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In this work, we use the results of plant developmental biology (such as molecular biology of pattern formation and cell cycle progression) and of plant physiology to develop a mathematical model of plant growth. Trying to describe the most essential features of growth mechanisms, we do not model some particular plant organs but the entire plant though with many simplifications, in particular, without taking into account root growth, leave and flower formation, or the biochemistry of photosynthesis. [ABSTRACT FROM AUTHOR]

In this chapter we examine the accuracy and efficiency of the simplified PNapproximations of radiative transfer for natural convection problems in a square enclosure. A Boussinesq approximation of the Navier—Stokes equations is employed for the fluid subject to combined natural convection and radiation. Coupled with the simplified PNmodels, the system of equations results into a set of partial differential equations independent of the angle variable. Numerical results for different Rayleigh numbers are presented. [ABSTRACT FROM AUTHOR]

We discuss the direct use of cubic-matrix splines to obtain continuous approximations to the unique solution of matrix models of the type Y ″(x) = f (x, Y (x)). For numerical illustration, an estimation of the approximation error, an algorithm for its implementation, and an example are given. [ABSTRACT FROM AUTHOR]

Industrial mathematical models often involve uncertainties in the data problem.In this chapter a vector random Euler method is proposed for constructing discrete mean square approximating processes of initial value problems for random differential equations with uncertainties.Convergence conditions and an illustrative example are included. [ABSTRACT FROM AUTHOR]

In this chapter an efficient conservation element—solution element (CE— SE)to construct numerical solutions of time-dependent advection-diffusion equation initial value problems is presented.Stability conditions of the method are established intermsofdata. [ABSTRACT FROM AUTHOR]

Fingerprints are currently the leading approach to biometric recognition [1]. The reasons are multiple — we mention on the one hand the more than centennial tradition of fingerprint use for forensic purposes and on the other hand the existence of some well-established experience — based rules derived along the line. Fingerprints have a specific flow dynamics, which comes in quite distinct flow patterns — these help define classes of fingerprints. The flow pattern carries various singularities, named minutiae — most important are line endings and bifurcations. [ABSTRACT FROM AUTHOR]

The second-order MUSCL schemes are considered in the present work. A new limitation procedure is detailed to enforce relevant robustness properties. The scheme is thus shown to preserve the invariant domain. [ABSTRACT FROM AUTHOR]

We present in this communication an index-1 characterization for differential-algebraic circuit models without passivity assumptions. The use of treebased methods together with the Cauchy—Binet formula makes it possible to generalize previous results in the literature. The approach can be extended to modified node analysis (MNA) models and higher index configurations. [ABSTRACT FROM AUTHOR]

Recognition of control chart patterns (CCPs) is one of the most important technique for monitoring and achieving appropriate control of process environments to raise production quality. In the last 10 years several approaches have been proposed for precise and fast CCP recognition, including rule-based and expert systems, or artificial neural networks, and many efforts have been focused on comparative studies of approximate training algorithms. This chapter presents a new approach for the identification of control chart patterns by using features dynamically extracted from raw data. Our strategy has the further advantage of avoiding the use of complex data structures and training processes. [ABSTRACT FROM AUTHOR]

Multidimensional integrals arise in the bayesian approach to positioning using measurements from satellites, mobile phone networks, wireless data networks, etc. Measurement geometries and nongaussian measurement errors produce distinctive features such as multiple peaks and curved ridges. In this chapter compare several subregion adaptive simplicial cubature methods and a Monte Carlo method for typical positioning situations. We find that subregion adaptive methods give the best accuracy for the same number of samples in many two- and three-dimensional problems but that in four dimensions the dimensionality effect favors the Monte Carlo method. [ABSTRACT FROM AUTHOR]

A novel hierarchical approach based on decision diagrams (DD) to modelling digital systems is introduced. Two new contributions are proposed: a new classof structurally synthesized binary DDs for modelling structural aspects of digital circuits, and DDs for high-level modelling of systems. Combination of both types of graphs allows to implement uniform formal approach to low- and high-level diagnostic modelling with increased efficiency of fault simulation and test generation for digital systems. [ABSTRACT FROM AUTHOR]

We combine the Lagrangian and Eulerian models of linear diffusion phenomena in a coherent differential-geometric framework. This approach is applied to the diffusion—advection equation and its implications are discussed. [ABSTRACT FROM AUTHOR]

The finite pointset method is a meshless Lagrangian particle method. In the application to incompressible viscous fluid flow the solution of Poisson problems on the cloud of particles is a fundamental subproblem. A valuable property of finite difference approximations to the Laplace operator is the positivity of stencils, i.e., all weights of neighboring points are positive. Classical least squares approaches do not guarantee positive stencils. We present a new approach, based on linear minimization, which enforces positivity of stencils and additionally yields a minimal number of nonzero stencil entries. The resulting system matrices are M-matrices, which is of particular interest with respect to multigrid solvers. [ABSTRACT FROM AUTHOR]

In the context of offshore oil production, we are interested in accurate and fast computation of two-phase flows in pipelines. A one-dimensional model of hyperbolic equations is solved numerically by an explicit Lagrange-projection method. This chapter shows that adaptive multiresolution techniques can speed up the computation significantly. Even more so when local time-stepping enhancement is used. [ABSTRACT FROM AUTHOR]

Game Theory provides suitable tools to share the total utility among the economic agents or players when the possibilities of cooperation enable obtaining the utility of each group or coalition. The semivalues are solution concepts for situations of competence—cooperation that assign to each player a weighted sum of his/her marginal contributions to the coalitions, where the weights only depend on the coalition size. The Shapley value and the Banzhaf value are semivalues. The solutions introduced here are modifications of the semivalues when we consider a priori coalition blocks in the player set. A computation procedure is also offered. [ABSTRACT FROM AUTHOR]

The proportional rule has a long tradition in collective problems where some kind of utility (costs, profits, savings) is to be shared among the agents. However, while its (apparent) simplicity might be a reason for applying it in pure bargaining affairs, where only the whole and the individual utilities matter, it seems much more questionable in the case of general cooperative problems, where all marginal contributions should be taken into account. We will contrast the proportional rule with the Shapley value in this kind of problems. [ABSTRACT FROM AUTHOR]

Let the homogeneous of L degree function g(x) be defined in Ndimensional space, and let the function G(y) be its Fourier transform in the distribution sense. The theorem that allows to present the function G(y) using only the values of function g(x) on the unit sphere is proved in the chapter for the case L > −N. The case N=3 and L = −1 corresponds to the properties of beam transform in 3D space. In the chapter it is shown how the theorem may be used for creation of numerical algorithms for cone-beam tomography. Let the homogeneous of L degree function g(x) be defined in N-dimensional space, and let the function G(y) be its Fourier transform. In view of homogeneity, the function g(x) and its Fourier transform in sense of distributions are defined by their values on the unit sphere [GS00]. We will prove the theorem that allows to present the function G(y) using only the value of function g(x) on the unit sphere for the case L > −N. [ABSTRACT FROM AUTHOR]

Multiple sequential recurrences are one of the most important characteristics of superficial transitional cell carcinoma (TCC) of the bladder. Many investigations have been done to identify predictive factors for the first recurrence, but very few studies have investigated multiple recurrences of this cancer and its clinicopathologic factors associated. We consider counting process methods for analysing timeto-event data with recurrent outcomes using the models developed by Andersen and Gill and, Prentice, Williams, and Peterson. A postoperative nomogram is developed to predict recurrences based on those predictive factors. [ABSTRACT FROM AUTHOR]

We consider a contrast invariant approach to motion estimation which uses the direction of the gradient fields. The approach is region-based and assumes an affine motion model for each region. We propose to check if the estimated motion parameters fit properly the apparent motion of the region by a motion significance analysis. Moreover, we propose a motion field improvement which consider those regions that are not properly estimated according to the significance analysis and reassign them a motion model of a properly estimated neighboring region. [ABSTRACT FROM AUTHOR]

This work presents a method for the segmentation of breast nodules in ultrasonography. Speckle noise is reduced using an anisotropic filter for which texture is described using Gabor filters. Afterwards, an initial segmentation is extracted using a front propagation scheme. Finally, the initial segmentation is refined using active contours. In order to delimit the nodules not only by means of image intensity, but also by texture pattern, we introduce certain terms in the classical active contours equations. [ABSTRACT FROM AUTHOR]

Two mathematical models for an electrochemical biosensor are proposed and compared with a view to determining the ratio of two immobilized enzymes which maximizes the amperometric signal amplitude. [ABSTRACT FROM AUTHOR]

An isothermal single-phase 3D/1D model for liquid-feed direct methanol fuel cells (DMFC) is presented and validated against experimental results. 3D mass, momentum and species transport in the anode channel and gas diffusion layer is modelled using a commercial CFD code complemented with user supplied subroutines. The 3D model is locally coupled to a 1D model that imposes a physically sound boundary condition for the velocity and the methanol concentration field at the anode gas-diffusion-layer/catalyst-layer interface. The 1D model assumes non- Tafel kinetics to account for the complex kinetics of the (multi-step) methanol oxidation reaction at the anode, and includes the mixed potential induced by methanol crossover due to diffusion and electro-osmotic drag. Polarization curves obtained for various methanol feed concentrations, temperatures, and methanol feed velocities show good agreement with recent experimental results. [ABSTRACT FROM AUTHOR]

Primary Open Angle Glaucoma (POAG) is a major cause of blindness, affecting 65-70 million sufferers worldwide ([ERC04]). The eye produces aqueous humour (AH: a water-like substance secreted by the ciliary body) which flows behind the iris, through the pupil aperture, out into the anterior chamber (AC) and drains from the eye via the drainage angle. From the drainage angle the AH passes through a biological filter (the trabecular meshwork or TM) into the canal of Schlemm (SC), the main drainage route from the eye, and finally exhausts into "collector channels". POAG occurs when this drainage mechanism is somehow compromised [FW92]. Essentially the AH cannot be removed quickly enough and as a result the intraocular pressure (IOP) increases in the eye. Contrary to popular belief, glaucoma and elevated IOP are not synonymous. Though very often associated with elevated IOP, glaucoma is, in reality, an optic nerve neuropathy. Notwithstanding this, elevated IOP is always regarded as potentially harmful to the eye. In the current study we therefore seek to model the flow of AH from the AC through the TM and into the SC and to couple this flow to predictions of changes in IOP. [ABSTRACT FROM AUTHOR]

Indoor location systems using 802.11 standard, based on the comparison of the received and predicted levels of the received signals from the Access Points, are a very interesting research area. The location information is computed by searching the nearest neighbour of the measured signal strength within the radio map. In this chapter, we apply a global optimization algorithm to obtain the Access Points location distribution that yields the best performance of these location systems. [ABSTRACT FROM AUTHOR]

The goal of this chapter is to analyze a finite element method to solve the magnetostatic problem in terms of scalar potentials. Several FEM have been developed to solve the magnetostatic problem in the last decades, because of its application in engineering; see, for instance, [BAL96,MSP98,PAL91,ST79, ST80]. The main difference in the numerical methods lies in the choice of the primary unknowns (vector potential, magnetic field or scalar potentials). The published numerical results ([MSP98,PAL91]) show that the combination of two different potentials, the so called reduced scalar potential and total scalar potential, seems to be the most effective in terms of accuracy and computer cost. This formulation, was introduced by Simkin and Trowbridge in [ST79] and is very well known in the engineering literature; however, to the best of the author's knowledge, the approximation of this formulation in bounded domains by standard finite elements has not been analyzed from a mathematical point of view. This is the aim of the present chapter in the context of three-dimensional domains. [ABSTRACT FROM AUTHOR]

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented. [ABSTRACT FROM AUTHOR]