Using of intermediate point predictions to predict chaotic time series with many steps forward

The proposed work (within the clustering prediction paradigm) presents an approach to predicting chaotic time series by many steps at least for those points for which such a forecast is possible. This is used to forecast the forecast values at intermediate points of the forecasting interval and proposes algorithms for estimating the reliability of these forecast values. The above tasks require the use of clustering algorithms based on the apparatus of graph theory to find characteristic sequences (motives) in a known part of the predicted series and their use in obtaining the forecast. When predicting many steps forward, the predicted values at intermediate points are obtained using the algorithm. Namely, the use of the concept of inconsistent observation patterns proposed by the authors in the formation of sample vectors to be clustered at the stage of motive identification allows one to obtain many (albeit correlated) forecasts for one point; analysis of many forecasts allows you to drop obviously erroneous forecasts. In addition, three estimates for the projected points were constructed: the top estimate is the estimate obtained by applying motives to all observed points; lower estimate - an estimate obtained by applying motives only to those points on which you can rely; we will know these points; approximation of the lower estimate - the estimate obtained by applying motives only to those points on which you can rely, while the support points will be selected according to the value of their invariant measure. The following can be indicated as the main planned research results: (1) establishing the nature of the dependence of the number of unpredictable points and the average forecast error for points for which a forecast is possible, as a function of the length of the forecast interval; (2) algorithms for assessing the reliability of the obtained forecast values at intermediate points of the forecasting interval and evaluating their impact on the quality of forecasting; (3) the construction of a system of algorithms that allows predicting chaotictime series many steps forward.

Predicting the Motion of an Intruder in a Vertically Vibrated 2D-Granular-Bed using Contact Points Approximation

<p class="TTPAbstract">In this study, 2-dimensional Brazil nut effect experiments were setup. An intruder moves from its initial position at the middle-bottom of a container to its final position at the top of the granular bed. To predict the motion of the intruder, the number of contact points for each grain around the intruder was counted manually for grains in the first layer until the third layer. The average numbers of contact points from grains in each of 8 directions respected to the center of the intruder were calculated to determine the direction of total force acting on the intruder by grains in the first layer, in the first two-layers, and in the first three-layers.The result will be more acceptable using the data of two or three layers of grains in predicting intruder movement.</p>

Predicting the Motion of an Intruder in a Vertically Vibrated 2D-Granular-Bed using Contact Points Approximation

<p class="TTPAbstract">In this study, 2-dimensional Brazil nut effect experiments were setup. An intruder moves from its initial position at the middle-bottom of a container to its final position at the top of the granular bed. To predict the motion of the intruder, the number of contact points for each grain around the intruder was counted manually for grains in the first layer until the third layer. The average numbers of contact points from grains in each of 8 directions respected to the center of the intruder were calculated to determine the direction of total force acting on the intruder by grains in the first layer, in the first two-layers, and in the first three-layers.The result will be more acceptable using the data of two or three layers of grains in predicting intruder movement.</p>

A comparison of some fixed point iteration procedures by using the basins of attraction

Several iterative processes have been defined by researchers to approximate the fixed points of various classes operators. In this paper we present, by using the basins of attraction for the roots of some complex polynomials, an empirical comparison of some iteration procedures for fixed points approximation of Newton’s iteration operator. Some numerical results are presented. The Matlab m-files for generating the basins of attraction are presented, too.

Robust Scattered Data Points Approximation Using Finite Element Biomechanical Model

Many enabling technologies like non-rigid registration in medical image computing rely on the construction of a function by interpolating scattered points; however, the outliers contained in the data and the approximation error make the robust and accurate estimation difficult. This paper presents an ITK implementation of a robust Finite Element (FE) solver, which can effectively deal with the above difficulties. The experiment results of synthetic data and real cases demonstrate the characteristics of the robust solver and its typical application.

Common Fixed Points Approximation for Asymptotically Nonexpansive Semigroup in Banach Spaces

Let be a real Banach space satisfying local uniform Opial's condition, whose duality map is weakly sequentially continuous. Let be a uniformly asymptotically regular family of asymptotically nonexpansive semigroup of with function . Let and be weakly contractive map. Let be -strongly accretive and -strictly pseudocontractive map with . Let be an increasing sequence in and let and be sequences in satisfying some conditions. For some positive real number appropriately chosen, let be a sequence defined by , , , . It is proved that converges strongly to a common fixed point of the family which is also the unique solution of the variational inequality .