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We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death, and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

Most planning studies used traditional methods for differentiation and evaluation between alternatives and proposals for decision-making and determining the best alternative. One of the disadvantages of these methods is their significant reliance on subjectivity and linear evaluation to compare alternatives and the weak importance of measuring other effects between and within alternatives. It also involves costs, time, and effort to make the most accurate decision. This research attempts to highlight the importance of one of the computer methods used to compare alternatives and identify the best, especially in the transport sector, by applying the Analytic Network Process ANP method using the super decision software SDS. It is characterized by an organized and analytical method to address a wide range of factors rather than relying on intuition to assess the unperceived factors. This is making it a tool to support the decision-making process of complex situations, through the existence of interrelated relationships between elements within a network system. To implement the SDS as an application in the field of transportation, the research suggested three alternatives to construct parking in the Baghdad city center. With a set of primary and secondary criteria, by creating a decision-making structure to extract the relative weights of criteria and priority, thus choosing the best alternative. After the implementation, the software, one of the alternatives, was selected and demonstrated the importance of this application in transport sector studies in particular and planning in general.

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide (https://github.com/nfadai/Fadai_Allee2019) simulation tools for others to repeat this analysis.

Objective: This study aimed to investigate the protective role of licorice on indomethacin-induced gastric ulcer in male albino rats compared to anti-ulcer drug; ranitidine. Methods: Fifty male adult rats were randomly allocated into five groups (10 rats/each); control, licorice, indomethacin, licorice/indomethacin, and ranitidine/indomethacin treated groups. Serum, gastric juice, and gastric tissues were collected for biochemical and histopathological analysis. Results: The obtained results revealed that licorice pre-treatment showed potent anti-ulcerative effect as; volume and total acidity of gastric secretion were markedly decreased, attenuated the severity of gastric lesion as confirmed by PM and histopathological examination showed preservation of gastric epithelium and ulcer healing. Moreover, gastric ulcer score, gastric MDA, and serum IL-6 were obviously decreased along with increased gastric GSH, CAT activity and NO. Interestingly licorice had no side effects on the liver and kidney evidenced by increased serum total protein, and albumin besides declined the activities of serum aminotransferases without significant changes in the serum urea, uric acid, sodium, potassium, and chloride levels. Conclusion: It was concluded that the used dose of licorice showed potent anti-ulcerative activity and more safer on the liver and kidney functions compared to the standard commercial drug; ranitidine.

Two-dimensional hydromagnetic flow of an incompressible Williamson nanofluid over a stretching sheet in a porous media is examined during this work. Convective heat and mass transfer in the presence of Dufour, Soret, radiation absorption, heat generation, viscous dissipation, chemical reaction, Brownain motion and thermophoresis effects are taken in consideration. The system of partial differential equations which describe the momentum, energy and nanofluid solid volume fraction equations of the fluid is transformed to an ordinary differential equations by using the suitable transformations. Then these equations have been solved numerically using Runge–Kutta method of order four with shooting technique. The effects of various physical parameters on dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and local Sherwood numbers are analyzed and presented graphically.

The problem of laminar nano non-Newtonian fluid through the boundary layer, which results from the stretching of a flat surface, has been investigated. The model of Eyring–Powell is used for the fluid. Constant normal magnetic field, mixed convection, chemical reaction, viscous dissipation, ohmic dissipation, Brownian and thermophoresis effects are considered. The problem is modulated mathematically by a system of partial differential equations, which describe the motion. A similarity solution is presented to transform this system to ordinary non-linear differential equations. The numerical solutions of these equations are obtained as functions of the physical parameters of the problem. Such as, Brownian number Nb, thermophoresis number Nt, Lewis number Le, Prandtl number Pr, Magnetic parameter M and Elastic parameter β. Graphical evaluation is displayed to depict the intrinsic behavior of embedded parameters on velocity, temperature, and nanoparticle concentration profiles.

In this work, the peristaltic motion of a Williamson nanofluid through a non-Darcy porous medium inside an asymmetric channel is investigated. The Hall current, viscous dissipation and Joule heating are considered. The problem is modulated mathematically by a set of nonlinear partial differential equations which describe the conservation of mass, momentum, energy and concentration of nanoparticles. The non-dimensional form of these equations is simplified under the assumption of long wavelength and low Reynolds number. Then, resulting equations of coupled nonlinear differential equations are then tackled numerically with appropriate boundary conditions by using NDSolve technique. Graphical results are presented for dimensionless velocity, temperature and concentration in order to illustrate the variations of various parameters of this problem on these obtained solutions.

Steady two-dimensional motion of an incompressible non-Newtonian Nanofluid through porous medium over a semi-infinite moving plate is studied . The system is stressed by an external uniform magnetic field. The heat and mass transfer are considered with the flow of non-Newtonian fluid which obeys the Eyring–Powell model. The problem is mathematically formulated and solved numerically using the ParametricNDSolve-Mathematica package. The effects of the physical parameters of the problem such as, permeability, chemical reaction as well as the fluid material parameters Hartmann number, Eckert number and Reynolds number are discussed and illustrated in figures with some important applications. The results show that the fluid velocity increases with the increases of porosity parameter as well as the material parameter, but it decreases with the increase of the magnetic field. Increasing the magnetic field decreases porosity, temperature and concentration. The effects of some physical quantities on fluid velocity distribution can be neglected.

The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The blood is considered as the base Carreau non-Newtonian fluid and gold (Au) as nanoparticles stressed upon. The Fronchiener effect of the non-Darcian medium is taken in consideration. The system is stressed upon a strong magnetic field and the Hall currents are completed. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the fluid velocity, temperature and concentration. The system is reformulated under the approximation of long wavelength and low Reynolds number. It is solved on using multi-step differential transform method (Ms-DTM) as a semi-analytical method. A gold nanoparticle has increased the temperature distribution which is of great importance in destroying the cancer cells.

Recent modelling of coffee bean roasting suggests that in the early stages of roasting, within each coffee bean, there are two emergent regions: a dried outer region and a saturated interior region. The two regions are separated by a transition layer (or, drying front). In this paper, we consider the asymptotic analysis of a recent multiphase model in order to gain a better understanding of its salient features. The model consists of a PDE system governing the thermal, moisture, and gas pressure profiles throughout the interior of the bean. By obtaining asymptotic expansions for these quantities in relevant limits of the physical parameters, we are able to determine the qualitative behaviour of the outer and interior regions, as well as the dynamics of the drying front. Although a number of simplifications and scalings are used, we take care not to discard aspects of the model which are fundamental to the roasting process. Indeed, we find that for all of the asymptotic limits considered, our approximate solutions faithfully reproduce the qualitative features evident from numerical simulations of the full model. From these asymptotic results, we have a better qualitative understanding of the drying front (which is hard to resolve precisely in numerical simulations), and hence, of the various mechanisms at play including heating, evaporation, and pressure changes. This qualitative understanding of solutions to the multiphase model is essential when creating more involved models that incorporate chemical reactions and solid mechanics effects.

The present analysis discusses the effects of thermal-diffusion with thermal radiation, Joule heating and internal heat generation on peristaltic flow of a non-Newtonian fluid obeying Jeffery model. Heat and mass transfer are also taken into consideration, the flow is between two co-axial tubes under the effect of radially varying magnetic field. The inner tube is uniform and at rest, while the outer tube is flexible with sinusoidal wave traveling. The problem is modulated mathematically by a system of partial differential equations which describes the equations of momentum, heat, and mass transfer. These equations are solved analytically under the assumptions of long wave length and low-Reynolds number in non-dimensional form. The solutions are obtained as a functions of physical parameters of the problem. The radially varying magnetic field effect on the temperature and concentration distributions is analyzed and it is shown that the increase of Hartman number tends to reduce the temperature, while it increases the concentration.

The motion of a nano-Casson fluid with heat and mass transfer over a semi-infinite flat plate under the effect of a uniform magnetic field through porous medium is investigated. The Ohmic heating and viscous dissipation with chemical reaction are also considered. The problem is formulated mathematically by a system of non-linear partial differential equations (PDEs). Suitable similarity transformations are used to transform this system to non-linear ordinary differential equations (ODEs) in dimensionless form and solved numerically. The effect of the physical quantities of the problem, such as, permeability parameter, Casson parameter, chemical reaction parameter, Eckert parameter a well as Reynolds number and Hartmann number on the fluid behavior are discussed and illustrated graphically.

We study the spectrum of a new class of nonlocal eigenvalue problems (NLEPs) that characterize the linear stability properties of localized spike solutions to the singularly perturbed two-component Gierer-Meinhardt (GM) reaction-diffusion (RD) system with a fixed time-delay \begin{document}$T$\end{document} in only the nonlinear autocatalytic activator kinetics. Our analysis of this model is motivated by the computational study of Seirin Lee et al. [Bull. Math. Bio., 72(8), (2010)] on the effect of gene expression time delays on spatial patterning for both the GM and some related RD models. For various limiting forms of the GM model, we show from a numerical study of the associated NLEP, together with an analytical scaling law analysis valid for large delay \begin{document}$T$\end{document} , that a time-delay in only the activator kinetics is stabilizing in the sense that there is a wider region of parameter space where the spike solution is linearly stable than when there is no time delay. This enhanced stability behavior with a delayed activator kinetics is in marked contrast to the de-stabilizing effect on spike solutions of having a time-delay in both the activator and inhibitor kinetics. Numerical results computed from the RD system with delayed activator kinetics are used to validate the theory for the 1-D case.

In this contribution, the MHD pulsatile mechanism with heat transfer of an incompressible non-Newtonian nanofluid between two permeable parallel vertical plates is investigated. The effects of non-Darcy porous medium, radiation, Ohmic and viscous dissipation are included. By using the homotopy perturbation method, a solution is obtained, which is in a good agreement with the momentum, energy and nanoparticles equations. Numerical results for the velocity, temperature and nanoparticles distributions are obtained. Keywords: Pulsatile flow, Non-Newtonian nanofluid, Non-Darcy porous medium, Heat transfer, 76: Fluid mechanics, 34: Ordinary differential equations, 80: Classical thermodynamics, Heat transfer

Objectives: To report the prevalence and types of biopsied oral and maxillofacial lesions (OMLs) in South-Western (Jazan Province) region, , Kingdom of Saudi Arabia (KSA). Methods: This retrospective study was based on the retrieval of clinicopathological data for a period of 6 years between January 2009 and December 2014. These data were obtained between October 2014 and June 2015 from the histopathology records of King Fahad Central Hospital, Jazan, KSA, which is the only referral center for biopsy services. Results: Out of the 32149 biopsies received, 714 (2.2%) were OMLs. The age ranged from 0 (neonatal) to 100 years, with a mean age of 46.8±23.4 and a male-to-female ratio of 1:1.3. The tongue was the most common site for OMLs and for malignant neoplasms, in particular. The most common category was malignant neoplasm (38.7%), followed by inflammatory lesions (16.5%). Oral malignancies accounted for 15.8% of all malignancies. Oral squamous cell carcinoma (OSCC) (36.1%) was the most frequent type, followed by pyogenic granuloma and mucocele (7% each). Shammah-associated OSCC and epithelial dysplasia were twice as common in females. Conclusion: The number of non-malignant OMLs was much lower than expected in comparison to oral malignancies. This difference can likely be explained by the fact that the biopsies were taken only when malignancy was suspected. The higher rate of OSCC reported from this region is attributed to shammah usage. This study emphasizes the importance of biopsy services for all OMLs and the prevention of shammah use. Saudi Med J 2017; Vol. 38 (4): 405-412 doi: 10.15537/smj.2017.4.18760 How to cite this article: Saleh SM, Idris AM, Vani NV, Tubaigy FM, Alharbi FA, Sharwani AA, et al. Retrospective analysis of biopsied oral and maxillofacial lesions in South-Western Saudi Arabia. Saudi Med J. 2017 Apr;38(4):405-412. doi: 10.15537/smj.2017.4.18760.

A linear stability analysis of localized spike solutions to the singularly perturbed two-component Gierer--Meinhardt (GM) reaction-diffusion (RD) system with a fixed time delay $T$ in the nonlinear reaction kinetics is performed. Our analysis of this model is motivated by the computational study of Lee, Gaffney, and Monk [Bull. Math. Bio., 72 (2010), pp. 2139--2160] on the effect of gene expression time delays on spatial patterning for both the GM model and some related RD models. It is shown that the linear stability properties of such localized spike solutions are characterized by the discrete spectra of certain nonlocal eigenvalue problems (NLEP). Phase diagrams consisting of regions in parameter space where the steady-state spike solution is linearly stable are determined for various limiting forms of the GM model in both 1-dimensional and 2-dimensional domains. On the boundary of the region of stability, the spike solution is found to undergo a Hopf bifurcation. For a special range of exponents in the nonlinearities for the 1-dimensional GM model, and assuming that the time delay only occurs in the inhibitor kinetics, this Hopf bifurcation boundary is readily determined analytically. For this special range of exponents, the challenging problem of locating the discrete spectrum of the NLEP is reduced to the much simpler problem of locating the roots to a simple transcendental equation in the eigenvalue parameter. By using a hybrid analytical-numerical method, based on a parametrization of the NLEP, it is shown that qualitatively similar phase diagrams occur for general GM exponent sets and for the more biologically relevant case where the time delay occurs in both the activator and inhibitor kinetics. Overall, our results show that there is a critical value $T_{\star}$ of the delay for which the spike solution is unconditionally unstable for $T>T_{*}$, and that the parameter region where linear stability is assured is, in general, rather limited. A comparison of the theory with full numerical results computed from the RD system with delayed reaction kinetics for a particular parameter set suggests that the Hopf bifurcation can be subcritical, leading to a global breakdown of a robust spatial patterning mechanism.