Related papers: Expanding the Temporal Analysis in Single-Molecule…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
This work introduces a generic quantitative framework for studying dynamical processes that involve interactions of polymer sequences. Possible applications range from quantitative studies of the reaction kinetics of polymerization…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic.…
Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved…
In many longitudinal microarray studies, the gene expression levels in a random sample are observed repeatedly over time under two or more conditions. The resulting time courses are generally very short, high-dimensional, and may have…
From the point of view of statistical mechanics, a full characterisation of a molecular system requires the experimental determination of its possible states, their populations and the respective interconversion rates. Well-established…
Many psychological experiments have subjects repeat a task to gain the statistical precision required to test quantitative theories of psychological performance. In such experiments, time-on-task can have sizable effects on performance,…
We present a functional data analysis approach for studying time-dependent, continuous glucose monitoring data with repeated measures for each individual in an experiment. After scaling the glucose concentration curves to the interval [0,…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
Single molecule time traces reveal the time evolution of unsynchronized kinetic systems. Especially single molecule F\"orster resonance energy transfer (smFRET) provides access to enzymatically important timescales, combined with molecular…
This thesis investigates the mechanically controlled break junctions, with a particular emphasis on elucidating the behaviour of molecular currents at room temperature. The core of this experimental investigation involves a detailed…
Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We propose a detailed investigation of the schematic mode-coupling approach to experimental data, a method based on the use of simple mode-coupling equations to analyze the dynamics of supercooled liquids. Our aim here is to clarify…
A variety of experimental techniques have improved the 2D and 3D spatial resolution that can be extracted from \emph{in vivo} single-molecule measurements. This enables researchers to quantitatively infer the magnitude and directionality of…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now…
We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or…
We provide a novel approach and an exploratory study for modelling life event choices and occurrence from a probabilistic perspective through causal discovery and survival analysis. Our approach is formulated as a bi-level problem. In the…