For a martingale (Xn) converging almost surely to a random variable X , the sequence (Xn − X) is called martingale tail sum. Recently, Neininger [Random Structures Algorithms, 46 (2015), 346-361] proved a central limit theorem for the martingale tail sum of Régnier’s martingale for the path length in random binary search trees. Grübel and Kabluchko [2014, preprint, arXiv 1410.0469] gave an alte...

Using a continuous wavelet transform we have detected the presence of intermittency in the beta oscillations of the local field potentials (LFPs) that were recorded from the subthalamic nucleus (STN) of patients with Parkinson’s disease. The intermittent behavior was identified by plotting the wavelet power spectrum of the LFP signal on a time–frequency plane. We also computed the temporal vari...

This paper describes three new results for volume rendering algorithms utilizing splatting. First, an antialiasing extension to the basic splatting algorithm is introduced that mitigates the spatial aliasing for high-resolution volumes. Aliasing can be severe for high-resolution volumes or volumes where a high depth of field leads to converging samples along the perspective axis. Next, an analy...

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-bas...

Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix-based calculations. Thanks to the extended Lagrangian description, the electronic degrees of freedom can be integrated by stable geometric schemes that conserve the free energy. For the local orbital r...

The average rates of change of the invariants of the velocity gradient tensor (Q and R) have been determined experimentally in the outer layer of a turbulent boundary layer as a function of the invariants themselves. Subsequent integration yields trajectories in the QR plane describing the average evolution of the local flow topology following a fluid particle. The trajectories reveal inward sp...

Many cell behaviors involve cell-shape transformations that impose considerable changes in the cell's surface area, requiring a constant adaptation of the cell's plasma membrane area to prevent cell lysis. Here, we theoretically describe the interplay between the plasma membrane dynamics and a physically connected cell cortex or wall, accounting for spatial variations in membrane recycling and ...

Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the (A,M) parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A,M >>1. It is shown that there exists a critic...