Segmentation Given Partial Grouping Constraints

We consider data clustering problems where partial grouping is known a priori. We formulate such biased grouping problems as a constrained optimization problem, where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping. We enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data. Considering the normalized cuts criterion in particular, our formulation leads to a constrained eigenvalue problem. By generalizing the Rayleigh-Ritz theorem to projected matrices, we find the global optimum in the relaxed continuous domain by eigendecomposition, from which a near-global optimum to the discrete labeling problem can be obtained effectively. We apply our method to real image segmentation problems, where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations. We demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process, but also that objects can be segregated from the background without specific object knowledge

Examples of diffeomorphic complete intersections with different Hodge numbers

In this paper, we give three pairs of complex 3-dim complete intersections and a pair of complex 5-dim complete intersections, and every pair of them is diffeomorphic but with different Hodge numbers. Moreover, the diffeomorphic complex 3-dim complete intersections have different Chern mumbers $c_1^3, c_1c_2$.Comment: 7 pages, 2 table

Elliptic genera of level NN for complete intersections

We study the elliptic genera of level $N$ at the cusps of $\Gamma_1(N)$ for any complete intersection. These genera are described as the summations of generalized binomial coefficients, where each generalized binomial coefficient is related to the dimension and multi-degree of complete intersection. For complete intersection $X_n(\underline{d})$, write $c_1(X_n(\underline{d}))=c_1x$, where $x\in H^2(X_n(\underline{d});\mathbb{Z})\cong\mathbb{Z}$ is a generator. We mainly discuss the values of the elliptic genera of level $N$ for $X_n(\underline{d})$ in the case of $c_1>0, =0$ or $<0$. In particular, the values about the Todd genus, $\hat{A}$-genus and $A_k$-genus of $X_n(\underline{d})$ can be derived from the elliptic genera of level $N$.Comment: 18 pages, 1 tabl

Methyl mercury concentrations in seafood collected from Zhoushan Islands, Zhejiang, China, and their potential health risk for the fishing community

Seafood is an important exposure route for mercury, especially methyl mercury (MeHg). Therefore, we quantified MeHg concentrations in 69 species of seafood including fish, crustaceans and mollusks collected from Zhoushan Islands, China. MeHg concentrations ranged from 1. The daily dietary intake and hazard quotient for MeHg were calculated to estimate exposure and health risk through seafood consumption by local inhabitants. The calculated HQ was lower than 1, thus indicating that the exposure was below the risk threshold of related chronic diseases. However, higher MeHg concentrations in fish species such as Scoliodon sorrakowah and Auxis thazard are concerning and may pose health risk through continuous consumption by local inhabitants.China Spark Program (2015GA700094); Medical Health Science Foundation Program of the Health Department of Zhejiang Province (2020RC137); Science and technology Program of Zhoushan City (2017C32089); Medical Health Science Foundation Program of the Health Department of Zhoushan City (2018G02)) and the Chinese Academy of Sciences Fellowships under the Chinese Academy of Sciences President's International Fellowship for Visiting Scientists (2018VCC0002).info:eu-repo/semantics/publishedVersio