A semi-analytical approach to molecular dynamics

Despite numerous computational advances over the last few decades, molecular dynamics still favors explicit (and thus easily-parallelizable) time integrators for large scale numerical simulation. As a consequence, computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size. In this paper, we present a semi-analytical integration scheme that offers a total speedup of a factor 30 compared to the Verlet method on typical MD simulation by allowing over three orders of magnitude larger step sizes. By efficiently approximating the exact integration of the strong (harmonic) forces of covalent bonds through matrix functions, far improved stability with respect to time step size is achieved without sacrificing the explicit, symplectic, time-reversible, or fine-grained parallelizable nature of the integration scheme. We demonstrate the efficiency and scalability of our integrator on simulations ranging from DNA strand unbinding and protein folding to nanotube resonators

Lie Symmetry Analysis for Cosserat Rods

We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary functions in t. Assuming analyticity of the arbitrary functions in a domain under consideration, we prove that the obtained solution is analytic and general. The Special Cosserat Theory of Rods describes the dynamic equilibrium of 1-dimensional continua, i.e. slender structures like fibers, by means of a system of partial differential equations.Comment: 12 Pages, 1 Figur

Zero-Level-Set Encoder for Neural Distance Fields

Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., to compute a signed distance or occupancy value at a specific spatial position. Previous methods tend to rely on the auto-decoder paradigm, which often requires densely-sampled and accurate signed distances to be known during training and testing, as well as an additional optimization loop during inference. This introduces a lot of computational overhead, in addition to having to compute signed distances analytically, even during testing. In this paper, we present a novel encoder-decoder neural network for embedding 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. Furthermore, the network is trained to solve the Eikonal equation and only requires knowledge of the zero-level set for training and inference. Additional volumetric samples can be generated on-the-fly, and incorporated in an unsupervised manner. This means that in contrast to most previous work, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. In other words, our network computes approximate solutions to the boundary-valued Eikonal equation. It also requires only a single forward pass during inference, instead of the common latent code optimization. We further propose a modification of the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surface-meshes and non-manifold geometry. We finally demonstrate the efficacy, generalizability and scalability of our method on datasets consisting of deforming 3D shapes, single class encoding and multiclass encoding, showcasing a wide range of possible applications

Outcome Prediction in Patients with Severe COVID-19 Requiring Extracorporeal Membrane Oxygenation—A Retrospective International Multicenter Study

The role of veno-venous extracorporeal membrane oxygenation therapy (V-V ECMO) in severe COVID-19 acute respiratory distress syndrome (ARDS) is still under debate and conclusive data from large cohorts are scarce. Furthermore, criteria for the selection of patients that benefit most from this highly invasive and resource-demanding therapy are yet to be defined. In this study, we assess survival in an international multicenter cohort of COVID-19 patients treated with V-V ECMO and evaluate the performance of several clinical scores to predict 30-day survival. Methods: This is an investigator-initiated retrospective non-interventional international multicenter registry study (NCT04405973, first registered 28 May 2020). In 127 patients treated with V-V ECMO at 15 centers in Germany, Switzerland, Italy, Belgium, and the United States, we calculated the Sequential Organ Failure Assessment (SOFA) Score, Simplified Acute Physiology Score II (SAPS II), Acute Physiology And Chronic Health Evaluation II (APACHE II) Score, Respiratory Extracorporeal Membrane Oxygenation Survival Prediction (RESP) Score, Predicting Death for Severe ARDS on V-V ECMO (PRESERVE) Score, and 30-day survival. Results: In our study cohort which enrolled 127 patients, overall 30-day survival was 54%. Median SOFA, SAPS II, APACHE II, RESP, and PRESERVE were 9, 36, 17, 1, and 4, respectively. The prognostic accuracy for all these scores (area under the receiver operating characteristic—AUROC) ranged between 0.548 and 0.605. Conclusions: The use of scores for the prediction of mortality cannot be recommended for treatment decisions in severe COVID-19 ARDS undergoing V-V ECMO; nevertheless, scoring results below or above a specific cut-off value may be considered as an additional tool in the evaluation of prognosis. Survival rates in this cohort of COVID-19 patients treated with V-V ECMO were slightly lower than those reported in non-COVID-19 ARDS patients treated with V-V ECMO