Degeneracy degrees of constraint collections

New product development is one of the most powerful but difficult activities in business. It is also a very important factor affecting final product quality. There are many techniques available for new product development. Experimental design is now regarded as one of the most significant techniques. In this article, we will discuss how to use the technique of experimental design in developing a new product - an extrusion press. In order to provide a better understanding of this specific process, a brief description of the extrusion press is presented. To ensure the successful development of the extrusion press, customer requirements and expectations were obtained by detailed market research. The critical and non-critical factors affecting the performance of the extrusion press were identified in preliminary experiments. Through conducting single factorial experiments, the critical factorial levels were determined. The relationships between the performance indexes of the extrusion press and the four critical factors were determined on the basis of multi-factorial experiments. The mathematical models for the performance of the extrusion press were established according to a central composite rotatable design. The best combination of the four critical factors and the optimum performance indexes were determined by optimum design. The results were verified by conducting a confirmatory experiment. Finally, a number of conclusions became evident.

Linear Global Translation Estimation with Feature Tracks

This paper derives a novel linear position constraint for cameras seeing a common scene point, which leads to a direct linear method for global camera translation estimation. Unlike previous solutions, this method deals with collinear camera motion and weak image association at the same time. The final linear formulation does not involve the coordinates of scene points, which makes it efficient even for large scale data. We solve the linear equation based on $L_1$ norm, which makes our system more robust to outliers in essential matrices and feature correspondences. We experiment this method on both sequentially captured images and unordered Internet images. The experiments demonstrate its strength in robustness, accuracy, and efficiency.Comment: Changes: 1. Adopt BMVC2015 style; 2. Combine sections 3 and 5; 3. Move "Evaluation on synthetic data" out to supplementary file; 4. Divide subsection "Evaluation on general data" to subsections "Experiment on sequential data" and "Experiment on unordered Internet data"; 5. Change Fig. 1 and Fig.8; 6. Move Fig. 6 and Fig. 7 to supplementary file; 7 Change some symbols; 8. Correct some typo

Valence-Bond Crystal, and Lattice Distortions in a Pyrochlore Antiferromagnet with Orbital Degeneracy

We discuss the ground state properties of a spin 1/2 magnetic ion with threefold $t_{2g}$ orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti$^{3+}$ ion in B-spinel MgTi$_2$O$_4$. We formulate an effective spin-orbital Hamiltonian and study its low energy sector by constructing several exact-eigenstates in the limit of vanishing Hund's coupling. We find that orbital degrees of freedom modulate the spin-exchange energies, release the infinite spin-degeneracy of pyrochlore structure, and drive the system to a non-magnetic spin-singlet manifold. The latter is a collection of spin-singlet dimers and is, however, highly degenerate with respect of dimer orientations. This ``orientational'' degeneracy is then lifted by a magneto-elastic interaction that optimizes the previous energy gain by distorting the bonds in suitable directions and leading to a tetragonal phase. In this way a valence bond crystal state is formed, through the condensation of dimers along helical chains running around the tetragonal c-axis, as actually observed in MgTi$_2$O$_4$. The orbitally ordered pattern in the dimerized phase is predicted to be of ferro-type along the helices and of antiferro-type between them. Finally, through analytical considerations as well as numerical ab-initio simulations, we predict a possible experimental tool for the observation of such an orbital ordering, through resonant x-ray scattering.Comment: 15 pages, 8 figure