Representation Synthesis by Probabilistic Many-Valued Logic Operation in Self-Supervised Learning

Self-supervised learning (SSL) using mixed images has been studied to learn various image representations. Existing methods using mixed images learn a representation by maximizing the similarity between the representation of the mixed image and the synthesized representation of the original images. However, few methods consider the synthesis of representations from the perspective of mathematical logic. In this study, we focused on a synthesis method of representations. We proposed a new SSL with mixed images and a new representation format based on many-valued logic. This format can indicate the feature-possession degree, that is, how much of each image feature is possessed by a representation. This representation format and representation synthesis by logic operation realize that the synthesized representation preserves the remarkable characteristics of the original representations. Our method performed competitively with previous representation synthesis methods for image classification tasks. We also examined the relationship between the feature-possession degree and the number of classes of images in the multilabel image classification dataset to verify that the intended learning was achieved. In addition, we discussed image retrieval, which is an application of our proposed representation format using many-valued logic.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Robustness of predicted CMB fluctuations in Cartan F(R)F(R) gravity

The cosmology of the $F(R)$ gravity rebuilding by the Cartan formalism is investigated. This is called Cartan $F(R)$ gravity. The well-known $F(R)$ gravity has been introduced to extend the standard cosmology, e.g. to explain the cosmological accelerated expansion as the inflation. Cartan $F(R)$ gravity is based on the Riemann-Cartan geometry. The curvature $R$ can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the matter-independent spin connection, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. This feature simplifies building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.Comment: 14pages, 4figure

Pb(Mg1/3Nb2/3)O3 (PMN) Relaxor: Dipole Glass or Nano-Domain Ferroelectric?

Combining our comprehensive investigations of polarization evolution, soft-mode by Raman scattering and microstructure by TEM, and the results reported in the literatures, we show that prototypical relaxor Pb(Mg1/3Nb2/3)O3 (PMN) is essentially ferroelectric for T<Tc~225 K. Its anomalous dielectric behavior over a broad temperature range results from the reorientation of domains in the crystal. A physic picture of the structure evolution in relaxor is also revealed. It is found that nanometric ferroelectric domains (gennerally called as polar nano-region (PNR)) interact cooperatively to form micrometric domain. Such multiscale inhomogeneities of domain structure in addition to the well-known inhomogeneities of chemical composition and local symmetry are considered to play a crucial role in producing the enigmatic phenomena in relaxor system.Comment: 16 pages, 10 figures; http://www.intechopen.com/books/advances-in-ferroelectrics/pb-mg1-3nb2-3-o3-pmn-relaxor-dipole-glass-or-nano-domain-ferroelectric