Comment on "correlated noise in a logistic growth model"

We argue the results published by Bao-Quan Ai et al [Phys. Rev E 67, 022903 (2003)] on "correlated noise in a logistic growth model " are not correct. Their conclusion that for larger values of the correlation parameter, lambda, the cell population is peaked at x=0, which denotes the high extinction rate is also incorrect. We find the reverse behaviour corresponding to their results, that increasing lambda, promotes the stable growth of tumour cells. In particular, their results for steady-state probability, as a function of cell number, at different correlation strengths, presented in figures 1 and 2 show different behaviour than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation at small values of cell number that the steady state probability increases as they increase the correlation parameter is also questionable. Another striking feature in their figures (1 and 3) is that for the same values of the parameter lambda and alpha, their simulation produces two different curves both qualitatively and quantitatively.

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

The influence of transforming growth factor-beta1 gene polymorphisms on the severity of gingival overgrowth associated with concomitant use of cyclosporin A and a calcium channel blocker

The purpose of this study was to determine whether the prevalence and severity of gingival overgrowth in renal transplant recipients concomitantly treated with cyclosporin and a calcium channel blocker was associated with functional polymorphisms within the signal sequence of the transforming growth factor-(TGF)beta1 gene.

Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise oil the Gompertzian growth of tumours. Our results are obtained by Solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In Our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under Study. We perform simulations to analyze various aspects, of the probability distribution. of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (tau) to the steady-state distribution as a function of (i) of the correlation strength (lambda) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (alpha). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.

Collapse versus growth for a Bose-Einstein condensate with attractive interactions

Using a model potential approach, we study the time-dependent behavior of a Bose-Einstein condensate with negative scattering length during its collapse in the zero-temperature limit. The condensate is modeled through an effective potential, which linearizes the Schrodinger equation, in order to obtain an intuitive visualization of the dynamics of the condensate. We find that a substantial fraction of the condensate survives the collapse. The origin for this survival is the reappearance of a barrier in the effective potential during the collapse. In contrast to previous calculations, the present calculations indicate that the size of the residual condensate strongly depends on the growth rate of the condensate. The present results are compared to other theoretical calculations and to experimental work.

Retinal pigment epithelial atrophy in patients with exudative age-related macular degeneration undergoing anti-vascular endothelial growth factor therapy

PURPOSE:: To evaluate the occurrence of retinal pigment epithelial atrophy in patients with age-related macular degeneration undergoing anti-vascular endothelial growth factor therapy. METHODS:: The study is a retrospective review. Eligible were patients with age-related macular degeneration and choroidal neovascular membranes treated with anti-vascular endothelial growth factor between October 2007 and February 2011; they were followed for >3 months, with fundus photographs and fluorescein angiography at baseline and with autofluorescence and near-infrared autofluorescence images at baseline and follow-up. Demographics, visual acuity, the type of choroidal neovascular membranes, the number of treatments performed, and the length of follow-up were recorded. Autofluorescence and near-infrared autofluorescence images were evaluated for the presence or absence of areas of reduced signal. A multilevel logistic regression model was used to investigate the factors that may be associated with progression of atrophy at follow-up, which was the primary outcome of this study. RESULTS:: Sixty-three patients (72 eyes) were followed for a median of 16 months (range, 3-36 months). Atrophy at baseline was observed in 47% (34/72) of eyes; progression of atrophy occurred in 62% (45/72) of eyes at the last visit. The number of anti-vascular endothelial growth factor injections received was statistically significantly associated with the progression of atrophy at follow-up (odds ratio, 1.35; 95% confidence interval, 1.05-1.73; P = 0.02). CONCLUSION:: Atrophy was frequently observed in patients with age-related macular degeneration and choroidal neovascular membranes undergoing anti-vascular endothelial growth factor therapy.