Synchronization in the quaternionic Kuramoto model

In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we analyze the case when the coupling strength is weak. For $N=2$, when coupling strength is weak (below the critical coupling strength $\lambda_c$), we show that new periodic orbits emerge near each equilibrium point, and hence phase-locking state exists. This phenomenon is different from the real Kuramoto system since it is impossible to arrive at any synchronization when $\lambda<\lambda_c$. A theorem is proved which states that the closed contours form a set of "Baumkuchen" that is dense near each equilibrium point. In other words, the trajectory of phase difference lies on a $4D$-torus surface. Therefore, this implies that the phase-locking state is Lyapunov stable but not asymptotically stable. The proof uses a new infinite buffer method ("$\delta/n$ criterion") and a Lyapunov function argument. This has been studied both analytically and numerically. For $N=3$, we consider Lion Dance flow, the analog of Cherry flow, to demonstrate that the quaternionic synchronization exists even when the coupling strength is "super weak" (when $\lambda/\omega 3$, the stable manifold of Lion Dance flow exists, and the number of these equilibria is $\lfloor \frac{N-1}{2}\rfloor$. Therefore, we conjecture that quaternionic synchronization always exists.Comment: 35 pages, 6 figure

Improvement of LiDAR Data Accuracy Using 12 Parameter Affine Transformation

LiDAR data in a local coordinate system may need to be georeferenced and converted into a geographic or projected system. In coordinate transformation, the 7-parameter Helmet transformation method is usually used in measurements to eliminate the systematic errors made by a laser scanner. However, 7-parameter coordinate transformation assumes that there is only one scale error in all of the systematic errors. This study used 12 parameter affine transformation for coordinate transformation of airborne LiDAR data and terrestrial LiDAR data. The LiDAR data accuracy results upon 6-parameter similarity transformation, 7-parameter similarity transformation, and 12-parameter affine transformation were compared. The results showed that using 12-parameter affine transformation the airborne LiDAR and terrestrial LiDAR data have 2-3 times greater accuracy than do 7-parameter or 6-parameter transformations

Ellagic Acid, the Active Compound of Phyllanthus urinaria, Exerts In Vivo Anti-Angiogenic Effect and Inhibits MMP-2 Activity

This study aimed to assess the potential anti-angiogenic mechanism of Phyllanthus urinaria (P. urinaria) and characterize the major compound in P. urinaria that exerts anti-angiogenic effect. The water extract of P. urinaria and Ellagic Acid were used to evaluate the anti-angiogenic effect in chorioallantoic membrane (CAM) in chicken embryo and human vascular endothelial cells (HUVECs). The matrix metalloproteinase-2 (MMP-2) activity was determined by gelatin zymography. The mRNA expressions of MMP-2, MMP-14 and tissue inhibitor of metalloproteinase-2 (TIMP-2) were analyzed by reverse transcription polymerase chain reaction (RT-PCR). Level of MMP-2 proteins in conditioned medium or cytosol was determined by western blot analysis. We confirmed that P. urinaria's in vivo anti-angiogenic effect was associated with a reduction in MMP-2 activity. Ellagic acid, one of the major polyphenolic components as identified in P. urinaria by high performance liquid chromatography mass spectrometry (HPLC/MS), exhibited the same anti-angiogenic effect in vivo. Both P. urinaria and Ellagic Acid inhibited MMP-2 activity in HUVECs with unchanged mRNA level. The mRNA expression levels of MMP-14 and TIMP-2 were not altered either. Results from comparing the change of MMP-2 protein levels in conditioned medium and cytosol of HUVECs after the P. urinaria or Ellagic Acid treatment revealed an inhibitory effect on the secretion of MMP-2 protein. This study concluded that Ellagic Acid is the active compound in P. urinaria to exhibit anti-angiogenic activity and to inhibit the secretion of MMP-2 protein from HUVECs

Major interventions are associated with survival of out of hospital cardiac arrest patients - a population based survey

Background. The overall survival rate of out-of-hospital cardiac arrest (OHCA) in Taiwan or even in the whole of Asia is relatively low. Major interventions, such as target temperature management (TTM), coronary artery angiography, and extracorporeal membrane oxygenation (ECMO), have been associated with better patient outcome. However, studies in Taiwan revealing evidence of the benefits of these interventions are limited. Methods. A population-based study used an 8-year database to analyze overall survival and risk factors ˝among OHCA patients. All adult non-trauma OHCA patients were identified through diagnostic and procedure codes. Hospital survival and return of spontaneous circulation (ROSC) were primary and secondary outcomes. Logistic regression and Cox regression analyses were conducted. Results. There was a relationship between major interventions (including TTM, coronary artery angiography, and ECMO) and better hospital survival. Age, income, major interventions, and acute myocardial infarction history were associated with hospital survival. The adjusted hazard ratios (HRs) were 0.406 (95% CI, 0.295 to 0.558), 1.109 (95% CI, 1.027 to 1.197), 1.075 (95% CI, 1.002 to 1.154), 1.097 (95% CI, 1.02 to 1.181) and 0.799(95% CI, 0.677 to 0.942) for patients with major interventions, age≥50, medium low and low income, middle income, and acute myocardial infarction history, respectively. Conclusion. This population-based study in Taiwan revealed that older age (≥50), medium low and low income were associated with a lower rate of survival. Major interventions, including TTM, coronary angiography, and ECMO, were related to better survival

Production of Active Nonglycosylated Recombinant B-Chain of Type-2 Ribosome-Inactivating Protein from Viscum articulatum and Its Biological Effects on Peripheral Blood Mononuclear Cells

Type-2 ribosome-inactivating proteins, composed of a toxic A-chain and lectin-like B-chain, display various biological functions, including cytotoxicity and immunomodulation. We here cloned the lectin-like B-chain encoding fragment of a newly identified type-2 RIP gene, articulatin gene, from Viscum articulatum, into a bacterial expression vector to obtain nonglycosylated recombinant protein expressed in inclusion bodies. After purification and protein refolding, soluble refolded recombinant articulatin B-chain (rATB) showed lectin activity specific toward galactoside moiety and was stably maintained while stored in low ionic strength solution. Despite lacking glycosylation, rATB actively bound leukocytes with preferential binding to monocytes and in vitro stimulated PBMCs to release cytokines without obvious cytotoxicity. These results implicated such a B-chain fragment as a potential immunomodulator

Extinction-free Census of AGNs in the AKARI/IRC North Ecliptic Pole Field from 23-band Infrared Photometry from Space Telescopes

In order to understand the interaction between the central black hole and the whole galaxy or their co-evolution history along with cosmic time, a complete census of active galactic nuclei (AGN) is crucial. However, AGNs are often missed in optical, UV and soft X-ray observations since they could be obscured by gas and dust. A mid-infrared (mid-IR) survey supported by multiwavelength data is one of the best ways to find obscured AGN activities because it suffers less from extinction. Previous large IR photometric surveys, e.g., WISE and Spitzer, have gaps between the mid-IR filters. Therefore, star forming galaxy (SFG)-AGN diagnostics in the mid-IR were limited. The AKARI satellite has a unique continuous 9-band filter coverage in the near to mid-IR wavelengths. In this work, we take advantage of the state-of-the-art spectral energy distribution (SED) modelling software, CIGALE, to find AGNs in mid-IR. We found 126 AGNs in the NEP-Wide field with this method. We also investigate the energy released from the AGN as a fraction of the total IR luminosity of a galaxy. We found that the AGN contribution is larger at higher redshifts for a given IR luminosity. With the upcoming deep IR surveys, e.g., JWST, we expect to find more AGNs with our method