Projective Dynamics: Fusing Constraint Projections for Fast Simulation

We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuumbased potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation

Parabolic opers and differential operators

Parabolic SL(r,C)-opers were defined and investigated in [BDP] in the set-up of vector bundles on curves with a parabolic structure over a divisor. Here we introduce and study holomorphic differential operators between parabolic vector bundles over curves. We consider the parabolic SL(r,C)-opers on a Riemann surface X with given singular divisor S and with fixed parabolic weights satisfying the condition that all parabolic weights at any point $x_i$ in S are integral multiples of $\frac{1}{2N_i+1}$, where $N_i > 1$ are fixed integers. We prove that this space of opers is canonically identified with the affine space of holomorphic differential operators of order r between two natural parabolic line bundles on X (depending only on the divisor S and the weights $N_i$) satisfying the conditions that the principal symbol of the differential operators is the constant function 1 and the sub-principal symbol vanishes identically. The vanishing of the sub-principal symbol ensures that the logarithmic connection on the rank r bundle is actually a logarithmic SL(r, C)-connection.Comment: Final version accepted for publication in Journal of Geometry and Physic

Cardiac Macrophages and Their Effects on Arrhythmogenesis

Cardiac electrophysiology is a complex system established by a plethora of inward and outward ion currents in cardiomyocytes generating and conducting electrical signals in the heart. However, not only cardiomyocytes but also other cell types can modulate the heart rhythm. Recently, cardiac macrophages were demonstrated as important players in both electrophysiology and arrhythmogenesis. Cardiac macrophages are a heterogeneous group of immune cells including resident macrophages derived from embryonic and fetal precursors and recruited macrophages derived from circulating monocytes from the bone marrow. Recent studies suggest antiarrhythmic as well as proarrhythmic effects of cardiac macrophages. The proposed mechanisms of how cardiac macrophages affect electrophysiology vary and include both direct and indirect interactions with other cardiac cells. In this review, we provide an overview of the different subsets of macrophages in the heart and their possible interactions with cardiomyocytes under both physiologic conditions and heart disease. Furthermore, we elucidate similarities and differences between human, murine and porcine cardiac macrophages, thus providing detailed information for researchers investigating cardiac macrophages in important animal species for electrophysiologic research. Finally, we discuss the pros and cons of mice and pigs to investigate the role of cardiac macrophages in arrhythmogenesis from a translational perspective