Related papers: Expanding the Temporal Analysis in Single-Molecule…
For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…
Discrete temporal transitions occur in a variety of domains, but this work is mainly motivated by applications in molecular biology: explaining and analyzing observed transcriptome and proteome time series by literature and database…
Metabonomics time-course experiments provide the opportunity to understand the changes to an organism by observing the evolution of metabolic profiles in response to internal or external stimuli. Along with other omic longitudinal profiling…
Biological molecules, like all active matter, use free energy to generate force and motion which drive them out of thermal equilibrium, and undergo inherent dynamic interconversion between metastable free energy states separated by levels…
The analysis of live-cell single-molecule imaging experiments can reveal valuable information about the heterogeneity of transport processes and interactions between cell components. These characteristics are seen as motion changes in the…
We present a simple and robust technique to extract kinetic rate models and thermodynamic quantities from single molecule time traces. SMACKS (Single Molecule Analysis of Complex Kinetic Sequences) is a maximum likelihood approach that…
Molecular-scale computation is crucial for smart materials and nanoscale devices, yet creating single-molecule systems capable of complex computations remains challenging. We present a theoretical framework for a single-molecule computer…
While providing a highly accurate framework for simulating laser-induced many-electron dynamics in atom and molecules, including linear and nonlinear steady-state and transient absorption spectra, time-dependent coupled-cluster theory does…
Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption…
This thesis aims at the logical analysis of discrete processes, in particular of such generated by gene regulatory networks. States, transitions and operators from temporal logics are expressed in the language of Formal Concept Analysis. By…
In immunological studies, the characterization of small, functionally distinct cell subsets from blood and tissue is crucial to decipher system level biological changes. An increasing number of studies rely on assays that provide…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in…
Biological systems are often modeled as a system of ordinary differential equations (ODEs) with time-invariant parameters. However, cell signaling events or pharmacological interventions may alter the cellular state and induce multi-mode…
Quantitatively predictive models of biomolecular circuits are important tools for the design of synthetic biology and molecular communication circuits. The information content of typical time-lapse single-cell data for the inference of…
Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of the evolution are obscured when observing a statistical ensemble…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Correlation matrices are widely used to analyze the interdependence of variables in various real-world scenarios. Often, a perturbation in a few variables leads to mild differences in many correlation coefficients associated with these…