Notes on Supersymmetric Connes’s Model

We introduce an example of noncommutative geometry-like supersymmetric standard model. We give a spectral triple based on Minkowskian superspace. Its Dirac operator fluctuated by its algebra gives supersymmetric matter kinematic term and mass term of the matter fields. The squared Dirac operator gives gauge kinematic terms and Higgs kinematic terms. Traceless condition of the gauge kinematic term gives every matter particle a hypercharge identical to that of standard model. Coupling constants of gauge symmetries coincide like as nonsupersymmetric noncommutative theory. We show mathematically unsettled problems of the model which we will overcome in a short span of time

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

Imaging Multimodalities for Dissecting Alzheimer\u27s Disease: Advanced Technologies of Positron Emission Tomography and Fluorescence Imaging.

The rapid progress in advanced imaging technologies has expanded our toolbox for monitoring a variety of biological aspects in living subjects including human. In vivo radiological imaging using small chemical tracers, such as with positron emission tomography, represents an especially vital breakthrough in the efforts to improve our understanding of the complicated cascade of neurodegenerative disorders including Alzheimer\u27s disease (AD), and it has provided the most reliable visible biomarkers for enabling clinical diagnosis. At the same time, in combination with genetically modified animal model systems, the most recent innovation of fluorescence imaging is helping establish diverse applications in basic neuroscience research, from single-molecule analysis to animal behavior manipulation, suggesting the potential utility of fluorescence technology for dissecting the detailed molecular-based consequence of AD pathophysiology. In this review, our primary focus is on a current update of PET radiotracers and fluorescence indicators beneficial for understanding the AD cascade, and discussion of the utility and pitfalls of those imaging modalities for future translational research applications. We will also highlight current cutting-edge genetic approaches and discuss how to integrate individual technologies for further potential innovations