Deep density estimation via invertible block-triangular mapping

In this work,we develop an invertible transport map,called KRnet,for density estimation by coupling the Knothe–Rosenblatt(KR)rearrangement and the flow-based generative model,which generalizes the real-valued non-volume preserving(real NVP)model(arX-iv:1605.08803v3).The triangular structure of the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange of information between dimensions,which not only accelerates the training process but also improves the accuracy significantly.We have also introduced several new layers into the generative model to improve both robustness and effectiveness,including a reformulated affine coupling layer,a rotation layer and a component-wise nonlinear invertible layer.The KRnet can be used for both density estimation and sample generation especially when the dimensionality is relatively high.Numerical experiments have been presented to demonstrate the performance of KRnet.

Synthesis, Characterization and Performance of a New Type of Alkylene Triphenyl Double Quaternary Phosphonium Salt

ByBimolecular Nucleophilic Substitution, four new types of alkylene triphenyl double quaternary phosphonium salt were synthesized respectively by using triphenylphosphine, 1,3-dibromopropane, 1,6-dibromohexane,1,10-dibromo- decane, 1,12-dibromododecane as raw materials and using DMAC as the solvent, under a certain temperature and reac- tion time. The productivity is 58% - 83%. The molecular structures of the products were characterized by IR, NMR and elemental analysis. The sterilizing effect of 1,6-hexylidene triphenyl double phosphonium bromide(HTDPB) and 1,12- dodecylidene triphenyl double phosphonium bromide(DoTDPB) was evaluated by using extinct dilution method.The experimental result shows that the sterilizing effect of DoTDPB is better than the effect of HTDPB under the same drug concentration and contact time. When the concentration of DoTDPB was 20 mg/L and the contact time was 0.5 h, the sterilizing rate of DoTDPB used to kill saprophytic bacteria (TGB), sulfate-reducing bacteria (SRB) and iron bacteria (IB) was 95.56%, 84% and 99.58% respectively.

Tensor Train Random Projection

This work proposes a Tensor Train Random Projection(TTRP)method for dimension reduction,where pairwise distances can be approximately preserved.Our TTRP is systematically constructed through a Tensor Train(TT)representation with TT-ranks equal to one.Based on the tensor train format,this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy,comparedwith existingmethods.We provide a theoretical analysis of the bias and the variance of TTRP,which shows that this approach is an expected isometric projectionwith bounded variance,and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores.Detailed numerical experiments with synthetic datasets and theMNIST dataset are conducted to demonstrate the efficiency of TTRP.