We extend results proven by the second author ([Oh]) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spacesX with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X),W2) satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obt...

We derive a fully computable, optimal a posteriori error estimate for the finite element approximation of a total variation regularized model problem and devise an adaptive refinement strategy. Numerical experiments reveal a significant improvement over related approximations on uniformly refined triangulations.

For a large class of additive random utility discrete choice models with income effects, we compute the probability distribution of the compensating variation. We show that the cumulative distribution function only depends on the choice probabilities. Our results are used to compute the distribution of equivalent variation. The moments of the compensating variation are a onedimensional integral...

Against to the different regions of membership functions indicated image in the traditional image segmentation variational model, resulting segmentation is not clear, de-noising effect is not obvious problems, this paper proposes multi-target model for image segmentation and the splitting algorithm. The model uses a sparse regularization method to maintain the boundaries of segmented regions, t...

Most denoising and enhancement methods for color images have been formulated on linear color models, namely, the channel-by-channel model and vectorial model. In this paper, we study the total variation (TV) restoration based on the two nonlinear (or nonflat) color models: the chromaticity–brightness model and hue–saturation– value model. These models are known to be closer to human perception....

We consider a Palatini variation on a general N -Dimensional second order, torsionfree dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter action under simple coordinate transformations, and the special case of N = 2 is examined. We also examine a sub-class of theories whereby a Palat...

Abstract. This paper extends the result of [9] on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a Γ-convergence analysis, we identify the homogenized energy in the space of functions of bounded variation. It turns out to be finite for BV -maps with values in the manifold. The bulk and Cantor parts of the energy ...

Abstract. This paper extends the result of [9] on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a Γ-convergence analysis, we identify the homogenized energy in the space of functions of bounded variation. It turns out to be finite for BV -maps with values in the manifold. The bulk and Cantor parts of the energy ...

Structural variations (SVs) are the largest source of genetic variation, but remain poorly understood because of limited genomics technology. Single molecule long read sequencing from Pacific Biosciences and Oxford Nanopore has the potential to dramatically advance the field, although their high error rates challenge existing methods. Addressing this need, we introduce open-source methods for l...