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Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques…
A new method describing nuclear rotational motion microscopically is proposed. We extract the rotational Hamiltonian by introducing the intrinsic pair modes which commute with the rotational mode. Thereby the rotational mode is not treated…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a non-equilibrium projection…
Cardiac magnetic resonance (CMR) sequences visualise the cardiac function voxel-wise over time. Simultaneously, deep learning-based deformable image registration is able to estimate discrete vector fields which warp one time step of a CMR…
A human is a thing that moves in space. Like all things that move in space, we can in principle use differential equations to describe their motion as a set of functions that maps time to position (and velocity, acceleration, and so on).…
Given an unknown dynamic system such as a coupled harmonic oscillator with $n$ springs and point masses. We are often interested in gaining insights into its physical parameters, i.e. stiffnesses and masses, by observing trajectories of…
Nuclear magnetic resonance (NMR) spectroscopy provides detailed information pertaining to dynamic processes through line-shape changes, which have been traditionally limited to equilibrium conditions. However, there is a wealth of…
Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavour, determining nucleation mechanisms and rates for phase separation requires an…
Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…
Magneto-mechanical resonators (MMRs) represent a recently proposed type of passive sensor that enables the estimation of its pose as well as sensing other parameters in its environment. The working principle of MMRs entails an excitation of…
The Monte Carlo simulation of the dynamics of complex molecules produces trajectories with a large number of different configurations to sample configuration space. It is expected that these configurations can be classified into a small…
The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical…
Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an…
The transition between ballistic and diffusive motion poses difficult problems in several fields of physics. In this work we show how to calculate the spectra of the correlation functions between fields of arbitrary spatial dependence as…
Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule F\"orster resonance…
A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states.…
Multirate characterization of spin responses in nuclear magnetic resonance (NMR) is a promising approach to fingerprinting complex molecules in the presence of multiple relaxation mechanisms. Here we present experimental and theoretical…
Training of neural networks is a computationally intensive task. The significance of understanding and modeling the training dynamics is growing as increasingly larger networks are being trained. We propose in this work a model based on the…