The 33-colorable subgroup of Thompson's group and tricolorability of links

Starting from the work by Jones on representations of Thompson's group $F$, subgroups of $F$ with interesting properties have been defined and studied. One of these subgroups is called the $3$-colorable subgroup $\mathcal{F}$, which consists of elements whose ``regions'' given by their tree diagrams are $3$-colorable. On the other hand, in his work on representations, Jones also gave a method to construct knots and links from elements of $F$. Therefore it is a natural question to explore a relationship between elements in $\mathcal{F}$ and $3$-colorable links in the sense of knot theory. In this paper, we show that all elements in $\mathcal{F}$ give 3-colorable links.Comment: 9 pages, 11 figure

Alexander's theorem for stabilizer subgroups of Thompson's group

In 2017, Jones studied the unitary representations of Thompson's group $F$ and defined a method to construct knots and links from $F$. One of his results is that any knot or link can be obtained from an element of this group, which is called Alexander's theorem. On the other hand, Thompson's group $F$ has many subgroups and it is known that there exist various subgroups which satisfy or do not satisfy Alexander's theorem. In this paper, we prove that almost all stabilizer subgroups under the natural action on the unit interval satisfy Alexander's theorem.Comment: 14 pages, 13 figure

Artificial Extracellular Matrix Proteins Containing Phenylalanine Analogues Biosynthesized in Bacteria Using T7 Expression System and the PEGylation

In vivo incorporation of phenylalanine (Phe) analogues into an artificial extracellular matrix protein (aECM-CS5-ELF) was accomplished using a bacterial expression host that harbors the mutant phenylalanyl-tRNA synthetase (PheRS) with an enlarged binding pocket. Although the Ala294Gly/Thr251Gly mutant PheRS (PheRS**) under the control of T5 promoter allows incorporation of some Phe analogues into a protein, the T5 system is not suitable for material science studies because the amount of materials produced is not sufficient due to the moderate strength of the T5 promoter. This limitation can be overcome by using a pair of T7 promoter and T7 RNA polymerase instead. In the T7 expression system, it is difficult, however, to achieve a high incorporation level of Phe analogues, due to competition of Phe analogues for incorporation with the residual Phe that is required for synthesis of active T7 RNA polymerase. In this study, we prepared the PheRS** under T7 promoter and optimized culture condition to improve both the incorporation level of recombinant aECM protein and the incorporation level of Phe analogues. Incorporation and expression levels tend to increase in the case of p-azidophenylalanine, p-iodophenylalanine, and p-acetylphenylalanine. We evaluated the lower critical transition temperature, which is dependent on the incorporation ratio and the turbidity decreased when the incorporation level increased. Circular dichromism measurement indicated that this tendency is based on conformational change from random coil to β-turn structure. We demonstrated that polyethylene glycol (PEG) can be conjugated at reaction site of Phe analogues incorporated. We also demonstrated that the increased hydrophilicity of elastin-like sequences in the aECM-CS5-ELF made by PEG conjugation could suppress nonspecific adhesion of human umbilical vein endothelial cells (HUVEC)

Fans and polytopes in tilting theory II: gg-fans of rank 2

The $g$-fan of a finite dimensional algebra is a fan in its real Grothendieck group defined by tilting theory. We give a classification of complete $g$-fans of rank 2. More explicitly, our first main result asserts that every complete sign-coherent fan of rank 2 is a $g$-fan of some finite dimensional algebra. Our proof is based on three fundamental results, Gluing Theorem, Rotation Theorem and Subdivision Theorem, which realize basic operations on fans in the level of finite dimensional algebras. For each of 16 convex sign-coherent fans $\Sigma$ of rank 2, our second main result gives a characterization of algebras $A$ of rank 2 satisfying $\Sigma(A)=\Sigma$. As a by-product of our method, we prove that for each positive integer $N$, there exists a finite dimensional algebra $A$ of rank 2 such that the Hasse quiver of the poset of 2-term silting complexes of $A$ has precisely $N$ connected components.Comment: 37 pages, v2: Fixed typos, updated references and added section

Fans and polytopes in tilting theory

For a finite dimensional algebra $A$ over a field $k$, the 2-term silting complexes of $A$ gives a simplicial complex $\Delta(A)$ called the $g$-simplicial complex. We give tilting theoretic interpretations of the $h$-vectors and Dehn-Sommerville equations of $\Delta(A)$. Using $g$-vectors of 2-term silting complexes, $\Delta(A)$ gives a nonsingular fan $\Sigma(A)$ in the real Grothendieck group $K_0(\mathrm{proj } A)_\mathbb{R}$ called the $g$-fan. For example, the fan of $g$-vectors of a cluster algebra is given by the $g$-fan of a Jacobian algebra of a non-degenerate quiver with potential. We give several properties of $\Sigma(A)$ including idempotent reductions, sign-coherence, Jasso reductions and a connection with Newton polytopes of $A$-modules. Moreover, $\Sigma(A)$ gives a (possibly infinite and non-convex) polytope $P(A)$ in $K_0(\mathrm{proj } A)_\mathbb{R}$ called the $g$-polytope of $A$. We call $A$ $g$-convex if $P(A)$ is convex. In this case, we show that it is a reflexive polytope, and that the dual polytope is given by the 2-term simple minded collections of $A$. We give an explicit classification of $g$-convex algebras of rank $2$. We classify algebras whose $g$-polytopes are smooth Fano. We classify classical and generalized preprojective algebras which are $g$-convex, and also describe their $g$-polytope as the dual polytopes of short root polytopes of type $A$ and $B$. We also classify Brauer graph algebras which are $g$-convex, and describe their $g$-polytopes as root polytopes of type $A$ and $C$.Comment: 70 page

High-temperature properties of Fe-Pt film-magnets prepared by electroplating method

We prepared L10 ordered Fe50Pt50 thick-films on Cu substrates using the electroplating method and evaluated their high-temperature properties in the temperature range of 25-200○C. The Hc and the (BH)max at 150○C for the Fe50Pt50 films annealed by ordinary annealing method(700○C, 60 min) were 500 kA/m and 50 kJ/m3, respectively, and the thermal coefficient of Hc was -0.3%/○C. To improve the high-temperature properties, we employed a flash annealing method using an infrared furnace (8 kW). The flash annealing method improved the hightemperatureproperties (Hc = 700 kA/m, (BH)max = 70 kJ/m3 at 150○C) and the thermal coefficient (-0.21%/○C). The thermal stability ofthe films is comparable to those for Sm-Co-system magnets and better than for Nd-Fe-B-system ones. We, therefore, found the L10 ordered Fe50Pt50 films prepared by the electroplating and the flash annealing are one of the hopeful small magnets in the wide temperature range

Underwater Acoustic Positioning Based on MEMS Microphone for a Portable Autonomous Underwater Vehicle

Autonomous Underwater Vehicle positioning is important for accurate control and high-quality data collection. Conventional positioning systems are expensive. This paper describes the design and performance results of control using equations of motion and an inexpensive acoustic positioning system implemented on a lightweight AUV “KYUBIC” for Underwater Robotic competition in Okinawa 2021. The velocity used to estimate the self-position of the AUV is calculated form the equation of motion without integrating the acceleration. The acoustic positioning method is based on Super-short baseline (SSBL) principle. The system design comprises of self-made hydrophone module using MEMS microphone. The estimated distance and angle are integrated for dynamic control of AUV to locate the position of a Pinger.The 2022 International Conference on Artificial Life and Robotics (ICAROB 2022), January 20-23, 2022, on line, Oita, Japa

Editorial: Conflicts

The Editorial Board reflects on the theme of 'conflict', as observed in the work published in this issue, and in the wider world

Extracellular nanovesicles for packaging of CRISPR-Cas9 protein and sgRNA to induce therapeutic exon skipping

Prolonged expression of the CRISPR-Cas9 nuclease and gRNA from viral vectors may cause off-target mutagenesis and immunogenicity. Thus, a transient delivery system is needed for therapeutic genome editing applications. Here, we develop an extracellular nanovesicle-based ribonucleoprotein delivery system named NanoMEDIC by utilizing two distinct homing mechanisms. Chemical induced dimerization recruits Cas9 protein into extracellular nanovesicles, and then a viral RNA packaging signal and two self-cleaving riboswitches tether and release sgRNA into nanovesicles. We demonstrate efficient genome editing in various hard-to-transfect cell types, including human induced pluripotent stem (iPS) cells, neurons, and myoblasts. NanoMEDIC also achieves over 90% exon skipping efficiencies in skeletal muscle cells derived from Duchenne muscular dystrophy (DMD) patient iPS cells. Finally, single intramuscular injection of NanoMEDIC induces permanent genomic exon skipping in a luciferase reporter mouse and in mdx mice, indicating its utility for in vivo genome editing therapy of DMD and beyond

Autosomal dominant pseudohypoaldosteronism type 1 with a novel splice site mutation in MR gene

<p>Abstract</p> <p>Background</p> <p>Autosomal dominant pseudohypoaldosteronism type 1 (PHA1) is a rare inherited condition that is characterized by renal resistance to aldosterone as well as salt wasting, hyperkalemia, and metabolic acidosis. Renal PHA1 is caused by mutations of the human mineralcorticoid receptor gene (<it>MR</it>), but it is a matter of debate whether <it>MR </it>mutations cause mineralcorticoid resistance via haploinsufficiency or dominant negative mechanism. It was previously reported that in a case with nonsense mutation the mutant mRNA was absent in lymphocytes because of nonsense mediated mRNA decay (NMD) and therefore postulated that haploinsufficiency alone can give rise to the PHA1 phenotype in patients with truncated mutations.</p> <p>Methods and Results</p> <p>We conducted genomic DNA analysis and mRNA analysis for familial PHA1 patients extracted from lymphocytes and urinary sediments and could detect one novel splice site mutation which leads to exon skipping and frame shift result in premature termination at the transcript level. The mRNA analysis showed evidence of wild type and exon-skipped RT-PCR products.</p> <p>Conclusion</p> <p>mRNA analysis have been rarely conducted for PHA1 because kidney tissues are unavailable for this disease. However, we conducted RT-PCR analysis using mRNA extracted from urinary sediments. We could demonstrate that NMD does not fully function in kidney cells and that haploinsufficiency due to NMD with premature termination is not sufficient to give rise to the PHA1 phenotype at least in this mutation of our patient. Additional studies including mRNA analysis will be needed to identify the exact mechanism of the phenotype of PHA.</p