segmentation of human motion data into distinct actions and compositing motion primitives based on self-similar structures in the motion sequence. We use neighbourhood graphs for the partitioning and the similarity information in the graph is further exploited to cluster the motion primitives into larger entities of semantic significance. The method requires no assumptions about the motion sequences at hand and no user interaction is required for the segmentation or clustering. In addition, we introduce a feature bundling preprocessing technique to make the segmentation more robust to noise, as well as a notion of motion symmetry for more refined primitive detection. We test our method on several sensor modalities, including markered and markerless motion capture as well as on electromyograph and accelerometer recordings. The results highlight our system's capabilities for both segmentation and for analysis of the finer structures of motion data, all in a completely unsupervised manner.

cs.CV↗
arXiv2015

Symbolic dynamics of biochemical pathways as finite states machines

We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a number of states that is inferior to the number of biochemical species. For nonlinear pathways, we propose a general approach to approximate their dynamics by finite state machines working on the metastable states of the network (long life states where the system has slow dynamics). For networks with polynomial rate functions we propose to compute metastable states as solutions of the tropical equilibration problem. Tropical equilibrations are defined by the equality of at least two dominant monomials of opposite signs in the differential equations of each dynamic variable. In algebraic geometry, tropical equilibrations are tantamount to tropical prevarieties, that are finite intersections of tropical hypersurfaces.

q-bio.MN↗
arXiv2013

$L^p$ spectrum and heat dynamics of locally symmetric spaces of higher rank

The aim of this paper is to study the spectrum of the $L^p$ Laplacian and the dynamics of the $L^p$ heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank one case, it turns out that the $L^p$ heat semigroup on $M$ has a certain chaotic behavior if $p\in(1,2)$ whereas for $p\geq 2$ such a chaotic behavior never occurs.

math.DG↗
arXiv2010

Pointwise bounds for $L^2$ eigenfunctions on locally symmetric spaces

We prove pointwise bounds for $L^2$ eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with $\mathbb{Q}$-rank one if the corresponding eigenvalues lie below the continuous part of the $L^2$ spectrum. Furthermore, we use these bounds in order to obtain some results concerning the $L^p$ spectrum.

math.SP↗
arXiv2010

Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap

In this paper we study the Riesz transform on complete and connected Riemannian manifolds $M$ with a certain spectral gap in the $L^2$ spectrum of the Laplacian. We show that on such manifolds the Riesz transform is $L^p$ bounded for all $p \in (1,\infty)$. This generalizes a result by Mandouvalos and Marias and extends a result by Auscher, Coulhon, Duong, and Hofmann to the case where zero is an isolated point of the $L^2$ spectrum of the Laplacian.

math.SP↗
arXiv2010

Dynamics of the heat semigroup on symmetric spaces

The aim of this paper is to show that the dynamics of $L^p$ heat semigroups ($p>2$) on a symmetric space of non-compact type is very different from the dynamics of the $L^p$ heat semigroups if $p\leq 2$. To see this, it is shown that certain shifts of the $L^p$ heat semigroups have a chaotic behavior if $p>2$ and that such a behavior is not possible in the cases $p\leq 2$. These results are compared with the corresponding situation for euclidean spaces and symmetric spaces of compact type where such a behavior is not possible.

math.DG↗
arXiv2010

$L^p$ spectral theory and heat dynamics of locally symmetric spaces

In this paper we first derive several results concerning the $L^p$ spectrum of arithmetic locally symmetric spaces whose $\Q$-rank equals one. In particular, we show that there is an open subset of $\C$ consisting of eigenvalues of the $L^p$ Laplacian if $p <2$ and that corresponding eigenfunctions are given by certain Eisenstein series. On the other hand, if $p>2$ there is at most a discrete set of real eigenvalues of the $L^p$ Laplacian. These results are used in the second part of this paper in order to show that the dynamics of the $L^p$ heat semigroups for $p<2$ is very different from the dynamics of the $L^p$ heat semigroups if $p\geq 2$.

math.DG↗
arXiv2007

$L^p$-Spectral theory of locally symmetric spaces with $Q$-rank one

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=Γ\backslash X$ with finite volume and arithmetic fundamental group $Γ$ whose universal covering $X$ is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.

math.SP↗
arXiv1994

Phase structure and monopoles in U(1) gauge theory

We investigate the phase structure of pure compact U(1) lattice gauge theory in 4 dimensions with the Wilson action supplemented by a monopole term. To overcome the suppression of transitions between the phases in the simulations we make the monopole coupling a dynamical variable. We determine the phase diagram and find that the strength of the first order transition decreases with increasing weight of the monopole term, the transition thus ultimately getting of second order. After outlining the appropriate topological characterization of networks of currents lines, we present an analysis of the occurring monopole currents which shows that the phases are related to topological properties.

hep-lat↗