High Balanced Biorthogonal Multiwavelets with Symmetry

Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results

Fast Analytic Sampling Approximation from Cauchy Kernel

The paper aims at establishing a fast numerical algorithm for Bk(f), where f is any function in the Hardy space H2(Td) and k is the scale level. Here, Bk(f) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of Bk(f) and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute Bk(f). The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm

Synthesized Magnolol Derivatives Improve Anti-Micropterus salmoides Rhabdovirus (MSRV) Activity In Vivo

Micropterus salmoides rhabdovirus (MSRV) is a primary viral pathogen in largemouth bass aquaculture, which leads to tremendous economic losses yearly. Currently, there are no approved drugs for the treatment and control of this virus. Our previous studies screened the herb Magnolia officinalis from many traditional Chinese medicines, and we isolated and identified magnolol as its main active compound against multiple rhabdoviruses, including MSRV. On the basis of the structure–activity relationship and pharmacophore model of magnolol, two new magnolol derivatives, namely, hydrogenated magnolol and 2,2′-dimethoxy-magnolol, were designed and synthesized. Their anti-MSRV activities were systematically investigated both in vitro and in vivo. By comparing the half-maximal inhibitory concentration (IC50), it was found that hydrogenated magnolol possessed a higher anti-MSRV activity than magnolol and 2,2′-dimethoxy-magnolol, with an IC50 of 13.37 μM. Furthermore, hydrogenated magnolol exhibited a protective effect on the grass carp ovary (GCO) cell line by reducing the cytopathic effect induced by MSRV. Further studies revealed that hydrogenated magnolol did not directly impact virions or interfere with MSRV adsorption. It worked within the 6–8 h of the phase of virus replication. In vivo treatment of MSRV infection with magnolol and hydrogenated magnolol showed that they significantly improved the survival rate by 44.6% and 62.7%, respectively, compared to MSRV-infected groups. The viral load measured by the expression of viral glycoprotein in the organs including the liver, spleen, and kidney also significantly decreased when fish were intraperitoneally injected at a dose of 20 mg/kg. Altogether, the structural optimization of magnolol via hydrogenation of the propylene groups increased its anti-MSRV activity both in vitro and in vivo. These results may provide a valuable reference for anti-MSRV drug discovery and development in aquaculture