High-dimensional wave atoms and compression of seismic datasets

Wave atoms are a low-redundancy alternative to curvelets, suitable for high-dimensional seismic data processing. This abstract extends the wave atom orthobasis construction to 3D, 4D, and 5D Cartesian arrays, and parallelizes it in a shared-memory environment. An implementation of the algorithm for NVIDIA CUDA capable graphics processing units (GPU) is also developed to accelerate computation for 2D and 3D data. The new transforms are benchmarked against the Fourier transform for compression of data generated from synthetic 2D and 3D acoustic models.National Science Foundation (U.S.); Alfred P. Sloan Foundatio

A mode elimination technique to improve convergence of iteration methods for finding solitary waves

We extend the key idea behind the generalized Petviashvili method of Ref. \cite{gP} by proposing a novel technique based on a similar idea. This technique systematically eliminates from the iteratively obtained solution a mode that is "responsible" either for the divergence or the slow convergence of the iterations. We demonstrate, theoretically and with examples, that this mode elimination technique can be used both to obtain some nonfundamental solitary waves and to considerably accelerate convergence of various iteration methods. As a collateral result, we compare the linearized iteration operators for the generalized Petviashvili method and the well-known imaginary-time evolution method and explain how their different structures account for the differences in the convergence rates of these two methods.Comment: to appear in J. Comp. Phys.; 24 page

The role of the striatum in effort-based decision-making in the absence of reward

Decision-making involves weighing costs against benefits, for instance, in terms of the effort it takes to obtain a reward of a given magnitude. This evaluation process has been linked to the dorsal anterior cingulate cortex (dACC) and the striatum, with activation in these brain structures reflecting the discounting effect of effort on reward. Here, we investigate how cognitive effort influences neural choice processes in the absence of an extrinsic reward. Using functional magnetic resonance imaging in humans, we used an effort-based decision-making task in which participants were required to choose between two options for a subsequent flanker task that differed in the amount of cognitive effort. Cognitive effort was manipulated by varying the proportion of incongruent trials associated with each choice option. Choice-locked activation in the striatum was higher when participants chose voluntarily for the more effortful alternative but displayed the opposite trend on forced-choice trials. The dACC revealed a similar, yet only trend-level significant, activation pattern. Our results imply that activation levels in the striatum reflect a cost-benefit analysis, in which a balance is made between effort discounting and the intrinsic motivation to choose a cognitively challenging task. Moreover, our findings indicate that it matters whether this challenge is voluntarily chosen or externally imposed. As such, the present findings contrast with classical findings on effort discounting that found reductions in striatum activation for higher effort by finding enhancements of the same neural circuits when a cognitively challenging task is voluntarily selected and does not entail the danger of losing reward

Wavelets on the sphere : Implementation and approximations

We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional spherical wavelet, i.e., wavelets on the sphere that are sensitive to directions. Then we present a calculation method for data given on a regular spherical grid . This technique, which uses the FFT, is based on the invariance of under discrete rotations around the z axis preserving the sampling. Next, a numerical criterion is given for controlling the scale interval where the spherical wavelet transform makes sense, and examples are given, both academic and realistic. In a second part, we establish conditions under which the reconstruction formula holds in strong Lp sense, for 1p<. This opens the door to techniques for approximating functions on the sphere, by use of an approximate identity, obtained by a suitable dilation of the mother wavelet

Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.Comment: 40 page