In this study, the trends, stabilities of temperature, and rainfall data have been analyzed in detail for hydrometeorology time series recorded since 1870 Oxford city England. The innovative trend analysis (ITA) method has used to identify analyze piecewise trends selected series. To compare results, modified Mann–Kendall (MMK) Sen’s slope (SS) methods applied each as a ITA application. obtain ...

We test the efficiency of two pairwise comparison methods. The methods studied are Salminen’s piecewise linear prospect theory (PLP) method and the convex cone method by Korhonen, Wallenius, and Zionts (KWZ). The PLP method is based on a piecewise linear difference function. The KWZ method assumes a quasi-concave utility or value function. These methods are tested using randomly generated data ...

An algorithm for monotropic piecewise quadratic programming is developed. It converges to an exact solution in finitely many iterations and can be thought of as an extension of the simplex method for convex programming and the active set method for quadratic programming. Computational results show that solving a piecewise quadratic program is not much harder than solving a quadratic program of ...

We introduce the Forget-me-not Process, an efficient, non-parametric metaalgorithm for online probabilistic sequence prediction for piecewise stationary, repeating sources. Our method works by taking a Bayesian approach to partitioning a stream of data into postulated task-specific segments, while simultaneously building a model for each task. We provide regret guarantees with respect to piecew...

abstract: We introduce a discretization method of boundary value problems (BVP) in the case of the two dimensional diffusion equation on a rectangular mesh with refined zones. The method consists in representing the unknown distribution and its derivatives by piecewise constant distributions (PCD) on distinct meshes together with an appropriate approximate variational formulation of the exact B...

The radiosity equation occurs in computer graphics, and its solution leads to more realistic illumination for the display of surfaces. We consider the behavior of the radiosity integral operator, for smooth and piecewise smooth surfaces. A collocation method for solving the radiosity equation is proposed and analyzed. The method uses piecewise linear interpolation; and for one particular choice...

Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...

We apply the Piecewise Constant Level Set Method (PCLSM) to interface problems, especially for elliptic inverse and multiphase motion problems. PCLSM allows using one level set function to represent multiple phases, and the interfaces are represented implicitly by the discontinuity of a piecewise constant level set function. The inverse problem is solved using a variational penalization method ...