Differential Dynamic Programming for time-delayed systems

Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a second-order approximation of the problem to find the control. It is fast enough to allow real-time control and has been shown to work well for trajectory optimization in robotic systems. Here we extend classic DDP to systems with multiple time-delays in the state. Being able to find optimal trajectories for time-delayed systems with DDP opens up the possibility to use richer models for system identification and control, including recurrent neural networks with multiple timesteps in the state. We demonstrate the algorithm on a two-tank continuous stirred tank reactor. We also demonstrate the algorithm on a recurrent neural network trained to model an inverted pendulum with position information only.Comment: 7 pages, 6 figures, conference, Decision and Control (CDC), 2016 IEEE 55th Conference o

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field $E$, which produces tidal forces, and the frame-drag field $B$, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of $E$) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes' horizon tendicity and vorticity (the normal-normal components of $E$ and $B$ on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon's intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities ($E$, $B$, the tendex lines and vortex lines, the lines' tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. [Abstract is abbreviated.]Comment: 19 pages, 7 figures, v2: Changed to reflect published version (changes made to color scales in Figs 5, 6, and 7 for consistent conventions). v3: Fixed Ref

Actin and dynamin2 dynamics and interplay during clathrin-mediated endocytosis.

Clathrin-mediated endocytosis (CME) involves the recruitment of numerous proteins to sites on the plasma membrane with prescribed timing to mediate specific stages of the process. However, how choreographed recruitment and function of specific proteins during CME is achieved remains unclear. Using genome editing to express fluorescent fusion proteins at native levels and live-cell imaging with single-molecule sensitivity, we explored dynamin2 stoichiometry, dynamics, and functional interdependency with actin. Our quantitative analyses revealed heterogeneity in the timing of the early phase of CME, with transient recruitment of 2-4 molecules of dynamin2. In contrast, considerable regularity characterized the final 20 s of CME, during which ∼26 molecules of dynamin2, sufficient to make one ring around the vesicle neck, were typically recruited. Actin assembly generally preceded dynamin2 recruitment during the late phases of CME, and promoted dynamin recruitment. Collectively, our results demonstrate precise temporal and quantitative regulation of the dynamin2 recruitment influenced by actin polymerization

Equipment Replacement Decision Making:Opportunities and Challenges

The primary function of equipment managers is to replace the right equipment at the right time and at the lowest overall cost. In this paper, the opportunities and challenges associated with equipment replacement optimization (ERO) are discussed in detail. First, a comprehensive review of the state-of-the art and state-of-the practice literature for the ERO problem is conducted. Second, a dynamic programming (DP) based optimization solution methodology is presented to solve the ERO problem. The Bellman’s formulation for the ERO deterministic (DDP) and stochastic dynamic programming (SDP) problems are discussed in detail. Finally, comprehensive ERO numerical results and implications are given

Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy

Relativistic electrons in a structured medium generate radiative losses such as Cherenkov and transition radiation that act as a virtual light source, coupling to the photonic densities of states. The effect is most pronounced when the imaginary part of the dielectric function is zero, a regime where in a non-retarded treatment no loss or coupling can occur. Maps of the resultant energy losses as a sub-5nm electron probe scans across finite waveguide structures reveal spatial distributions of optical modes in a spectral domain ranging from near-infrared to far ultraviolet.Comment: 18 pages, 4 figure