Freie Universität Berlin
Repository: Freie Universität Berlin (FU), Math Department (fu_mi_publications)Not a member yet
2251 research outputs found
Sort by
Definition, detection and tracking of persistent structures in atmospheric flows
No full textLong-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence
An Interpretable Deep Learning Approach for Biomarker Detection in LC-MS Proteomics Data
No full textAnalyzing mass spectrometry-based proteomics data with deep learning (DL) approaches poses several challenges due to the high dimensionality, low sample size, and high level of noise. Additionally, DL-based workflows are often hindered to be integrated into medical settings due to the lack of interpretable explanation. We present DLearnMS, a DL biomarker detection framework, to address these challenges on proteomics instances of liquid chromatography-mass spectrometry (LC-MS) - a well-established tool for quantifying complex protein mixtures. Our DLearnMS framework learns the clinical state of LC-MS data instances using convolutional neural networks. Based on the trained neural networks, we show how biomarkers can be identified using layer-wise relevance propagation. This enables detecting discriminating regions of the data and the design of more robust networks. One of the main advantages over other established methods is that no explicit preprocessing step is needed in our DLearnMS framework. Our evaluation shows that DLearnMS outperforms conventional LC-MS biomarker detection approaches in identifying fewer false positive peaks while maintaining a comparable amount of true positives peaks. Code availability: The code is available from the following GIT repository: https://github.com/SaharIravani/DlearnMS
Stein Variational Gradient Descent:many-particle and long-time asymptotics
Get PDFStein variational gradient descent (SVGD) refers to a class of methods for Bayesian inference based on in-teracting particle systems. In this paper, we consider the originally proposed deterministic dynamics as well asa stochastic variant, each of which represent one of the two main paradigms in Bayesian computational statis-tics:variational inferenceandMarkov chain Monte Carlo. As it turns out, these are tightly linked througha correspondence between gradient flow structures and large-deviation principles rooted in statistical physics.To expose this relationship, we develop the cotangent space construction for the Stein geometry, prove its ba-sic properties, and determine the large-deviation functional governing the many-particle limit for the empiricalmeasure. Moreover, we identify theStein-Fisher information(orkernelised Stein discrepancy) as its leadingorder contribution in the long-time and many-particle regime in the sense ofΓ-convergence, shedding some lighton the finite-particle properties of SVGD. Finally, we establish a comparison principle between the Stein-Fisherinformation and RKHS-norms that might be of independent interes
Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator
Get PDFAbstract.We introduce a family of various finite volume discretization schemes for the Fokker–Planck
operator, which are characterized by different Stolarsky weight functions on the edges. This family
particularly includes the well-established Scharfetter–Gummel discretization as well as the recently
developed square-root approximation (SQRA) scheme. We motivate this family of discretizations both
from the numerical and the modeling point of view and provide a uniform consistency and error analysis.
Our main results state that the convergence order primarily depends on the quality of the mesh and
in second place on the choice of the Stolarsky weights. We show that the Scharfetter–Gummel scheme
has the analytically best convergence properties but also that there exists a whole branch of Stolarsky
means with the same convergence quality. We show by numerical experiments that for small convection
the choice of the optimal representative of the discretization family is highly non-trivial, while for large
gradients the Scharfetter–Gummel scheme stands out compared to the others
EDP-convergence for a linear reaction-diffusion system with fast reversible reaction
Get PDFWe perform a fast-reaction limit for a linear reaction-diffusion system consisting of two
diffusion equations coupled by a linear reaction.We understand the linear reaction-diffusion
system as a gradient flow of the free energy in the space of probability measures equipped
with a geometric structure, which contains the Wasserstein metric for the diffusion part and
cosh-type functions for the reaction part. The fast-reaction limit is done on the level of
the gradient structure by proving EDP-convergence with tilting. The limit gradient system
induces a diffusion system with Lagrange multipliers on the linear slow-manifold.Moreover,
the limit gradient system can be equivalently described by a coarse-grained gradient system,
which induces a diffusion equation with a mixed diffusion constant for the coarse-grained
slow variable
Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation
No full textAbstract
We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor
Feature space approximation for kernel-based supervised learning
No full textAbstract
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage consumption and computational complexity. Furthermore, the method can be regarded as a regularization technique, which improves the generalizability of learned target functions. We demonstrate significant improvements in comparison to the computation of data-driven predictions involving the full training data set. The method is applied to classification and regression problems from different application areas such as image recognition, system identification, and oceanographic time series analysis
Basement membrane stiffness determines metastases formation
No full textThe basement membrane (BM) is a special type of extracellular matrix and presents the major barrier cancer cells have to overcome multiple times to form metastases. Here we show that BM stiffness is a major determinant of metastases formation in several tissues and identify netrin-4 (Net4) as a key regulator of BM stiffness. Mechanistically, our biophysical and functional analyses in combination with mathematical simulations show that Net4 softens the mechanical properties of native BMs by opening laminin node complexes, decreasing cancer cell potential to transmigrate this barrier despite creating bigger pores. Our results therefore reveal that BM stiffness is dominant over pore size, and that the mechanical properties of ‘normal’ BMs determine metastases formation and patient survival independent of cancer-mediated alterations. Thus, identifying individual Net4 protein levels within native BMs in major metastatic organs may have the potential to define patient survival even before tumour formation. The ratio of Net4 to laminin molecules determines BM stiffness, such that the more Net4, the softer the BM, thereby decreasing cancer cell invasion activity
Formation of olivine-rich veins by reactive fluid flow in a dehydrating serpentinite
No full textMany exposed high-pressure meta-serpentinites comprise a channelized network of olivine-rich veins which formed during dehydration at depth and served as pathway for fluid escape. Previous studies showed that the formation of an olivine enriched vein-like interconnected porosity network on the µm-scale is controlled by chemical heterogeneities in the rock. However, the evolution towards larger scale and nearly pure olivine veins is not yet well understood. Here we study the effects of reactive fluid flow on a developing vein system during dehydration. We use thermodynamic equilibrium calculations to investigate the effects of bulk silica content variations in serpentinites on the dehydration reaction of antigorite + brucite = olivine + free fluid and silica content of this fluid phase. We develop a numerical model combining the effects of intrinsic chemical heterogeneities with reactive silica transport. Increasing temperatures lead to local fluid overpressure and the liberation of a silica-poor fluid in a subdomain with initially increased bulk iron and decreased silica content. The fluid overpressure drives fluid flow into other subdomains where the fluid enhances dehydration and leads to olivine enrichment in an iron-enriched vein. Our model shows how reactive silica transport can lead to vein widening and olivine enrichment within the veins as observed in the Erro Tobbio meta-serpentinites. Thus, reactive fluid flow is a critical step in the evolution towards a larger scale vein system and a dynamic porosity evolution by accounting for a chemical feedback between the dehydrating rock and the liberated fluid