Groups with the Minimal Conditions for Subgroups and for Nonabelian Subgroups

For some very wide classes $\mathfrak{D}$ and $\mathfrak{B}\subset\mathfrak{D}$ of groups, the author proves that an arbitrary (nonabelian) group $G\in \mathfrak{D}$ (respectively $G\in \mathfrak{B}$) satisfies the minimal condition for (nonabelian) subgroups iff it is Cherniko

Certified Functions for Mesh Generation

Formal methods allow for building correct-by-construction software with provable guarantees. The formal development presented here resulted in certified executable functions for mesh generation. The term certified means that their correctness is established via an artifact, or certificate, which is a statement of these functions in a formal language along with the proofs of their correctness. The term is meaningful only when qualified by a specific set of properties that are proven. This manuscript elaborates on the precise statements of the properties being proven and their role in an implementation of a version of the Isosurface Stuffing algorithm by Labelle and Shewchuk. This work makes use of the Calculus of Inductive Constructions for defining executable functions, stating their properties, and proving these properties via a direct examination of these functions (the property of liveness). The certificate is made available for inspection and execution using the Coq proof assistant

Homeomorphic Tetrahedral Tessellation for Biomedical Images

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes for biomedical images. The method uses an octree as the background grid from which to build the final graded conforming meshes. The algorithm is fast and robust. It produces meshes with high quality since it provides dihedral angle lower bound for the output tetrahedra. Moreover, the mesh boundary is a geometrically and topologically accurate approximation of the object surface in the sense that it allows for guaranteed bounds on the two-sided Hausdorff distance and the homeomorphism between the boundaries of the mesh and the boundaries of the materials. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data

Homeomorphic Tetrahedralization of Multi-material Images with Quality and Fidelity Guarantees

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces meshes with high quality since it provides a guaranteed dihedral angle bound of up to 19.47° for the output tetrahedra. In addition, it allows for user-specified guaranteed bounds on the two-sided Hausdorff distance between the boundaries of the mesh and the boundaries of the materials. Moreover, the mesh boundary is proved to be homeomorphic to the object surface. The algorithm is fast and robust, it produces a sufficiently small number of mesh elements that comply with these guarantees, as compared to other software. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data

Automatic Curvilinear Quality Mesh Generation Driven by Smooth Boundary and Guaranteed Fidelity

The development of robust high-order finite element methods requires the construction of valid high-order meshes for complex geometries without user intervention. This paper presents a novel approach for automatically generating a high-order mesh with two main features: first, the boundary of the mesh is globally smooth; second, the mesh boundary satisfies a required fidelity tolerance. Invalid elements are eliminated. Example meshes demonstrate the features of the algorithm

Multitissue Tetrahedral Image-to-Mesh Conversion with Guaranteed Quality and Fidelity

We present a novel algorithm for tetrahedral image-to-mesh conversion which allows for guaranteed bounds on the smallest dihedral angle and on the distance between the boundaries of the mesh and the boundaries of the tissues. The algorithm produces a small number of mesh elements that comply with these bounds. We also describe and evaluate our implementation of the proposed algorithm that is compatible in performance with a state-of-the art Delaunay code, but in addition solves the small dihedral angle problem. Read More: http://epubs.siam.org/doi/10.1137/10081525

Inflaton Decay in an Alpha Vacuum

We study the alpha vacua of de Sitter space by considering the decay rate of the inflaton field coupled to a scalar field placed in an alpha vacuum. We find an {\em alpha dependent} Bose enhancement relative to the Bunch-Davies vacuum and, surprisingly, no non-renormalizable divergences. We also consider a modified alpha dependent time ordering prescription for the Feynman propagator and show that it leads to an alpha independent result. This result suggests that it may be possible to calculate in any alpha vacuum if we employ the appropriate causality preserving prescription.Comment: 16 pages, 1 figure, Revtex 4 preprin

Baryogenesis from the amplification of vacuum fluctuations during inflation

We propose that the baryon asymmetry of the Universe may originate from the amplification of quantum fluctuations of a light complex scalar field during inflation. CP-violation is sourced by complex mass terms, which are smaller than the Hubble rate, as well as non-standard kinetic terms. We find that, when assuming 60 e-folds of inflation, an asymmetry in accordance with observation can result for models where the energy scale of inflation is of the order of 10^16 GeV. Lower scales may be achieved when assuming substantially larger amounts of e-folds.Comment: 18 page