Protein universe is a complex system with critical problem of protein evolution to be analyzed. Early studies have used geometric distances and polygenetic-trees to solve this problem. However, the traditional methods are bivariate, whose taxonomy classification relies on bivariate branching. This is not sufficient to describe the complex nature of protein universe. Therefore, we propose a novel approach on multivariate protein classification. The new method bases on the theory of information and network, can be used to analyze multivariate relationships of proteins. The new method is alignment-free and have wide-applications to both sequences and 3D structures. We demonstrate the new method on six protein examples, results show that the new method is efficient and can potentially be used for future protein classifications.
For the purpose of isogeometric analysis, one of the most common ways is to construct structured hexahedral meshes, which have regular tensor product structure, and fit them by volumetric T-Splines. This theoretic work proposes a novel surface quadrilateral meshing method, colorable quad-mesh, which leads to the structured hexahedral mesh of the enclosed volume for high genus surfaces.
The work proves the equivalence relations among colorable quad-meshes, finite measured foliations and Strebel differentials on surfaces. This trinity theorem lays down the theoretic foundation for quadrilateral/hexahedral mesh generation, and leads to practical, automatic algorithms.
The work proposes the following algorithm: the user inputs a set of disjoint, simple loops on a high genus surface, and specifies a height parameter for each loop; a unique Strebel differential is computed with the combinatorial type and the heights prescribed by the user’s input; the Strebel differential assigns a flat metric on the surface and decomposes the surface into cylinders; a colorable quad-mesh is generated by splitting each cylinder into two quadrilaterals, followed by subdivision; the surface cylindrical decomposition is extended inward to produce a solid cylindrical decomposition of the volume; the hexadhedral meshing is generated for each volumetric cylinder and then glued together to form a globally consistent hex-mesh.
The method is rigorous, geometric, automatic and conformal to the geometry. This work focuses on the theoretic aspects of the framework, the algorithmic details and practical evaluations will be given in the future expositions.
In this paper, we give a simultaneous vanishing principle for the $v$-adic Carlitz multiple polylogarithms (abbreviated as CMPLs) at algebraic points, where $v$ is a finite place of the rational function field over a finite field. This principle establishes the fact that the $v$-adic vanishing of CMPLs at algebraic points is equivalent to its $\infty$-adic counterpart being Eulerian. This reveals a nontrivial connection between the $v$-adic and $\infty$-adic worlds in positive characteristic.
3D scene modeling has long been a fundamental problem in computer graphics and computer vision. With the popularity of consumer-level RGB-D cameras, there is a growing interest in digitizing real-world indoor 3D scenes. However, modeling indoor
3D scenes remains a challenging problem because of the complex structure of interior objects and poor quality of RGB-D data acquired by consumer-level sensors. Various methods have been proposed to tackle these challenges. In this survey, we provide an overview of recent advances in indoor scene modeling techniques, as well as public datasets and code libraries which can facilitate experiments and evaluation.
This article presents a novel and flexible bubble modelling technique for multi-fluid simulations using a volume fraction representation. By combining the volume fraction data obtained from a primary multi-fluid simulation with simple and efficient secondary bubble simulation, a range of real-world bubble phenomena are captured with a high degree of physical realism, including large bubble deformation, sub-cell bubble motion, bubble stacking over the liquid surface, bubble volume change, dissolving of bubbles, etc. Without any change in the primary multi-fluid simulator, our bubble modelling approach is applicable to any multi-fluid simulator based on the volume fraction representation.
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.)
Johann Carl Friedrich Gauss was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, astronomy, matrix theory, and optics.