A Comparison between Markov Chain and Koopman Operator Based Data-Driven Modeling of Dynamical Systems

Markov chain-based modeling and Koopman operator-based modeling are two popular frameworks for data-driven modeling of dynamical systems. They share notable similarities from a computational and practitioner's perspective, especially for modeling autonomous systems. The first part of this paper aims to elucidate these similarities. For modeling systems with control inputs, the models produced by the two approaches differ. The second part of this paper introduces these models and their corresponding control design methods. We illustrate the two approaches and compare them in terms of model accuracy and computational efficiency for both autonomous and controlled systems in numerical examples

Investigating the contribution of the upper and lower lumbar spine, relative to hip motion, in everyday tasks

Background: It is commonplace for clinicians to measure range of motion (ROM) in the assessment of the lumbar spine. Traditional single 'joint' models afford measuring only a limited number of regions along the spine and may, therefore, over-simplify the description of movement. It remains to be determined if additional, useful information can be gleaned by considering the traditional 'lumbar region' as two regions. Objective: The aim of this study was to determine whether modelling the lumbar spine as two separate regions (i.e. upper and lower), yields a different understanding of spinal movement relative to hip motion, than a traditional single-joint model. This study is unique in adopting this approach to evaluate a range of everyday tasks. Method: Lumbar spine motion was measured both by being considered as a whole region (S1 to T12), and where the lumbar spine was modelled as two regions (the upper (L3-T12) and lower (S1-L3)). Results: A significant difference was evident between the relative contribution from the lower and upper spine across all movements, with the lower lumbar spine consistently contributing on average 63% of the total ROM. A significant difference was also evident between the whole lumbar spine-hip ratio, and the lower lumbar spine-hip ratio, for the movement of lifting only. The lower lumbar spine achieved greater velocity for all tasks, when compared to the upper lumbar spine. Conclusion: This study has consistently demonstrated differences in the contribution of the upper and lower spinal regions across a range of everyday tasks; hence, it would appear that greater focus should be given to performing more detailed assessments to fully appreciate spinal movement

Key residues in TLR4-MD2 tetramer formation identified by free energy simulations.

Toll-like receptors (TLRs) play a central role in both the innate and adaptive immune systems by recognizing pathogen-associated molecular patterns and inducing the release of the effector molecules of the immune system. The dysregulation of the TLR system may cause various autoimmune diseases and septic shock. A series of molecular dynamics simulations and free energy calculations were performed to investigate the ligand-free, lipopolysaccharide (LPS)-bound, and neoseptin3-bound (TLR4-MD2)2 tetramers. Compared to earlier simulations done by others, our simulations showed that TLR4 structure was well maintained with stable interfaces. Free energy decomposition by molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method suggests critical roles that two hydrophobic clusters I85-L87-P88 and I124-L125-P127 of MD2, together with LPS and neoseptin3, may play in TLR4 activation. We propose that 1) direct contacts between TLR4 convex surface and LPS and neoseptin3 at the region around L442 significantly increase the binding and 2) binding of LPS and neoseptin3 in the central hydrophobic cavity of MD2 triggers burial of F126 and exposure of I85-L87-P88 that facilitate formation of (TLR4-MD2)2 tetramer and activation of TLR4 system

Key residues in TLR4-MD2 tetramer formation identified by free energy simulations.

Toll-like receptors (TLRs) play a central role in both the innate and adaptive immune systems by recognizing pathogen-associated molecular patterns and inducing the release of the effector molecules of the immune system. The dysregulation of the TLR system may cause various autoimmune diseases and septic shock. A series of molecular dynamics simulations and free energy calculations were performed to investigate the ligand-free, lipopolysaccharide (LPS)-bound, and neoseptin3-bound (TLR4-MD2)2 tetramers. Compared to earlier simulations done by others, our simulations showed that TLR4 structure was well maintained with stable interfaces. Free energy decomposition by molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method suggests critical roles that two hydrophobic clusters I85-L87-P88 and I124-L125-P127 of MD2, together with LPS and neoseptin3, may play in TLR4 activation. We propose that 1) direct contacts between TLR4 convex surface and LPS and neoseptin3 at the region around L442 significantly increase the binding and 2) binding of LPS and neoseptin3 in the central hydrophobic cavity of MD2 triggers burial of F126 and exposure of I85-L87-P88 that facilitate formation of (TLR4-MD2)2 tetramer and activation of TLR4 system