Finite Invariance of Cayley Calibration Form

In the further development of the string theory, one needs to understand 3 or 4-dimensional volume minimizing subvarieties in 7 or 8-dimensional manifolds. As one example, one would like to understand 4-dimensional volume minimizing cycles in a torus T8. The Cayley calibration form can be used to find all volume minimizing cycles in each homology class of T8. In order to apply the Cayley form to 8-dimensional tori, we need to understand the finite symmetry of the Cayley form, which has a continuous symmetry group Spin(7). We have found one finite symmetry group of order eight generated by three elements. We have also studied the symmetry groups of tori based on the results of H.S.M. Coxeter, and have had a simple description of the four crystallographic groups in O(8). They can be used to classify all finite symmetry groups of the Cayley form

Study of the adsorption of Co(II) on the chitosan-hydroxyapatite

The adsorption of cobalt ions (Co2+) from aqueous solution onto chitosan-hydroxyapatite composite is investigated in this study. The effects of adsorption time, initial concentration, temperature, and pH are studied in details. Kinetics and thermodynamics of the adsorption of Co2+ onto the chitosan-hydroxyapatite are also investigated and the adsorption kinetics is found to follow the pseudo-second-order model with an activation energy (Ea) of 10.73 kJ/mol. Thermodynamic studies indicates that the adsorption follows the Langmuir adsorption equation. The value of entropy change (∆Sө) and enthalpy change (∆Hө) are found to be 83.50 and 18.09 kJ/mol, respectively. The Gibbs free energy change (∆Gө) is found to be negative at all fives temperatures, demonstrating that the adsorption process is spontaneous and endothermic.

Semi-supervised Medical Image Segmentation through Dual-task Consistency

Deep learning-based semi-supervised learning (SSL) algorithms have led to promising results in medical images segmentation and can alleviate doctors' expensive annotations by leveraging unlabeled data. However, most of the existing SSL algorithms in literature tend to regularize the model training by perturbing networks and/or data. Observing that multi/dual-task learning attends to various levels of information which have inherent prediction perturbation, we ask the question in this work: can we explicitly build task-level regularization rather than implicitly constructing networks- and/or data-level perturbation-and-transformation for SSL? To answer this question, we propose a novel dual-task-consistency semi-supervised framework for the first time. Concretely, we use a dual-task deep network that jointly predicts a pixel-wise segmentation map and a geometry-aware level set representation of the target. The level set representation is converted to an approximated segmentation map through a differentiable task transform layer. Simultaneously, we introduce a dual-task consistency regularization between the level set-derived segmentation maps and directly predicted segmentation maps for both labeled and unlabeled data. Extensive experiments on two public datasets show that our method can largely improve the performance by incorporating the unlabeled data. Meanwhile, our framework outperforms the state-of-the-art semi-supervised medical image segmentation methods. Code is available at: https://github.com/Luoxd1996/DTCComment: 9 pages, 4 figure