A note on the effect of quadratic term on final pattern in Turing model

The effect of the quadratic term on the final pattern in Turing model is disscussed numerically. Turing models are non linear reaction diffusion equations. Linear analysis for wave length is very useful to find evolving waves. But when a quadratic term appear in the equation, an initial wave can disappears and changes drastically to a spot which is independent of linear analysis

The discrete potential Boussinesq equation and its multisoliton solutions

An alternate form of discrete potential Boussinesq equation is proposed and its multisoliton solutions are constructed. An ultradiscrete potential Boussinesq equation is also obtained from the discrete potential Boussinesq equation using the ultradiscretization technique. The detail of the multisoliton solutions is discussed by using the reduction technique. The lattice potential Boussinesq equation derived by Nijhoff et al. is also investigated by using the singularity confinement test. The relation between the proposed alternate discrete potential Boussinesq equation and the lattice potential Boussinesq equation by Nijhoff et al. is clarified.Comment: 17 pages,To appear in Applicable Analysis, Special Issue of Continuous and Discrete Integrable System

Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.Comment: 19 page

Simple generation of hairless mice for in vivo imaging

The in vivo imaging of mice makes it possible to analyze disease progress non-invasively through reporter gene expression. As the removal of hair improves the accuracy of in vivo imaging, gene-modified mice with a reporter gene are often crossed with Hos:HR-1 mutant mice homozygous for the spontaneous Hrhr mutation that exhibit a hair loss phenotype. However, it is time consuming to produce mice carrying both the reporter gene and mutant Hrhr gene by mating. In addition, there is a risk that genetic background of the gene-modified mice would be altered by mating. To resolve these issues, we established a simple method to generate hairless mice maintaining the original genetic background by CRISPR technology. First, we constructed the pX330 vector, which targets exon 3 of Hr. This DNA vector (5 ng/µl) was microinjected into the pronuclei of C57BL/6J mice. Induced Hr gene mutations were found in many founders (76.1%) and these mutations were heritable. Next, we performed in vivo imaging using these gene-modified hairless mice. As expected, luminescent objects in their body were detected by in vivo imaging. This study clearly showed that hairless mice could be simply generated by the CRISPR/Cas9 system, and this method may be useful for in vivo imaging studies with various gene-modified mice

An iterative approach for the global estimation of sentence similarity.

Measuring the similarity between two sentences is often difficult due to their small lexical overlap. Instead of focusing on the sets of features in two given sentences between which we must measure similarity, we propose a sentence similarity method that considers two types of constraints that must be satisfied by all pairs of sentences in a given corpus. Namely, (a) if two sentences share many features in common, then it is likely that the remaining features in each sentence are also related, and (b) if two sentences contain many related features, then those two sentences are themselves similar. The two constraints are utilized in an iterative bootstrapping procedure that simultaneously updates both word and sentence similarity scores. Experimental results on SemEval 2015 Task 2 dataset show that the proposed iterative approach for measuring sentence semantic similarity is significantly better than the non-iterative counterparts

Xylene Recognition in Flexible Porous Coordination Polymer by Guest-Dependent Structural Transition

Xylene isomers are crucial chemical intermediates in great demand worldwide; the almost identical physicochemical properties render their current separation approach energy consuming. In this study, we utilized the soft porous coordination polymer (PCP)'s isomer-specific structural transformation, realizing o-xylene (oX) recognition/separation from the binary and ternary isomer mixtures. This PCP has a flexible structure that contains flexible aromatic pendant groups, which both work as recognition sites and induce structural flexibility of the global framework. The PCP exhibits guest-triggered "breathing"-type structural changes, which are accompanied by the rearrangement of the intraframework π-π interaction. By rebuilding π-π stacking with isomer species, the PCP discriminated oX from the other isomers by its specific guest-loading configuration and separated oX from the isomer mixture via selective adsorption. The xylene-selective property of the PCP is dependent on the solvent; in diluted hexane solution, the PCP favors p-xylene (pX) uptake. The separation results combined with crystallographic analyses revealed the effect of the isomer selectivity of the PCP on xylene isomer separation via structural transition and demonstrated its potential as a versatile selective adsorptive medium for challenging separations