Formation of Rogue Waves and Modulational Instability with Zero-Wavenumber Gain in Multicomponent Systems with Coherent Coupling.

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multicomponent systems-in particular, in the massive Thirring model.

The line rogue wave solutions of the nonlocal Davey-Stewartson I equation with PT symmetry based on the improved physics-informed neural network.

In the paper, we employ an improved physics-informed neural network (PINN) algorithm to investigate the data-driven nonlinear wave solutions to the nonlocal Davey-Stewartson (DS) I equation with parity-time (PT) symmetry, including the line breather, kink-shaped and W-shaped line rogue wave solutions. Both the PT symmetry and model are introduced into the loss function to strengthen the physical constraint. In addition, since the nonlocal DS I equation is a high-dimensional coupled system, this leads to an increase in the number of output results. The PT symmetry also needs to be learned that is not given in advance, which increases challenges in computing for multi-output neural networks. To address these problems, our objective is to assign various levels of weight to different items in the loss function. The experimental results show that the improved algorithm has better prediction accuracy to a certain extent compared with the original PINN algorithm. This approach is feasible to investigate complex nonlinear waves in a high-dimensional model with PT symmetry.

Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers.

We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.

Early Prediction of Persistent Organ Failure by Serum Angiopoietin-2 in Patients with Acute Pancreatitis.

BACKGROUND: Biomarkers for the early prediction of the severity of acute pancreatitis (AP) are urgently needed for clinical management of the disease. Angiopoietin-2 (Ang-2), one of the autocrine peptides that reduce endothelial permeability, has been found to be associated with various diseases, including inflammatory disorders. AIMS: This study aimed to determine whether serum Ang-2 could serve as a noninvasive biomarker for the early prediction of persistent organ failure (POF) in acute pancreatitis. METHODS: A total of 120 AP patients were prospectively enrolled at Jinling Hospital. Serum samples were collected on admission. Clinical and laboratory data were recorded. Ang-2 levels were measured by enzyme-linked immunosorbent assay. RESULTS: A total of 37 patients developed POF and were classified as having severe AP (SAP). Ang-2 was significantly higher on admission in patients who developed POF than in those who did not (p < 0.001 for all). Furthermore, receiver operating characteristic (ROC) curve analysis revealed that Ang-2 could distinguish patients who developed POF from mild AP (MAP, area under ROC curve [AUC] = 0.88, 95 % CI 0.78-0.94) and moderately severe AP patients (MSAP, AUC = 0.74, 95 % CI 0.63-0.83). In addition, multivariate logistic regression showed that increased Ang-2 was an independent predictor of developing POF between subgroups with MSAP and SAP (OR 7.2, 95 % CI 2.7-19.4) and among all AP patients (OR 12.1, 95 % CI 4.8-30.3). CONCLUSIONS: Elevated serum Ang-2 levels on admission may be a promising biomarker for the prediction of POF in AP.

Rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime.

We consider instability and localized patterns arising from the long-wave-short-wave resonance in the nonintegrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and the instability with a bubblelike spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.

Periodic traveling waves in the ϕ

We consider the instability and stability of periodic stationary solutions to the classical ϕ^{4} equation numerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and the spectrum forms a figure eight intersecting at the origin of the spectral plane. The latter can be modulationally stable, and the spectrum near the origin in that case is represented by vertical bands along the purely imaginary axis. The instability of the cnoidal states in that case stems from elliptical bands of complex eigenvalues far from the spectral plane origin. In the subluminal regime, there exist only snoidal waves which are modulationally unstable. Considering the subharmonic perturbations, we show that the snoidal waves in the subluminal regime are spectrally unstable with respect to all subharmonic perturbations, while for the dnoidal and cnoidal waves in the superluminal regime, the transition between the spectrally stable state and the spectrally unstable state occurs through a Hamiltonian Hopf bifurcation. The dynamical evolution of the unstable states is also considered, leading to some interesting localization events on the spatio-temporal backgrounds.

Ultrasound classification and clinical analysis of ovarian pregnancy: A study of 12 cases.

OBJECTIVE: To evaluate the clinical significance of preoperative ultrasound diagnosis and classification of ovarian pregnancy (OP). METHODS: The ultrasonographic reports, medical records, and operative summaries were reviewed for twelve women with a confirmed diagnosis of OP. According to the ultrasonographic appearance, OP was classified into two types. For every type, we analyzed the possibility and clinical significance of preoperative ultrasound diagnosis, combining with its clinical manifestations and treatments. RESULTS: According to sonographic features, twelve cases of OP can be classified into ruptured type (n = 6) and unruptured type (n = 6), the latter was subclassified into embryo sac type (n = 2) and non-homogeneous mass type (n = 4). All the unruptured OP have the characteristic solid hyperechoic rings or masses, and 66.7% (4/6) were correctvly diagnosed by preoperative ultrasound. No characteristic ultrasonogram was detected in ruptured OP which were all diagnosed as ruptured ectopic pregnancy (EP) or corpus luteum by preoperative ultrasound. The diagnostic and surgical procedures of four cases diagnosed by preoperative ultrasound were all laparoscopy and removal of the gestational products, and their average hemoperitoneum, operation time, hospital days was 313 ± 278 ml, 57 ± 9 min, and 4.25 ± 0.5days, respectively. While ruptured OP cases (6 cases diagnosed at first visit and 1 underdiagnosed but ruptured after 6 days), the diagnostic procedures was laparoscopy(3/7) or laparotomy(4/7), the surgical procedure was removal of the gestational products(2/7), wedge resection(3/7), or adenexectomy(2/7), and their average hemoperitoneum, operation time, and hospital days was 1914 ± 1059 ml, 93 ± 17 min, and 5.9 ± 1.3days, respectively. CONCLUSIONS: Ultrasound plays a significant role in diagnosis of OP, and part of the unruptured OP based on the typical sonographic characteristics could be correctly diagnosed by an experienced sonographer, this is beneficial and effective in terms of the risk of patient's operation and life. Whereas ruptured OP were generally diagnosed as ruptured EP or corpus luteum because there were no characteristic ultrasound manifestations.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates.

To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Radix Tetrastigma hemsleyani flavone exhibits antitumor activity in colorectal cancer via Wnt/ß-catenin signaling pathway.

BACKGROUND: Radix Tetrastigma hemsleyani flavone (RTHF) is extracted from a traditional Chinese medicinal herb T. hemsleyani, which is conventionally used as a folk medicine for its anti-inflammation activity and antiviral activity. In this study, the effects of RTHF on inhibiting malignant biological properties in colorectal cancer (CRC) were evaluated by conducting both in vitro and in vivo experiments, and the underlying mechanism was investigated. MATERIALS AND METHODS: Cell Counting Kit-8, colony formation, and flow cytometry assays were performed to evaluate the proliferation of RTHF-treated colon tumor cells. Migration and invasion capacities were also tested by cell wound scratch assay and Transwell invasion assay. Moreover, the antitumor effects of RTHF on azoxymethane/dextran sulfate sodium-induced colitis-related CRC were investigated in C57BL/6 mice. In addition, Western blot and/or quantitative reverse transcription polymerase chain reaction analysis were used to evaluate the expressions of Lgr5, Cyclin D1, c-Myc, and E-cadherin. RESULTS: These experiments showed that RTHF could decrease the cell growth kinetics and clone-forming capacity. RTHF could also dose dependently induce cell cycle arrest at G0/G1 phase and inhibit epithelial-mesenchymal transition process. Furthermore, downregulation of ß-catenin activation and downstream protein expression were detected in CRC cells after being treated with RTHF. RTHF daily gavage suppressed the number and size of CRC in mice and inhibited Lgr5 and Cyclin D1 expressions in tumor tissue. CONCLUSION: In conclusion, RTHF treatment inhibits colorectal tumor growth, decreases Wnt/ß-catenin pathway activity, and downregulates target genes' expression.

Optical rogue waves associated with the negative coherent coupling in an isotropic medium.

Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves.