Surge of power transmission in flat and nearly flat band lattices.

Flat band systems can yield interesting phenomena, such as dispersion suppression of waves with frequency at the band. While linear transport vanishes, the corresponding nonlinear case is still an open question. Here, we study power transmission along nonlinear sawtooth lattices due to waves with the flat band frequency injected at one end. While there is no power transfer for small intensity, there is a threshold amplitude above which a surge of power transmission occurs, i.e., supratransmission, for defocusing nonlinearity. This is due to a nonlinear evanescent wave with the flat band frequency that becomes unstable. We show that dispersion suppression and supratransmission also exist even when the band is nearly flat.

Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks.

We consider the parity-time (PT)-symmetric, nonlocal, nonlinear Schrödinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for the simplest graph topologies, such as star and tree graphs. The integrability of the problem is shown by proving the existence of an infinite number of conservation laws. A model for soliton generation in such PT-symmetric optical fibers and their networks governed by the nonlocal nonlinear Schrödinger equation is proposed. Exact formulas for the number of generated solitons are derived for the cases when the problem is integrable. Numerical solutions are obtained for the case when integrability is broken.

Data-driven modeling and forecasting of COVID-19 outbreak for public policy making.

This paper presents a data-driven approach for COVID-19 modeling and forecasting, which can be used by public policy and decision makers to control the outbreak through Non-Pharmaceutical Interventions (NPI). First, we apply an extended Kalman filter (EKF) to a discrete-time stochastic augmented compartmental model to estimate the time-varying effective reproduction number (Rt). We use daily confirmed cases, active cases, recovered cases, deceased cases, Case-Fatality-Rate (CFR), and infectious time as inputs for the model. Furthermore, we define a Transmission Index (TI) as a ratio between the instantaneous and the maximum value of the effective reproduction number. The value of TI indicates the "effectiveness" of the disease transmission from a contact between a susceptible and an infectious individual in the presence of current measures, such as physical distancing and lock-down, relative to a normal condition. Based on the value of TI, we forecast different scenarios to see the effect of relaxing and tightening public measures. Case studies in three countries are provided to show the practicability of our approach.

Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model.

We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI). Based on the topology of the underlying spatial dynamical system, we establish the existence of nonlinear edge states (edge solitons) for all positive energies in the topological band gap. We discover that these edge solitons are stable at any energy when the ratio between the weak and strong couplings is below a critical value. Above the critical coupling ratio, there are energy intervals where the edge solitons experience an oscillatory instability. Though our paper focuses on a photonic system, we also discuss the broader relevance of our methods and results to 1D nonlinear mechanical TIs.

Mathematical models for assessing vaccination scenarios in several provinces in Indonesia.

To mitigate casualties from the COVID-19 outbreak, this study aims at assessing the optimal vaccination scenarios, considering several existing healthcare conditions and assumptions, by developing SIQRD (Susceptible-Infected-Quarantine-Recovery-Death) models for Jakarta, West Java, and Banten, in Indonesia. The models include an age-structured dynamic transmission model that naturally allows for different treatments among different age groups of the population. The simulation results show that the timing and period of the vaccination should be well planned and prioritizing particular age groups will give a significant impact on the total number of casualties.

Incidental Finding of Elevated Serum Cartilage Oligomeric Matrix Protein (sCOMP) in Knee Osteoarthritis Patient with Undiagnosed Colon Cancer: A Case Report.

BACKGROUND: The clinical utility of cartilage oligomeric matrix protein (COMP) as a diagnostic and prognostic biomarker is currently under intense study. COMP has been associated primarily with musculoskeletal disorders such as rheumatoid and osteoarthritis (OA) or muscular and ligament trauma. Aside from its established role as a biomarker of arthritis, an increasing number of studies have also suggested the role of COMP in tumorigenesis, based on findings of its expression in breast, prostate, and colon cancers. CASE PRESENTATION: We described the case of a 61-year-old man with knee osteoarthritis and was prescribed physical therapy and a course of prolotherapy injection. We found elevated sCOMP levels in our patient (twice higher than average). After a month of follow-up, he was diagnosed with colorectal cancer. CONCLUSION: It makes us wonder about other conditions of the patients. There is no standard COMP parameter to differentiate OA patients from colorectal cancer patients, but it considers the increase is higher in colorectal cancer patients. We suggest to clinicians who use the COMP level to monitor OA condition to be aware of other conditions when the level is much higher than average OA patients.

Snakes and ghosts in a parity-time-symmetric chain of dimers.

We consider linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time (PT)-symmetric coupler composed by a chain of dimers. We study uniform states and site-centered and bond-centered spatially localized solutions and present that each solution has a symmetric and antisymmetric configuration between the arms. The symmetric solutions can become unstable due to bifurcations of asymmetric ones, that are called ghost states, because they exist only when an otherwise real propagation constant is taken to be complex valued. When a parameter is varied, the resulting bifurcation diagrams for the existence of standing localized solutions have a snaking behavior. The critical gain and loss coefficient above which the PT symmetry is broken corresponds to the condition when bifurcation diagrams of symmetric and antisymmetric states merge. Past the symmetry breaking, the system no longer has time-independent states. Nevertheless, equilibrium solutions can be analytically continued by defining a dual equation that leads to ghost states associated with growth or decay, that are also identified and examined here. We show that ghost localized states also exhibit snaking bifurcation diagrams. We analyze the width of the snaking region and provide asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained.

Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs.

We consider a modified version of the spin-flip model (SFM) that describes optically pumped quantum dot (QD) spin-polarized vertical-cavity surface-emitting lasers (VCSELs). Maps showing different dynamical regions and those consisting of various key bifurcations are constructed by direct numerical simulations and a numerical path continuation technique, respectively. A comparison between them clarifies the physical mechanism that governs the underlying dynamics as well as routes to chaos in QD spin-VCSELs. Detailed numerical simulations illustrate the role played by the capture rate from wetting layer (WL) to QD ground state, the gain parameter, and the amplitude-phase coupling. By tuning the aforementioned key parameters in turn we show how the dynamical regions evolve as a function of the intensity and polarization of the optical pump, as well as in the plane of the spin relaxation rate and linear birefringence rate, which is of importance in the design of spin lasers promising potential applications. By increasing the capture rate from WL to QD our simulation accurately describes the transition from the QD spin-VCSEL to the quantum well case, in agreement with a previous mathematical derivation, and thus validates the modified SFM equations.

Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study.

We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.

Locking bandwidth of two laterally-coupled semiconductor lasers subject to optical injection.

We report here for the first time (to our knowledge), a new and universal mechanism by which a two-element laser array is locked to external optical injection and admits stably injection-locked states within a nontrivial trapezoidal region. The rate equations for the system are studied both analytically and numerically. We derive a simple mathematical expression for the locking conditions, which reveals that two parallel saddle-node bifurcation branches, not reported for conventional single lasers subject to optical injection, delimit the injection locking range and its width. Important parameters are the linewidth enhancement factor, the laser separation, and the frequency offset between the two laterally-coupled lasers; the influence of these parameters on locking conditions is explored comprehensively. Our analytic approximations are validated numerically by using a path continuation technique as well as direct numerical integration of the rate equations. More importantly, our results are not restricted by waveguiding structures and uncover a generic locking behavior in the lateral arrays in the presence of injection.

Secure communication systems based on chaos in optically pumped spin-VCSELs.

We report on a master and slave configuration consisting of two optically pumped spin-vertical-cavity surface-emitting lasers for chaos synchronization and secure communication. Under appropriate conditions, high-quality chaos synchronization is achieved. We propose two encryption schemes, where either the pump magnitude or polarization is modulated. The results show that these allow for Gb/s transmission of secure data, but exhibit different features: one indicates that the message can be recovered by the total intensity, but not the polarization components, whereas the other shows that the message can be better or exclusively retrieved from the polarization components at high bit rates.

High frequency continuous birefringence-induced oscillations in spin-polarized vertical-cavity surface-emitting lasers.

Sustained, large amplitude and tunable birefringence-induced oscillations are obtained in a spin-vertical cavity surface-emitting laser (spin-VCSEL). Experimental evidence is provided using a spin-VCSEL operating at 1300 nm, under continuous-wave optical pumping and at room temperature. Numerical and stability analyses are performed to interpret the experiments and to identify the combined effects of pump ellipticity, spin relaxation rate, and cavity birefringence. Importantly, the frequency of the induced oscillations is determined by the device's birefringence rate, which can be tuned to very large values. This opens the path for ultrafast spin-lasers operating at record frequencies exceeding those possible in traditional semiconductor lasers and with ample expected impact in disparate disciplines (e.g., datacomms, spectroscopy).

Homoclinic snaking in the discrete Swift-Hohenberg equation.

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

Interactions of bright and dark solitons with localized PT-symmetric potentials.

We study collisions of moving nonlinear-Schrödinger solitons with a PT-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solitons are found by means of numerical simulations, and in the approximate semi-analytical form. An exact solution for the dark soliton pinned by the complex PT-symmetric dipole is produced too.

Variational approximation and the use of collective coordinates.

We consider propagating, spatially localized waves in a class of equations that contain variational and nonvariational terms. The dynamics of the waves is analyzed through a collective coordinate approach. Motivated by the variational approximation, we show that there is a natural choice of projection onto collective variables for reducing the governing (nonlinear) partial differential equation (PDE) to coupled ordinary differential equations (ODEs). This projection produces ODEs whose solutions are exactly the stationary states of the effective Lagrangian that would be considered in applying the variational approximation method. We illustrate our approach by applying it to a modified Fisher equation for a traveling front, containing a non-constant-coefficient nonlinear term. We present numerical results that show that our proposed projection captures both the equilibria and the dynamics of the PDE much more closely than previously proposed projections.

Thresholdless discrete surface solitons and stability switchings in periodically curved waveguides.

We study numerically a parametrically driven discrete nonlinear Schrödinger equation modeling periodically curved waveguide arrays. We show that discrete surface solitons persist, but their threshold power is altered by the drive. There are critical drives at which the threshold values vanish. We also show that parametric drives can create resonance with a phonon making a barrier for discrete solitons. By calculating the corresponding Floquet multipliers, we find that the stability of symmetric and antisymmetric off-side discrete surface solitons switches approximately at the critical drives for thresholdless solitons.

Single-visit approach of cervical cancer screening: see and treat in Indonesia.

BACKGROUND: We performed a cross-sectional study in Indonesia to evaluate the performance of a single-visit approach of cervical cancer screening, using visual inspection with acetic acid (VIA), histology and cryotherapy in low-resource settings. METHODS: Women having limited access to health-care facilities were screened by trained doctors using VIA. If the test was positive, biopsies were taken and when eligible, women were directly treated with cryotherapy. Follow-up was performed with VIA and cytology after 6 months. When cervical cancer was suspected or diagnosed, women were referred. The positivity rate, positive predictive value (PPV) and approximate specificity of the VIA test were calculated. The detection rate for cervical lesions was given. RESULTS: Screening results were completed in 22 040 women, of whom 92.7% had never been screened. Visual inspection with acetic acid was positive in 4.4%. The PPV of VIA to detect CIN I or greater and CIN II or greater was 58.7% and 29.7%, respectively. The approximate specificity was 98.1%, and the detection rate for CIN I or greater was 2.6%. CONCLUSION: The single-visit approach cervical cancer screening performed well, showing See and Treat is a promising way to reduce cervical cancer in Indonesia.

Effect of membrane hydrophilization on ultrafiltration performance for biomolecules separation.

This paper compares the performance of different hydrophilization methods to prepare low fouling ultrafiltration (UF) membranes. The methods include post-modification with hydrophilic polymer and blending of hydrophilic agent during either conventional or reactive phase separation (PS). The post-modification was done by photograft copolymerization of water-soluble monomer, poly(ethylene glycol) methacrylate (PEGMA), onto a commercial polyethersulfone (PES) UF membrane. Hydrophilization via blend polymer membrane with hydrophilic additive was performed using non-solvent induced phase separation (NIPS). In reactive PS method, the cast membrane was UV-irradiated before coagulation. The resulting membrane characteristic, the performance and hydrophilization stability were systematically compared. The investigated membrane characteristics include surface hydrophilicity (by contact angle /CA/), surface chemistry (by FTIR spectroscopy), and surface morphology (by scanning electron microscopy). The membrane performance was examined by investigation of adsorptive fouling and ultrafiltration using solution of protein or polysaccharide or humic acid. The results suggest that all methods could increase the hydrophilicity of the membrane yielding less fouling. Post-modification decreased CA from 44.8±4.2o to 37.8±4.2o to 42.5±4.3o depending on the degree of grafting (DG). The hydrophilization via polymer blend decreased CA from from 65o to 54o for PEG concentration of 5%. Nevertheless, decreasing hydraulic permeability was observed after post-modification as well as during polymer blend modification. Stability examination showed that there was leaching out of modifier agent from the membrane matrix prepared via conventional PS after 10days soaking in both water and NaOH. Reactive PS could increase the stability of the modifier agent in membrane matrix.

Variational approximations to homoclinic snaking.

We investigate the snaking of localized patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, which are not accessible via standard multiple-scales asymptotic techniques. We obtain the symmetric snaking solutions and the asymmetric "ladder" states, and also predict the stability of the localized states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.

Variational approximations to homoclinic snaking in continuous and discrete systems.

Localized structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of length scales, the width of the pinning region is exponentially small and beyond the reach of standard asymptotic methods. We show how this behavior can be obtained using a variational method, for two systems. In the case of the quadratic-cubic Swift-Hohenberg equation, this gives results that are in agreement with recent work using exponential asymptotics. In addition, the method is applied to a discrete system with cubic-quintic nonlinearity, giving results that agree well with numerical simulations.