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Surface parameterizations have been widely applied in the computer-aided design for the geometric processing tasks of surface registration, remeshing, texture mapping, and so on. In this paper, we present an efficient balanced energy minimization (BEM) algorithm for the computation of simply connected open surface parameterizations with balanced angle and area distortions. The existence of a nontrivial accumulation function of the BEM algorithm is guaranteed under some mild conditions and the limiting function is shown to be one-to-one. Comparisons of the BEM algorithm with the angle- and the area-preserving parameterizations show that the angular distortion is close to that of the angle-preserving parameterization while the area distortion is significantly improved. An application of the BEM on the Chinese virtual broadcasting technique is demonstrated thereafter, which is consisted of surface remeshing, registration, and morphing.

Macrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrow-derived macrophages (BMDMs) engulf myelin debris, forming myelin-laden macrophages (mye-M). These mye-M promote disease progression through their pro-inflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of mye-M is the root of secondary injury, and that targeting mye-M represents an efficient strategy to improve the local inflammatory microenvironment in injured spinal cords and to further motor neuron function recovery. In this study, we administer murine embryonic stem cell conditioned media (ESC-M) as a cell-free stem cell based therapy to treat a mouse model of SCI. We showed that BMDMs, but not microglial cells, engulf myelin debris generated at the injury site. Phagocytosis of myelin debris leads to the formation of mye-M in the injured spinal cord, which are surrounded by activated microglia cells. These mye-M are pro-inflammatory and lose the normal macrophage phagocytic capacity for apoptotic cells. We therefore focus on how to trigger lipid efflux from mye-M and thus restore their function. Using ESC-M as an immune modulating treatment for inflammatory damage after SCI, we rescued mye-M function and improved functional locomotor recovery. ESC-M treatment on mye-M resulted in improved exocytosis of internalized lipids and a normal capacity for apoptotic cell phagocytosis. Furthermore, when ESC-M was administered

We study the existence of Artin–Schreier curves with large a‑number. We show that Artin–Schreier curves with large a‑number can be written in certain forms and discuss their supersingularity. We also give a basis of the de Rham cohomology of Artin–Schreier curves. By computing the rank of the Hasse–Witt matrix of the curve, we also give bounds on the a‑number of trigonal curves of genus 5 in small characteristic.

Nonlinear matrix equations are encountered in many applications of control and engineering problems. In this work, we establish a complete study for a class of nonlinear matrix equations. With the aid of Sherman Morrison Woodbury formula, we have shown that any equation in this class has the maximal positive definite solution under a certain condition. Furthermore, A thorough study of properties about this class of matrix equations is provided. An acceleration of iterative method with R-superlinear convergence with order $r>1$ is then designed to solve the maximal positive definite solution efficiently.