Cusp Type Research Articles

Saturation recovery leads to cusp type Bogdanov–Takens bifurcations of codimensions 3

We reconsider an SIS epidemic model studied by Cui et al. [1]. The model is shown that saturation recovery leads to backward bifurcation, Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. However, for the case when the Bogdanov–Takens bifurcation of codimension 2 is degenerate, the types and codimensions of Bogdanov–Takens bifurcation have not been investigated. In this paper we prove that this same model can undergo cusp type Bogdanov–Takens bifurcations of codimensions 3. Hence, more complex new phenomena, including degenerate Hopf bifurcation, degenerate homoclinic bifurcation and saddle–node bifurcation of limit cycles, exhibit. Furthermore, we get the bifurcation diagram of codimension 3 Bogdanov–Takens bifurcation with cusp type of the SIS epidemic model.

Prevalence of Cusp of Carabelli in Upper First Molars in Salahdin Governate and Its Caries Susptability

This study was performed to measure distribution of different types of Carabelli cusps among population and relationship of each cusp type with dental caries. Method: this study included the examination of 200 patients for both right and left sides, to find the distribution of Carabelli cusp and their caries susptability. Patients with severe destructed or extracted upper first molar from any side were excluded. Results: percentage of presence or appearance of prominent Carabelli cusp was approximately 23%. Groove obtained in 33% of total examined teeth. Prominent cusps showed higher rate of caries infection, while smooth surface had lower caries susptability. Conclusion: according to the anatomical differences of mesiopalatal surface of upper first molar, Carabelli cusp prevalence was high and caries susptability was increased in positive cusp expression

BIFURCATION ANALYSIS OF AN SIR MODEL WITH SATURATED INCIDENCE RATE AND STRONG ALLEE EFFECT

In this paper, rich dynamics and complex bifurcations of an SIR epidemic model with saturated incidence rate and strong Allee effect are investigated. First, the existence of disease-free and endemic equilibria is explored, and we prove that the system has at most three positive equilibria, which exhibit different types such as hyperbolic saddle and node, degenerate unstable saddle (node) of codimension 2, degenerate saddle-node of codimension 3 at disease-free equilibria, and cusp, focus, and elliptic types Bogdanov–Takens singularities of codimension 3 at endemic equilibria. Second, bifurcation analysis at these equilibria are investigated, and it is found that the system undergoes a series of bifurcations, including transcritical, saddle node, Hopf, degenerate Hopf, homoclinic, cusp type Bogdanov–Takens of codimensional 2, and focus and elliptic type Bogdanov–Takens bifurcation of codimension 3 which are composed of some bifurcations with lower codimension. The system shows very rich dynamics such as the coexistence of multiple periodic orbits and homoclinic loops. Finally, numerical simulations are conducted on the theoretical results.

Nilpotent Bicenters in Continuous Piecewise ℤ2-Equivariant Cubic Polynomial Hamiltonian Vector Fields: Cusp–Cusp Type

In this paper, we study the global dynamics for a class of continuous piecewise [Formula: see text]-equivariant cubic Hamiltonian vector fields with nilpotent bicenters at [Formula: see text]. We consider these polynomial vector fields with a challenging case where the bicenters [Formula: see text] come from the combination of two nilpotent cusps separated by [Formula: see text]. We call it a cusp–cusp type. We use the Poincaré compactification, the blow-up theory, the index theory and the theory of discriminant sequence for determining the number of distinct or negative real roots of a polynomial, to classify the global phase portraits of these vector fields in the Poincaré disc.

Fatigue behavior, failure mode, and stress distribution of occlusal veneers: influence of the prosthetic preparation cusp inclinations and the type of restorative material.

To evaluate the effects of cusp inclination of the prosthetic preparation's occlusal surface and type of restorative material on the fatigue behavior, failure mode, and stress distribution of occlusal veneers. Glass fiber-reinforced epoxy resin prosthetic preparations for occlusal veneers with three different occlusal surface cusp inclination degrees (0°, 15°, and 30°) were produced and assigned into six testing groups (n = 11) according to the cusp inclination (0°, 15°, or 30°) and type of restorative material (lithium disilicate-LD or resin composite-RC). Despite different substrate preparation cusp inclination degrees, the restorations were designed maintaining 30° inclination between the cusps at the occlusal surface and a thickness of 0.7mm at the central groove region of the restorations to be machined in a CAD/CAM system. After cementation, the specimens were stored for about 7days (under water at 37°C), and subsequently submitted to a load to failure test (n = 2) and an intermittent cyclic fatigue test (n = 9) (initial load: 100 N; step size: 50 N; cycles/step: 10,000; loading frequency: 20Hz; loading piston: 6-mm-diameter stainless steel) until observing cracks. The data were analyzed by two-way ANOVA, Kaplan-Meier, and Mantel-Cox post hoc tests. Finite element analysis (FEA) and fractographic analyses were performed. The fatigue performance of LD and RC occlusal veneers was evaluated based on different prosthetic preparation cusp inclinations. The 0° inclination showed the best fatigue performance for both materials (LD: 944N, RC: 861N), while the 15° and 30° inclinations had lower values (LD: 800N and 533N, RC: 739N and 717N, respectively). The study also found that for a 0° inclination, LD occlusal veneers performed better than RC ones (LD: 944 N > RC: 861N), while for a 30° inclination, RC occlusal veneers had better fatigue performance than LD ones (LD: 533N < RC: 717N). No significant difference was observed between the materials for a 15° inclination (LD: 800N = RC: 739N). The FEA results showed a higher tensile stress concentration on lithium disilicate than on resin composite occlusal veneers. All lithium disilicate occlusal veneers showed radial crack failures, while resin composite occlusal veneers showed Hertzian cone cracks and radial cracks combined. Considering mechanical perspective only, RC occlusal veneers should be indicated when prosthetic preparation cusps inclinations are 30°. When 0° prosthetic preparation cusps inclinations are observed, LD occlusal veneers will behave mechanically better. When a 15° cusp inclination is preserved, both restorative materials behave similarly.

PREVALENCE OF TWO VARIANTS OF MANDIBULAR SECOND PREMOLAR AT A TERTIARY CARE CENTER OF NEPAL

Background: Mandibular second premolar has two different types depending on the number of cusp present and each type has different groove patterns. There is difference in opinion regarding the influence on ethnicity in tooth morphology. This study aimed to determine the frequency of different type traits of mandibular second premolar in Nepalese population. Methods: A descriptive cross-sectional study was carried out in the Department of Oral and Maxillofacial Pathology, Dhulikhel Hospital, Kavre from December 2022 to February 2023. A total of 418 participants were included in the study. Mandibular second premolars of both right and left sides were examined and number of cusps and groove patterns were noted. The data were entered in Microsoft Excel Sheet and descriptive statistical analysis were done using SPSS version 23. Results: The frequency of two cusp type and three cusps type mandibular second premolar was noted to be 67% and 33% respectively. The predominant groove pattern in two cusp variant was H type in both males (32.8%) and females (38.1%). All the three-cusp variant showed Y shape groove in both males and females. Conclusions: The frequency of different types of mandibular second premolar varies depending upon the population. Two cusps type mandibular second premolar with H shape occlusal groove is more common than three cusp type in Nepalese subjects.

Bifurcations driven by generalist and specialist predation: mathematical interpretation of Fennoscandia phenomenon.

In this paper, we revisit a predator-prey model with specialist and generalist predators proposed by Hanski et al. (J Anim Ecol 60:353-367, 1991) , where the density of generalist predators is assumed to be a constant. It is shown that the model admits a nilpotent cusp of codimension 4 or a nilpotent focus of codimension 3 for different parameter values. As the parameters vary, the model can undergo cusp type (or focus type) degenerate Bogdanov-Takens bifurcations of codimension 4 (or 3). Our results indicate that generalist predation can induce more complex dynamical behaviors and bifurcation phenomena, such as three small-amplitude limit cycles enclosing one equilibrium, one or two large-amplitude limit cycles enclosing one or three equilibria, three limit cycles appearing in a Hopf bifurcation of codimension 3 and dying in a homoclinic bifurcation of codimension 3. In addition, we show that generalist predation stabilizes the limit cycle driven by specialist predators to a stable equilibrium, which clearly explains the famous Fennoscandia phenomenon.

Bifurcation analysis of an SIR model considering hospital resources and vaccination

In this paper, an SIR epidemic model considering hospital resources and vaccination is established and the rich dynamics and complex bifurcations are investigated. Firstly, the existence of disease-free equilibrium and endemic equilibria is explored. It is founded that when the vaccination rate is not high, the number of endemic equilibrium points changed easily with the number of hospital resources and vaccination, resulting in transcritical bifurcation and saddle–node bifurcations. Secondly, different types singularities such as degenerate saddle–node of codimension 1 at the disease-free equilibrium, and cusp or focus type Bogdanov–Takens singularities of codimension 3 at endemic equilibria are presented. Thirdly, bifurcation analysis at these equilibria is investigated, and it is found that the system undergoes a sequence of bifurcations, including Hopf, degenerate Hopf bifurcation, homoclinic bifurcation, the cusp type Bogdanov–Takens bifurcation of codimension 2, and the focus type Bogdanov–Takens bifurcation of codimension 3 which are the organizing centers for a series of bifurcations with lower codimension. And the system shows very rich dynamics such as the existence of multiple coexistent periodic orbits, homoclinic loops. Finally, numerical simulations are presented to verify the theoretical results.

A Bayesian constitutive model selection framework for biaxial mechanical testing of planar soft tissues: Application to porcine aortic valves

A variety of constitutive models have been developed for soft tissue mechanics. However, there is no established criterion to select a suitable model for a specific application. Although the model that best fits the experimental data can be deemed the most suitable model, this practice often can be insufficient given the inter-sample variability of experimental observations. Herein, we present a Bayesian approach to calculate the relative probabilities of constitutive models based on biaxial mechanical testing of tissue samples. Forty-six samples of porcine aortic valve tissue were tested using a biaxial stretching setup. For each sample, seven ratios of stresses along and perpendicular to the fiber direction were applied. The probabilities of eight invariant-based constitutive models were calculated based on the experimental data using the proposed model selection framework. The calculated probabilities showed that, out of the considered models and based on the information available through the utilized experimental dataset, the May–Newman model was the most probable model for the porcine aortic valve data. When the samples were further grouped into different cusp types, the May–Newman model remained the most probable for the left- and right-coronary cusps, whereas for non-coronary cusps two models were found to be equally probable: the Lee–Sacks model and the May–Newman model. This difference between cusp types was found to be associated with the first principal component analysis (PCA) mode, where this mode’s amplitudes of the non-coronary and right-coronary cusps were found to be significantly different. Our results show that a PCA-based statistical model can capture significant variations in the mechanical properties of soft tissues. The presented framework is applicable to other tissue types, and has the potential to provide a structured and rational way of making simulations population-based.

Regular black holes, universes without singularities, and phantom-scalar field transitions

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a nonsingular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. In this case, the potential of the scalar field has a nonanalyticity of the cusp type. This result is also readily reproduced in the case of an anisotropic Bianchi I universe. We have also found a spherically symmetric static solution of the Einstein equations, free of singularities and sustained by a scalar field.

On mappings of finite distortion that are quasiconformal in the unit disk

We study quasiconformal mappings of the unit disk that have homeomorphic planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the inverse map, which somewhat surprisingly is almost as good as for global quasiconformal maps. Furthermore, we give examples which improve the known bounds for the three point property of generalized quasidisks. Finally, we establish optimal regularity of such maps when the image of the unit disk has cusp type singularities.

898 ROLE OF 3D ECHOCARDIOGRAPHY IN AORTIC VALVE ABNORMALITIES: TWO CASES REPORT

Abstract Introduction Aortic valves with a number of cusps different from two or three are infrequent congenital anomalies that might manifest with valvular disease in young patients. We present two cases of unicuspid and quadricuspid aortic valve diagnosed in our Center. Clinical Cases Case 1. A 23-year-old asymptomatic male was admitted to our Hospital because of the necessity of bone marrow transplantation for Hodgkin lymphoma. He had a previous diagnosis of bicuspid aortic valve and presented a 5/6 mid-systolic harsh murmur, heard best at the right upper sternal border and radiating to the neck. ECG showed sinus rhythm with left ventricular hypertrophy. BNP was in normal range (31 pg/ml). At trans-thoracic echocardiography, there was severe aortic stenosis [peak/mean gradient of 100/67 mmHg with an aortic valve area of 1.04 cm2 (0.54 cm2/m2); V max was 5 m/s] without regurgitation and dilation of the ascending aorta (39 mm), however the morphology of the aortic valve remained undefined. Left ventricle showed hypertrophy (maximum wall thickness = 13 mm) with normal volumes and systolic function. Thus, the patient underwent to 3D-Transesophageal echocardiography, which demonstrated unicuspid aortic valve with a lone commissure between L-NC and anterior calcification. After multidisciplinary discussion, the patient underwent close follow-up and aortic valve replacement was planned after the bone marrow transplantation. Case 2. A 21-year-old male was referred by general practitioner to our outpatient clinic for palpitations. Cardiovascular physical examination and ECG were normal with no evidence of arrhyhtmia or cardiac murmurs. Transthoracic echocardiography revealed central mild aortic valve regurgitation in a suspected quadricuspid aortic valve (i.e., an X-shaped commissure pattern during diastole and a rectangular appearance during systole in the parasternal short-axis view). Left ventricular size and function and ascending aorta dimensions were normal. There was no associated congenital cardiovascular abnormality. 3D-Transesophageal echocardiography confirmed the evidence of a quadricuspid aortic valve. The cusps appeared to be of different size: two equal larger cusps and two equal smaller cusps (Type C, Hurwitz and Robert's classification), thin and mobile. The patient was advised to echocardiographic follow-up at intervals of 12 months. Conclusions We describe two cases of aortic valve congenital anomalies in two coetaneous patients with completely different impacts on hemodynamics. Severe aortic stenosis complicated unicuspid aortic valve whereas quadricuspid aortic valve was associated with mild aortic regurgitation. 3D-Transesophageal echocardiography was essential for accurate morphological characterization of the aortic valves.

On the regularity and symmetry of periodic traveling solutions to weakly dispersive equations with cubic nonlinearity

We consider the a priori regularity and symmetry of periodic traveling wave solutions to a class of weakly dispersive equations with cubic nonlinearity. We prove that any continuous periodic traveling wave solution of small amplitude is symmetric if it satisfies the reflection criterion proposed recently by Bruell and Pei. Moreover, we confirm that continuous periodic traveling waves with singular crests or troughs, which correspond to large‐amplitude waves, are also symmetric if some cancellation structure appears near the singular points or if the wave profile has only a single singular point per period. Included in the results as particular cases are periodic traveling waves with peak, cusp, or stump type singular structures. The argument and results also apply to dispersive equations with more general nonlinearity which is non‐smooth.

Multiple bifurcations in a predator–prey system of modified Holling and Leslie type with double Allee effect and nonlinear harvesting

In this paper, a modified Leslie-type predator–prey model with simplified Holling type IV functional response is established, in which double Allee effect on prey and nonlinear prey harvesting are considered. The analysis of the model shows that there exists a Bogdanov–Takens singularity (focus case) of codimension 4, and also multiple other nonhyperbolic and degenerate equilibria. Bifurcations are explored and it is found that transcritical bifurcation, saddle–node bifurcation, Bogdanov–Takens bifurcation of codimension 2, degenerate cusp type Bogdanov–Takens bifurcation of codimension 3, and degenerate focus type Bogdanov–Takens bifurcation of codimension 4 occur as parameters vary. The bifurcations result in complex dynamic behaviors, such as double limit cycle, triple limit cycle, quadruple limit cycle, cuspidal loop, (multiple) homoclinic loop, saddle–node loop, and limit cycle(s) simultaneously with homoclinic loop. We run numerical simulations to verify the theoretical results, and it is found that the system admits bistability, tristability, or even tetrastability.

Wave focusing by submerged islands and gravitational analogues

We study water waves propagating over a smooth obstacle in a fluid of varying depth, motivated by the observation that submerged islands in the ocean act as effective lenses that increase the amplitude and destructive power of tsunami waves near focal points. We show that islands of substantial height (compared to the water depth) lead to strong focusing in their immediate vicinity, and generate caustics of either cusp or butterfly type. We highlight similarities and differences with focusing of (high-frequency) gravitational waves by a neutron star. In the linear regime, the comparison is made precise through an effective-spacetime description of the island-fluid system. This description is then put to practical use: We identify caustics by solving the Raychaudhuri equation (a transport equation) along rays of the effective metric. Next, the island-fluid scattering processes are examined in detail (i.e., deflection angle, phase shifts, scattering amplitudes) using numerical simulations and analytical techniques, including the eikonal approximation and its generalisation in the form of the Gaussian beam approximation. We show that the techniques capture the key features of the simulations. Finally, we extend the eikonal approximation to the dispersive regime, demonstrating that the essential features are robust in dispersive settings. This paves the way for future exploration in a controlled laboratory set-up.

Cusp types of quotients of hyperbolic knot complements

This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, S 2 ( 2 , 4 , 4 ) S^2(2,4,4) cannot be the cusp cross-section of any orbifold quotient of a hyperbolic knot complement. Furthermore, if a knot complement covers an orbifold with a S 2 ( 2 , 3 , 6 ) S^2(2,3,6) cusp, it also covers an orbifold with a S 2 ( 3 , 3 , 3 ) S^2(3,3,3) cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.

P161 INCIDENTAL FINDING OF QUADRICUSPID AORTIC VALVE IN A YOUNG ASYMPTOMATIC PATIENT

Abstract Background Quadricuspid aortic valve (QAV) is a rare congenital heart disease, eventually leading to aortic regurgitation (AR) and heart failure. In up to one–third of patients, QAV is associated with other coexisting cardiac defects, particularly aortic dilation and coronary arteries abnormalities. Case Report A 48–years old man without significant past medical history was referred to the Cardiologist for newly diagnosed arterial hypertension. The patient was asymptomatic and no abnormal findings were noticed on physical examination. Transthoracic echocardiography showed normal end–diastolic volume and diameter of the left ventricle and preserved systolic function. However, a mild dilation of the aortic root (40 mm) and ascending aorta (38 mm) with concomitant moderate–to–severe AR were described. Transoesophageal echocardiogram (TOE) was performed to better visualize the aortic valve anatomy and to define the exact mechanism of the AR. 2D–TOE revealed a QAV with equal–sized cusps (type A according to the Hurwitz–Roberts classification), with a central quadrangular coaptation defect and a moderate AR (vena contracta width: 4 mm) [Fig. 1–2]. The regurgitant jet conditioned a pseudo–prolapse of anterior mitral leaflet with consequent mild–to–moderate mitral regurgitation. 3D–TOE allowed a better characterization of valve morphology and the individuation of the sole left coronary artery ostium. A coronary artery computed tomography was requested to investigate a probable abnormal origin of the right coronary artery. The patients was subsequently addressed to a regular clinic and echocardiographic follow–up for the surveillance of AR and aortic dimensions and a prompt management of an eventual symptoms onset. Discussion We describe a rare case of type A QAV with moderate AR, mild dilation of aortic root and ascending aorta and suspected anomalous origin of the right coronary ostium. The broad diffusion of imaging techniques has recently led to an increase of incidental diagnosis, even in asymptomatic patients. The complex valve anatomy, with many possible morphologies of the supernumerary cusp, and the association with other congenital defects, particularly anomalous coronary ostia location, pose many technical issues in case of valve replacement. A multimodality imaging approach is essential for a clear description of valve morphology and coronary anatomy to avoid intraoperative complications in both surgical and percutaneous valve replacement procedures.

Effects of axial magnetic field in a magnetic multipole line cusp ion source

Experiments have been performed to study the effects of axial magnetic field on plasma and ion beam parameters in a magnetic multipole line cusp ion source. Studies performed on ring cusp and Kaufmann type ion sources suggest that the axial component of magnetic field may help in improving the ion extraction current at a low discharge power. The line cusps ion sources have been used since long to produced uniform beams, however, they lack axial component of the magnetic field. These ion sources generally suffer from low efficiency possibly due the absence of axial magnetic field. In this work, an additional magnetic coil is added at various axial positions between the back-plate and the plasma grid of the multipole line cusp ion source. We have investigated the effects of axial magnetic field on the discharge efficiency and source parameters like beam current and uniformity in the multipole line cusp ion source. The beam profiles are obtained using an eleven-channel faraday cup array to estimate the effects of the axial magnetic field on beam uniformity and divergence. Initial studies suggest a reduction of beam divergence with increasing axial magnetic field. A significant rise in the beam current and the discharge current is also observed when the axial magnetic field is increased. Particle trajectory simulation using the CST-Studio suite is utilised in understanding the role of confinement of primary electrons behind the improved performance of the ion source.

Cardiac magnetic resonance to asess aortic valve anatomy in doubtful cases. Case series from a cardiology clinic

Funding AcknowledgementsType of funding sources: None.IntroductionBicuspid aortic valve (BAV) is the most common congenital cardiac malformation, affecting 1-2% of the population, and several types have been described, each one with different prevalence. Partial raphae have also been described and much rarer congenital affectations of aortic valve also exist (unicuspid, quadricuspid), with its own classification. Although echocardiogram is usually enough for diagnosis, sometimes other exams are needed to assess the anatomy of the valve. In these cases, due to lack of radiation, Magnetic Resonance (MRI) can be performed.MethodsWe reviewed cases from a single general cardiology clinic in which MRI was needed for asses aortic valve anatomy during a period of 9 non-consecutive (due to Covid-19 pandemic) months, Characteristics of the patients, as well as valvular and aortic characteristics, were reported.ResultsThere 8 doubtful cases. 5 men. Mean Age 60 years old (range 21-77, 6 patients 58 or more). 6 cases were non-tricuspid aortic valve: 5 bicuspid, 1 quadricuspid. Except in rare anatomies (bicuspid with 2 cusps type lateral and quadricuspid), with age 21 and 38 respectively (both men), the mean age was 70, ranging from 58 to 77, with 3 cases (50%) women. Except 2 cases, MRI was performed after the first visit, without follow-up time. Taking into account all patients, mean time from first visit to perform MRI was 1,12 years (maximum 6 years in the quadricuspid case). 6 cases had valvular functional anomalies greater than mild (3 women). 5 cases presented aortic dilatation (3 men), 1 man without valvular functional anomalies, 1 woman with tricuspid aortic valve. BAV with 2 cusps type lateral and quadricuspid cases had no aortic dilatation. There were no extracardiac findings in the exams. Figure shows characteristics of patients. Figure 2 shows images from exams (in the superior left and inferior right part of the image are shown BAV with 2 cusps and quadricuspid valve repectively, in diastole and systole).ConclusionsClinicians usually think BAV is a problem of young people, but can be even diagnosed in the eighth decade of life. In these cases, senile changes with valvular degeneration make diagnosis more challenging with doubtful cases. Rare anatomies may be also challenging. MRI seems useful to assess doubtful cases. Although usually performed in the first visit, in some cases it can take years before MRI is performed. In older cases, there may be no sex predominance for BAV. Table: Characteristics of patients Figure. Images from exams

Equilibria and Bogdanov‐Takens Bifurcation Analysis in the Bazykin’s Predator‐Prey System

In the paper, we proposed a Bazykin’s predator‐prey system to explore the equilibrium point and Bogdanov‐Takens bifurcation problems. Firstly, we derived some key parameter threshold conditions to ensure that the Bazykin’s predator‐prey system had a multiple focus of multiplicity one, weak focus of order 2, cusps of codimension 2 and a degenerate Bogdanov‐Takens singularity (focus or center case) of codimension 3. Furthermore, the distinction of two types of codimension 2 cusps was also discussed, which showed that the threshold of the two types of cusps could exhibit a cusp, which was a special case of the mentioned degenerate Bogdanov‐Takens singularity (focus or center case) of codimension 3. Secondly, we systematically calculated that the Bazykin’s predator‐prey system could undergo two types of Bogdanov‐Takens bifurcations of codimension 2 and a degenerate focus type Bogdanov‐Takens bifurcation of codimension 3. Finally, some numerical examples were implemented to verify the correctness and feasibility of mathematical theory derivation, which also directly showed all possible equilibrium points and Bogdanov‐Takens bifurcations of Bazykin’s predator‐prey system. In a word, all the research results could play an important theoretical support role in the study of controlling cyanobacteria bloom.