Convex Hull Characterization of Special Polytopes in n-ary Variables

This paper characterizes the convex hull of the set of n-ary vectors that are lexicographically less than or equal to a given such vector. A polynomial number of facets is shown to be sufficient to describe the convex hull. These facets generalize the family of cover inequalities for the binary case. They allow for advances relative to both the modeling of integer variables using base-n expansions, and the solving of n-ary knapsack problems with weakly super-decreasing coefficients

Almost sure well-posedness for incompressible Navier-Stokes equations with arbitrary regularity

In this paper, we study the random data problem for incompressible Navier-Stokes equations in Euclidean space. We prove that for any $s\in \mathbb{R}$, the almost sure local well-posedness holds in $H^s(\mathbb{R}^d)$ when $d\geq2$, and the almost sure global well-posedness holds in $H^s(\mathbb{R}^2)$. Our results have no regularity restriction, and thus can cover arbitrary rough data.Comment: 19 page

MILP Formulations for Unsupervised and Interactive Image Segmentation and Denoising

Image segmentation and denoising are two key components of modern computer vision systems. The Potts model plays an important role for denoising of piecewise defined functions, and Markov Random Field (MRF) using Potts terms are popular in image segmentation. We propose Mixed Integer Linear Programming (MILP) formulations for both models, and utilize standard MILP solvers to efficiently solve them. Firstly, we investigate the discrete first derivative (piecewise constant) Potts model with the ` 1 norm data term. We propose a novel MILP formulation by introducing binary edge variables to model the Potts prior. We look into the facet-defining inequalities for the associated integer polytope. We apply the model for generating superpixels on noisy images. Secondly, we propose a MILP formulation for the discrete piecewise affine Potts model. To obtain consistent partitions, the inclusion of multicut constraints is necessary, which is added iteratively using the cutting plane method. We apply the model for simultaneously segmenting and denoising depth images. Thirdly, MILP formulations of MRF models with global connectivity constraints were investigated previously, but only simplified versions of the problem were solved. We investigate this problem via a branch-and-cut method and propose a user-interactive way for segmentation. Our proposed MILPs are in general NP-hard, but they can be used to generate globally optimal solutions and ground-truth results. We also propose three fast heuristic algorithms that provide good solutions in very short time. The MILPs can be applied as a post-processing method on top of any algorithms, not only providing a guarantee on the quality, but also seek for better solutions within the branch-and-cut framework of the solver. We demonstrate the power and usefulness of our methods by extensive experiments against other state-of-the-art methods on synthetic images, standard image datasets, as well as medical images with trained probability maps

An ILP Solver for Multi-label MRFs with Connectivity Constraints

Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear Programing (LP) relaxations \cite{globalinter,globalconn} or simplified versions \cite{graphcutbase} of the problem were solved. This paper investigates the ILP of multi-label MRF with exact connectivity priors via a branch-and-cut method, which provably finds globally optimal solutions. The method enforces connectivity priors iteratively by a cutting plane method, and provides feasible solutions with a guarantee on sub-optimality even if we terminate it earlier. The proposed ILP can be applied as a post-processing method on top of any existing multi-label segmentation approach. As it provides globally optimal solution, it can be used off-line to generate ground-truth labeling, which serves as quality check for any fast on-line algorithm. Furthermore, it can be used to generate ground-truth proposals for weakly supervised segmentation. We demonstrate the power and usefulness of our model by several experiments on the BSDS500 and PASCAL image dataset, as well as on medical images with trained probability maps.Comment: 19 page

Subcellular Localization and RNA Interference of an RNA Methyltransferase Gene from Silkworm, Bombyx Mori

RNA methylation, which is a form of posttranscriptional modification, is catalyzed by S-adenosyl-L-methionone-dependent RNA methyltransterases (RNA MTases). We have identified a novel silkworm gene, BmRNAMTase, containing a 369-bp open reading frame that encodes a putative protein containing 122 amino acid residues and having a molecular weight of 13.88 kd. We expressed a recombinant His-tagged BmRNAMTase in E. coli BL21 (DE3), purified the fusion protein by metal-chelation affinity chromatography, and injected a New Zealand rabbit with the purified protein to generate anti-BmRNAMTase polyclonal antibodies. Immunohistochemistry revealed that BmRNAMTase is abundant in the cytoplasm of Bm5 cells. In addition, using RNA interference to reduce the intracellular activity and content of BmRNAMTase, we determined that this cytoplasmic RNA methyltransferase may be involved in preventing cell death in the silkworm

Dielectric barrier discharge-based defect engineering method to assist flash sintering

Oxygen vacancy OV plays an important role in a flash sintering (FS) process. In defect engineering, the methods of creating oxygen vacancy defects include doping, heating, and etching, and all of them often have complex processes or equipment. In this study, we used dielectric barrier discharge (DBD) as a new defect engineering technology to increase oxygen vacancy concentrations of green billets with different ceramics (ZnO, TiO2, and 3 mol% yttria-stabilized zirconia (3YSZ)). With an alternating current (AC) power supply of 10 kHz, low-temperature plasma was generated, and a specimen could be treated in different atmospheres. The effect of the DBD treatment was influenced by atmosphere, treatment time, and voltage amplitude of the power supply. After the DBD treatment, the oxygen vacancy defect concentration in ZnO samples increased significantly, and a resistance test showed that conductivity of the samples increased by 2–3 orders of magnitude. Moreover, the onset electric field (E) of ZnO FS decreased from 5.17 to 0.86 kV/cm at room temperature (RT); while in the whole FS, the max power dissipation decreased from 563.17 to 27.94 W. The defect concentration and conductivity of the green billets for TiO2 and 3YSZ were also changed by the DBD, and then the FS process was modified. It is a new technology to treat the green billet of ceramics in very short time, applicable to other ceramics, and beneficial to regulate the FS process

Psychological profiles of COVID vaccine-hesitant individuals and implications for vaccine message design strategies

COVID-19 has caused tremendous consequences in the U.S., and combating the pandemic requires a significant number of Americans to receive COVID-19 vaccines. Guided by prominent health communication theories, this project took a formative evaluation approach and employed a national sample (N = 1041) in the U.S. to explore the potential differences between vaccine-inclined vs. -hesitant individuals and to generate profiles of hesitant individuals as the foundation for audience segmentation and message targeting. Five distinct profiles emerged in the sample. Characteristics of each profile were described, and appropriate messaging strategies were identified to target each group. Theoretical and practical implications were discussed