Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials

In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomials $f_1$ and $f_2$ in the differential indeterminate $y$ with order one and arbitrary degree is given. That is, a non-singular matrix is constructed such that its determinant contains the differential resultant as a factor. Furthermore, the algebraic sparse resultant of $f_1, f_2, \delta f_1, \delta f_2$ treated as polynomials in $y, y', y"$ is shown to be a non-zero multiple of the differential resultant of $f_1, f_2$. Although very special, this seems to be the first matrix representation for a class of nonlinear generic differential polynomials

High-fidelity Facial Avatar Reconstruction from Monocular Video with Generative Priors

High-fidelity facial avatar reconstruction from a monocular video is a significant research problem in computer graphics and computer vision. Recently, Neural Radiance Field (NeRF) has shown impressive novel view rendering results and has been considered for facial avatar reconstruction. However, the complex facial dynamics and missing 3D information in monocular videos raise significant challenges for faithful facial reconstruction. In this work, we propose a new method for NeRF-based facial avatar reconstruction that utilizes 3D-aware generative prior. Different from existing works that depend on a conditional deformation field for dynamic modeling, we propose to learn a personalized generative prior, which is formulated as a local and low dimensional subspace in the latent space of 3D-GAN. We propose an efficient method to construct the personalized generative prior based on a small set of facial images of a given individual. After learning, it allows for photo-realistic rendering with novel views and the face reenactment can be realized by performing navigation in the latent space. Our proposed method is applicable for different driven signals, including RGB images, 3DMM coefficients, and audios. Compared with existing works, we obtain superior novel view synthesis results and faithfully face reenactment performance.Comment: 8 pages, 7 figure

Diagnosis and molecular characterization of rabies virus from a buffalo in China: a case report

<p>Abstract</p> <p>Background</p> <p>Rabies virus (RABV) can infect many different species of warm-blooded animals. Glycoprotein G plays a key role in viral pathogenicity and neurotropism, and includes antigenic domains that are responsible for membrane fusion and host cell receptor recognition.</p> <p>Case presentation</p> <p>A case of buffalo rabies in China was diagnosed by direct fluorescent antibody test, G gene reverse-transcriptase polymerase chain reaction, and RABV mouse inoculation test. Molecular characterization of the RABV was performed using DNA sequencing, phylogenetic analysis and amino acid sequence comparison based on the G gene from different species of animals.</p> <p>Conclusion</p> <p>The results confirmed that the buffalo with suspected rabies was infected by RABV, which was genetically closely related to HNC (FJ602451) that was isolated from cattle in China in 2007. Comparison of the G gene among different species of animal showed that there were almost no amino acid changes among RABVs isolated from the same species of animals that distributed in a near region. However, there were many changes among RABVs that were isolated from different species of animal, or the same species from different geographic regions. This is believed to be the first case report of buffalo rabies in China, and the results may provide further information to understand the mechanism by which RABV breaks through the species barrier.</p