Abstract The thesis of Weak Unrestricted Composition says that every pair objects has a fusion. This been argued by Contessa (Analysis 72(3):455–457, 2012) and Smith (Erkenntnis 84(1):41–55, 2019) to be compatible with the world being junky hence evade an argument against necessity Strong proposed Bohn 69(1):27–31, 2009a, Philos Q 59(235):193–201, 2009b). However, neither alone nor different va...

This chapter describes the steps involved in registering images of different subjects into roughly the same co-ordinate system, where the co-ordinate system is defined by a template image (or series of images). The method only uses up to a few hundred parameters, so can only model global brain shape. It works by estimating the optimum coefficients for a set of bases, by minimizing the sum of sq...

Polynomials suffice as finite element basis functions for triangles, parallelograms, and some other elements of little practical importance. Rational basis functions extend the range of allowed elements to the much wider class of well-set algebraic elements, where well-set is a convexity type constraint. The extension field from R(x, y) to R(x, y, √ x2 + y2) removes this quadrilateral constrain...

The Hermite Radial Basis Functions (HRBF) Implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e., unstructured points and their corresponding normals). Experiments suggest that HRBF Implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or nonuniform sampling...

In this paper we propose a framework, called mixtures of truncated basis functions (MoTBFs), for representing general hybrid Bayesian networks. The proposed framework generalizes both the mixture of truncated exponentials (MTEs) framework and the mixture of polynomials (MoPs) framework. Similar to MTEs and MoPs, MoTBFs are defined so that the potentials are closed under combination and marginal...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...