Origami fold as algebraic graph rewriting

AbstractWe formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system (O,↬), where O is the set of abstract origamis and ↬ is a binary relation on O, that models fold. An abstract origami is a structure (Π,∽,≻), where Π is a set of faces constituting an origami, and ∽ and ≻ are binary relations on Π, each representing adjacency and superposition relations between the faces.We then address representation and transformation of abstract origamis and further reasoning about the construction for computational purposes. We present a labeled hypergraph of origami and define fold as algebraic graph transformation. The algebraic graph-theoretic formalism enables us to reason about origami in two separate domains of discourse, i.e. pure combinatorial domain where symbolic computation plays the main role and geometrical domain R×R. We detail the program language for the algebraic graph rewriting and graph rewriting algorithms for the fold, and show how fold is expressed by a set of graph rewrite rules

Morley’s theorem revisited: Origami construction and automated proof

Morley’s theorem states that for any triangle, the intersections of its adjacent angle trisectors form an equilateral triangle. The construction of Morley’s triangle by the straightedge and compass method is impossible because of the well-known impossibility result for angle trisection. However, by origami, the construction of an angle trisector is possible, and hence that of Morley’s triangle. In this paper we present a computational origami construction of Morley’s triangle and an automated correctness proof of the generalized Morley’s theorem.During the computational origami construction, geometrical constraints in symbolic representation are generated and accumulated. Those constraints are then transformed into algebraic forms, i.e. a set of polynomials, which in turn are used to prove the correctness of the construction. The automated proof is based on the Gröbner bases method. The timings of the experiments of the Gröbner bases computations for our proofs are given. They vary greatly depending on the origami construction methods, the algorithms for the Gröbner bases computation, and variable orderings

Pathogenetic roles of beet necrotic yellow vein virus RNA5 in the exacerbation of symptoms and yield reduction, development of scab‐like symptoms, and Rz1‐resistance breaking in sugar beet

Beet necrotic yellow vein virus (BNYVV) generally has a four‐segmented positive‐sense RNA genome (RNAs 1–4), but some European and most Asian strains have an additional segment, RNA5. This study examined the effect of RNA5 and RNA3 on different sugar beet cultivars using a Polymyxa‐mediated inoculation system under field and laboratory conditions. In field tests, the degree of sugar yield served as an index for assessing the virulence of BNYVV strains. Japanese A‐II type isolates without RNA5 caused mostly 15%–90% sugar yield reductions, depending on the susceptibility of sugar beet cultivars, whereas the isolates with RNA5 induced more than 90% yield losses in the seven susceptible cultivars, but small yield losses in one Rz1‐resistant and Rizor cultivars. However, a laboratory‐produced isolate containing RNA5 but lacking RNA3 caused higher yield losses in Rizor than in susceptible plants, and induced scab‐like symptoms on the root surface of both susceptible and resistant plants. In laboratory tests, A‐II type isolates without RNA5 had low viral RNA accumulation levels in roots of Rizor and Rz1‐resistant plants at early stages of infection, but in the presence of RNA5, viral RNA3 accumulation levels increased remarkably. This increased RNA3 accumulation was not observed in roots of the WB42 accession with the Rz2 gene. In contrast, the presence of RNA3 did not affect RNA5 accumulation levels. Collectively, this study demonstrated that RNA5 is involved in the development of scab‐like symptoms and the enhancement of RNA3 accumulation, and suggests these characteristics of RNA5 are associated with Rz1‐resistance breaking

Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence

We design a new fast algorithm to automatically complete closed contours in a finite point cloud on the plane. The only input can be a scanned map with almost closed curves, a hand-drawn artistic sketch or any sparse dotted image in 2D without any extra parameters. The output is a hierarchy of closed contours that have a long enough life span (persistence) in a sequence of nested neighborhoods of the input points. We prove theoretical guarantees when, for a given noisy sample of a graph in the plane, the output contours geometrically approximate the original contours in the unknown graph

Identification of a Novel Quinvirus in the Family Betaflexiviridae That Infects Winter Wheat

Yellow mosaic disease in winter wheat is usually attributed to the infection by bymoviruses or furoviruses; however, there is still limited information on whether other viral agents are also associated with this disease. To investigate the wheat viromes associated with yellow mosaic disease, we carried out de novo RNA sequencing (RNA-seq) analyses of symptomatic and asymptomatic wheat-leaf samples obtained from a field in Hokkaido, Japan, in 2018 and 2019. The analyses revealed the infection by a novel betaflexivirus, which tentatively named wheat virus Q (WVQ), together with wheat yellow mosaic virus (WYMV, a bymovirus) and northern cereal mosaic virus (a cytorhabdovirus). Basic local alignment search tool (BLAST) analyses showed that the WVQ strains (of which there are at least three) were related to the members of the genus Foveavirus in the subfamily Quinvirinae (family Betaflexiviridae). In the phylogenetic tree, they form a clade distant from that of the foveaviruses, suggesting that WVQ is a member of a novel genus in the Quinvirinae. Laboratory tests confirmed that WVQ, like WYMV, is potentially transmitted through the soil to wheat plants. WVQ was also found to infect rye plants grown in the same field. Moreover, WVQ-derived small interfering RNAs accumulated in the infected wheat plants, indicating that WVQ infection induces antiviral RNA silencing responses. Given its common coexistence with WYMV, the impact of WVQ infection on yellow mosaic disease in the field warrants detailed investigation

Laparoscopic Gastrectomy for Gastric Cancer with Peritoneal Dissemination after Induction Chemotherapy

Gastric cancer with peritoneal dissemination may be diagnosed as unresectable. More recently, as a result of progress in chemotherapy, some patients with peritoneal dissemination have exhibited extended survival. We report on our experience with three patients in whom induction chemotherapy allowed for totally laparoscopic total gastrectomy (TLTG). All three patients were diagnosed as having advanced gastric cancer with peritoneal dissemination using staging laparoscopy. As induction chemotherapy, S-1 combined with cisplatin was administered to two patients and trastuzumab plus capecitabine combined with cisplatin to one patient. TLTG was performed in all patients and there were no postoperative complications. Adjuvant chemotherapy was initiated within 3 weeks after surgery in all three patients. Laparoscopic gastrectomy undertaken after induction chemotherapy was found to be effective and safe; this treatment has the potential to achieve good treatment outcomes in patients with stage IV gastric cancer

Characterization of burdock mottle virus, a novel member of the genus Benyvirus, and the identification of benyvirus-related sequences in the plant and insect genomes.

The complete nucleotide sequence of the burdock mottle virus (BdMoV) isolated from an edible burdock plant (Arctium lappa) in Japan has been determined. BdMoV has a bipartite genome, whose organization is similar to RNA1 and RNA2 of benyviruses, beet necrotic yellow vein virus (BNYVV), beet soil-borne mosaic virus (BSBMV), and rice stripe necrosis virus (RSNV). BdMoV RNA1 (7038 nt) contains a single open reading frame (ORF) encoding a 249-kDa polypeptide that consists of methyl-transferase, helicase, papain-like protease, AlkB-like, and RNA-dependent RNA polymerase domains. The AlkB-like domain sequence is not present in the proteins encoded by other known benyviruses, but is found in replication-associated proteins of viruses mainly belonging to the families Alfaflexiviridae and Betaflexiviridae. BdMoV RNA2 (4315 nt) contains six ORFs that are similar to those of benyviruses: these are coat protein (CP), CP readthrough, triple gene block movement and cysteine-rich proteins. Phylogenetic analyses showed that BdMoV is more closely related to BNYVV and BSBMV than to RSNV. Database searches showed that benyvirus replicase-related sequences are present in the chromosomes of a chickpea plant (Cicer arietinum) and a blood-sucking insect (Rhodnius prolixus). Some other benyvirus-related sequences are found in the transcriptome shotgun libraries of a few species of plants and a bark beetle. Our results show that BdMoV is a distinct species of the genus Benyvirus and that ancestral and extant benyviruses may have infected or currently infect a wide range of hosts, including plants and insects

Search for Outer Massive Bodies around Transiting Planetary Systems: Candidates of Faint Stellar Companions around HAT-P-7

We present results of direct imaging observations for HAT-P-7 taken with the Subaru HiCIAO and the Calar Alto AstraLux. Since the close-in transiting planet HAT-P-7b was reported to have a highly tilted orbit, massive bodies such as giant planets, brown dwarfs, or a binary star are expected to exist in the outer region of this system. We show that there are indeed two candidates for distant faint stellar companions around HAT-P-7. We discuss possible roles played by such companions on the orbital evolution of HAT-P-7b. We conclude that as there is a third body in the system as reported by Winn et al. (2009, ApJL, 763, L99), the Kozai migration is less likely while planet-planet scattering is possible.Comment: 8 pages, 3 figures, 2 tables, PASJ in pres

Spatial resolved high-energy particle diagnostic system using time-of-flight neutral particle analyzer in Large Helical Device

The time-of-flight-type neutral particle analyzer has an ability of horizontal scanning from 40 to 100° of the pitch angle. The information from the spatially resolved energy spectrum gives not only the ion temperature but also the information of the particle confinement and the electric field in plasmas. We have been studying the energy distributions at various magnetic configurations in the neutral beam injection (NBI) plasma. The spatially resolved energy spectra can be observed during long discharges of the NBI plasma by continuous scanning of the neutral particle analyzer. The shape of spectra is almost similar from 44° to 53°. However, the spectra from 55° are strongly varied. They reflect the injection pitch angle of the beam. The pitch angle scanning experiment during the long discharge of NBI plasma has also been made under the reversal of the magnetic field direction. NBI2 becomes counter injected with the reversal. We can easily observe the difference between co- and counter injections of NBI. During the electron cyclotron heating in the low-density plasma for the formation of the internal thermal barrier, large neutral particle increase or decease can be observed. The degree of the increase/decrease depends on the energy and the density. The reason for the variation of the particle flux is that the orbit of the trapped particle changes due to the electric field formed by the strong electron cyclotron heating