In this paper we report on a project to obtain a verified computation of homology groups of digital images. The methodology is based on programming and executing inside the COQ proof assistant. Though more research is needed to integrate and make efficient more processing tools, we present some examples partially computed in COQ from real biomedical images.

Flat connections for unitary gauge groups on a 3–torus with twisted boundary conditions as well as recently discovered topologically non-trivial flat connections with " nondiagonalizable " triples of holonomies for higher orthogonal and exceptional groups are constructed explicitly in terms of Jacoby theta functions with rational characteristics. The (fractional) Chern-Simons numbers of these v...

This paper presents LQ control problem based on numerical computation with guaranteed accuracy. By using the proposed methods, it is possible to guarantee numerical quality about design of control system. This paper also proposes a problem which finds the numerical optimal controller from a set of solutions solved by verified LQ control problem.

Our paper reviews Kallay’s results on a geometric version of the classic Newton-Raphson method, in the context of plane curve queries, e.g. curve-curve intersection, point-curve distance computation. Variants of the geometric Newton-Raphson methods are proposed and empirically verified.

A new reinforcement learning architecture for nonlinear control is proposed. A direct feedback controller, or the actor, is trained by a value-gradient based controller, or the tutor. This architecture enables both efficient use of the value function and simple computation for real-time implementation. Good performance was verified in multi-dimensional nonlinear control tasks using Gaussian sof...

Given the need to achieve maximum performance possible, offloading intensive computation workload to GPU is a key to achieve this goal. Offloading most of the workload to GPU may not results in desired performance, so a middle approach is more suitable such as splitting the workload between the CPU and the GPU can be considered as an optimized approach. In this study, we used a popular high per...

In 2008, an electronic cash scheme with multiple banks based on group signatures was proposed by Wang et al. They adopted a group blind signature scheme based on bilinear pairings to generate the electronic cash and it can be verified by the bilinear pairings operation. However, we find some security problems in their approach. By the way, the cost of communication and computation in their sche...

Iterative optimal calculation methods have been proposed for restoration of degraded static image based on wavelet multiresolution decomposition. However, it is quite difficult to apply these methods to process moving images due to the high computation cost. In this paper, we propose an effective restoration method for degraded moving image by modeling the motion of a moving object and predicti...

We use the idea of two-point stepsize gradient methods, developed to solve unconstrained minimization problems on R, for computing least-squares solutions of a given linear operator equation on Hilbert spaces. Among them we especially pay attention to corresponding modification of the scalar correction method. An application of this approach is presented related to computation of {1, 3} inverse...

We present some examples of extensions for C-XSC that have been developed lately. Among these are extensions that give access to further hardware and software environments as well as applications making use of these possibilities. The first area of extension is C-XSC usage in parallel environments. An MPI package for C-XSC data types allows to easily use C-XSC in parallel programs without bothe...