Structural stability of meandering-hyperbolic group actions

In his 1985 paper Sullivan sketched a proof of his structural stability theorem for group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of meandering hyperbolicity for group actions on general metric spaces. This generalization is substantial enough to encompass actions of certain non-hyperbolic groups, such as actions of uniform lattices in semisimple Lie groups on flag manifolds. At the same time, our notion is sufficiently robust and we prove that meandering-hyperbolic actions are still structurally stable. We also prove some basic results on meandering-hyperbolic actions and give other examples of such actions.Comment: 58 pages, 5 figures; [v2] Corollary 3.19 is wrong and thus removed; [v3] Introduced a new notion of meandering hyperbolicity, generalized the main structural stability theorem even further, and added a new Section 5 on uniform lattices and their structural stabilit

Fast Marching based Rendezvous Path Planning for a Team of Heterogeneous Vehicle

A formulation is developed for deterministically calculating the optimized paths for a multi-agent system consisting of heterogeneous vehicles. The essence of this formulation is the calculation of the shortest time for each agent to reach every grid point from its known initial position. Such arrival time map can be readily assessed using the Fast Marching Method (FMM), a computational algorithm originally designed for solving boundary value problems of the Eikonal equation. Leveraging the FMM method, we demonstrate that the minimal time rendezvous point and paths for all member vehicles can be uniquely determined with minimal computational concerns. To showcase the potential of our method, we use an example of a virtual rendezvous scenario that entails the coordination of a ship, an underwater vehicle, an aerial vehicle, and a ground vehicle to converge at the optimal location within the Tampa Bay area in minimal time. It illustrates the value of the developed framework in efficiently constructing continuous path planning, while accommodating different operational constraints of heterogeneous member vehicles

新外科教育コンバージェンス構築のための次世代型ダイナミック手術教材開発

科学研究費助成事業 研究成果報告書：基盤研究(C)2015-2017課題番号 : 15K0105

Shapes of hyperbolic triangles and once-punctured torus groups

Let $\Delta$ be a hyperbolic triangle with a fixed area $\varphi$. We prove that for all but countably many $\varphi$, generic choices of $\Delta$ have the property that the group generated by the $\pi$--rotations about the midpoints of the sides of the triangle admits no nontrivial relations. By contrast, we show for all $\varphi\in(0,\pi)\setminus\mathbb{Q}\pi$, a dense set of triangles does afford nontrivial relations, which in the generic case map to hyperbolic translations. To establish this fact, we study the deformation space $\mathfrak{C}_\theta$ of singular hyperbolic metrics on a torus with a single cone point of angle $\theta=2(\pi-\varphi)$, and answer an analogous question for the holonomy map $\rho_\xi$ of such a hyperbolic structure $\xi$. In an appendix by X.~Gao, concrete examples of $\theta$ and $\xi\in\mathfrak{C}_\theta$ are given where the image of each $\rho_\xi$ is finitely presented, non-free and torsion-free; in fact, those images will be isomorphic to the fundamental groups of closed hyperbolic 3--manifolds.Comment: 32 pages. To appear in Math.

Novel 3-dimensional virtual hepatectomy simulation combined with real-time deformation

AIM: To develop a novel 3-dimensional (3D) virtual hepatectomy simulation software, Liversim, to visualize the real-time deformation of the liver.METHODS: We developed a novel real-time virtual hepatectomy simulation software program called Liversim. The software provides 4 basic functions: viewing 3D models from arbitrary directions, changing the colors and opacities of the models, deforming the models based on user interaction, and incising the liver parenchyma and intrahepatic vessels based on user operations. From April 2010 through 2013, 99 patients underwent virtual hepatectomies that used the conventional software program SYNAPSE VINCENT preoperatively. Between April 2012 and October 2013, 11 patients received virtual hepatectomies using the novel software program Liversim; these hepatectomies were performed both preoperatively and at the same that the actual hepatectomy was performed in an operating room. The perioperative outcomes were analyzed between the patients for whom SYNAPSE VINCENT was used and those for whom Liversim was used. Furthermore, medical students and surgical residents were asked to complete questionnaires regarding the new software.RESULTS: There were no obvious discrepancies (i.e., the emergence of branches in the portal vein or hepatic vein or the depth and direction of the resection line) between our simulation and the actual surgery during the resection process. The median operating time was 304 min (range, 110 to 846) in the VINCENT group and 397 min (range, 232 to 497) in the Liversim group (P = 0.30). The median amount of intraoperative bleeding was 510 mL (range, 18 to 5120) in the VINCENT group and 470 mL (range, 130 to 1600) in the Liversim group (P = 0.44). The median postoperative stay was 12 d (range, 6 to 100) in the VINCENT group and 13 d (range, 9 to 21) in the Liversim group (P = 0.36). There were no significant differences in the preoperative outcomes between the two groups. Liversim was not found to be clinically inferior to SYNAPSE VINCENT. Both students and surgical residents reported that the Liversim image was almost the same as the actual hepatectomy.CONCLUSION: Virtual hepatectomy with real-time deformation of the liver using Liversim is useful for the safe performance of hepatectomies and for surgical education

N-benzyl-N-methyldecan-1-amine and its derivative mitigate 2,4- dinitrobenzenesulfonic acid-induced colitis and collagen-induced rheumatoid arthritis

As our previous study revealed that N-benzyl-N-methyldecan-1-amine (BMDA), a new molecule originated from Allium sativum, exhibits anti-neoplastic activities, we herein explored other functions of the compound and its derivative [decyl-(4-methoxy-benzyl)-methyl-amine; DMMA] including anti-inflammatory and anti-oxidative activities. Pretreatment of THP-1 cells with BMDA or DMMA inhibited tumor necrosis factor (TNF)-α and interleukin (IL)-1β production, and blocked c-jun terminal kinase (JNK), p38 mitogen-activated protein kinase (MAPK), MAPKAP kinase (MK)2 and NF-κΒ inflammatory signaling during LPS stimulation. Rectal treatment with BMDA or DMMA reduced the severity of colitis in 2,4-dinitrobenzenesulfonic acid (DNBS)-treated rat. Consistently, administration of the compounds decreased myeloperoxidase (MPO) activity (representing neutrophil infiltration in colonic mucosa), production of inflammatory mediators such as cytokine-induced neutrophil chemoattractant (CINC)-3 and TNF-α, and activation of JNK and p38 MAPK in the colon tissues. In addition, oral administration of these compounds ameliorated collagen-induced rheumatoid arthritis (RA) in mice. The treatment diminished the levels of inflammatory cytokine transcripts, and protected connective tissues through the expression of anti-oxidation proteins such as nuclear factor erythroid-related factor (Nrf)2 and heme oxygenase (HO)1. Additionally, aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels did not differ between the BMDA- or DMMA-treated and control animals, indicating that the compounds do not possess liver toxicity. Taken together, these findings propose that BMDA and DMMA could be used as new drugs for curing inflammatory bowel disease (IBD) and RA

STRUCTURAL STABILITY OF MEANDERING-HYPERBOLIC GROUP ACTIONS

Abstract: In his 1985 paper, Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper, we relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group actions on geodesic metric spaces. This generalization is substantial enough to encompass actions of certain nonhyperbolic groups, such as actions of uniform lattices in semisimple Lie groups on flag manifolds. At the same time, our notion is sufficiently robust, and we prove that meandering-hyperbolic actions are still structurally stable. We also prove some basic results on meandering-hyperbolic actions and give other examples of such actions

Structural stability of meandering-hyperbolic group actions

In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of "meandering hyperbolicity" for group actions on geodesic metric spaces. This generalization is substantial enough to encompass actions of certain non-hyperbolic groups, such as actions of "uniform lattices" in semisimple Lie groups on flag manifolds. At the same time, our notion is sufficiently robust and we prove that meandering-hyperbolic actions are still structurally stable. We also prove some basic results on meandering-hyperbolic actions and give other examples of such actions

Colon-Targeted Trans-Cinnamic Acid Ameliorates Rat Colitis by Activating GPR109A

We designed colon-targeted trans-cinnamic acid (tCA) and synthesized its conjugates with glutamic acid (tCA-GA) and aspartic acid (tCA-AA). We evaluated the anti-colitic activity of colon-targeted tCA using a dinitrobenzenesulfonic acid-induced rat colitis model. The conjugates lowered the distribution coefficient and Caco-2 cell permeability of tCA and converted to tCA in the cecum, with higher rates and percentages with tCA-GA than with tCA-AA. Following oral gavage, tCA-GA delivered a higher amount of tCA to the cecum and exhibited better anti-colitic effects than tCA and sulfasalazine (SSZ), which is the current treatment for inflammatory bowel disease. In the cellular assay, tCA acted as a full agonist of GPR109A (EC50: 530 µM). The anti-colitic effects of tCA-GA were significantly compromised by the co-administration of the GPR109A antagonist, mepenzolate. Collectively, colon-targeted tCA potentiated the anti-colitic activity of tCA by effectively activating GPR109A in the inflamed colon, enabling tCA to elicit therapeutic superiority over SSZ

Dapsone Azo-Linked with Two Mesalazine Moieties Is a “Me-Better” Alternative to Sulfasalazine

Dapsone (DpS) is an antimicrobial and antiprotozoal agent, especially used to treat leprosy. The drug shares a similar mode of action with sulfonamides. Additionally, it possesses anti-inflammatory activity, useful for treating autoimmune diseases. Here, we developed a “me-better” alternative to sulfasalazine (SSZ), a colon-specific prodrug of mesalazine (5-ASA) used as an anti-inflammatory bowel diseases drug; DpS azo-linked with two molecules of 5-ASA (AS-DpS-AS) was designed and synthesized, and its colon specificity and anti-colitic activity were evaluated. AS-DpS-AS was converted to DpS and the two molecules of 5-ASA (up to approximately 87% conversion) within 24 h after incubation in the cecal contents. Compared to SSZ, AS-DpS-AS showed greater efficiency in colonic drug delivery following oral gavage. Simultaneously, AS-DpS-AS substantially limited the systemic absorption of DpS. In a dinitrobenzene sulfonic acid-induced rat colitis model, oral AS-DpS-AS elicited better efficacy against rat colitis than oral SSZ. Moreover, intracolonic treatment with DpS and/or 5-ASA clearly showed that combined treatment with DpS and 5-ASA was more effective against rat colitis than the single treatment with either DpS or 5-ASA. These results suggest that AS-DpS-AS may be a “me-better” drug of SSZ with higher therapeutic efficacy, owing to the combined anti-colitic effects of 5-ASA and DpS