Minimum Supersymmetric Standard Model on the Noncommutative Geometry

We have obtained the supersymmetric extension of spectral triple which specify a noncommutative geometry(NCG). We assume that the functional space H constitutes of wave functions of matter fields and their superpartners included in the minimum supersymmetric standard model(MSSM). We introduce the internal fluctuations to the Dirac operator on the manifold as well as on the finite space by elements of the algebra A in the triple. So, we obtain not only the vector supermultiplets which meditate SU(3)xSU(2)xU(1)_Y gauge degrees of freedom but also Higgs supermultiplets which appear in MSSM on the same standpoint. Accoding to the supersymmetric version of the spectral action principle, we calculate the square of the fluctuated total Dirac operator and verify that the Seeley-DeWitt coeffients give the correct action of MSSM. We also verify that the relation between coupling constants of $SU(3)$,$SU(2)$ and $U(1)_Y$ is same as that of SU(5) unification theory

Supersymmetric Yang-Mills Theory on the Noncommutative Geometry

Recently, we found the supersymmetric counterpart of the spectral triple. When we restrict the representation space to the fermionic functions of matter fields, the counterpart which we name "the triple" reduces to the original spectral triple which defines noncommutative geometry. We see that the fluctuation to the supersymmetric Dirac operator induced by algebra in the triple generates vector supermultiplet which mediates gauge interaction. Following the supersymmetric version of spectral action principle, we calculate the heat kernel expansion of the square of fluctuated Dirac operator and obtain the correct supersymmetric Yang-Mills action with U(N) gauge symmetry.Comment: arXiv admin note: text overlap with arXiv:1201.344

DeepSaucer: Unified Environment for Verifying Deep Neural Networks

In recent years, a number of methods for verifying DNNs have been developed. Because the approaches of the methods differ and have their own limitations, we think that a number of verification methods should be applied to a developed DNN. To apply a number of methods to the DNN, it is necessary to translate either the implementation of the DNN or the verification method so that one runs in the same environment as the other. Since those translations are time-consuming, a utility tool, named DeepSaucer, which helps to retain and reuse implementations of DNNs, verification methods, and their environments, is proposed. In DeepSaucer, code snippets of loading DNNs, running verification methods, and creating their environments are retained and reused as software assets in order to reduce cost of verifying DNNs. The feasibility of DeepSaucer is confirmed by implementing it on the basis of Anaconda, which provides virtual environment for loading a DNN and running a verification method. In addition, the effectiveness of DeepSaucer is demonstrated by usecase examples