Representation Of Real-world Problems Research Articles

A new modern scheme for solving fractal–fractional differential equations based on deep feedforward neural network with multiple hidden layer

The recent development of knowledge in fractional calculus introduced an advanced superior operator known as fractal–fractional derivative (FFD). This operator combines memory effect and self-similar property that give better accurate representation of real world problems through fractal–fractional differential equations (FFDEs). However, the existence of fresh and modern numerical technique on solving FFDEs is still scarce. Originally invented for machine learning technique, artificial neural network (ANN) is cutting-edge scheme that have shown promising result in solving the fractional differential equations (FDEs). Thus, this research aims to extend the application of ANN to solve FFDE with power law kernel in Caputo sense (FFDEPC) by develop a vectorized algorithm based on deep feedforward neural network that consists of multiple hidden layer (DFNN-2H) with Adam optimization. During the initial stage of the method development, the basic framework on solving FFDEs is designed. To minimize the burden of computational time, the vectorized algorithm is constructed at the next stage for method to be performed efficiently. Several example have been tested to demonstrate the applicability and efficiency of the method. Comparison on exact solutions and some previous published method indicate that the proposed scheme have give good accuracy and low computational time.

Heuristic Planning for Hybrid Systems

Planning in hybrid systems has been gaining research interest in the Artificial Intelligence community in recent years. Hybrid systems allow for a more accurate representation of real world problems, though solving them is very challenging due to complex system dynamics and a large model feature set. We developed DiNo, a new planner designed to tackle problems set in hybrid domains.DiNo is based on the discretise and validate approach and uses the novel Staged Relaxed Planning Graph+ (SRPG+) heuristic.

Uncertainty in integrated assessment modelling: A labyrinthic path

Integrated Assessment is the practice of combining different strands of knowledge to accurately represent and analyse real word problems of interest to decision-makers. Since these problems rarely observe disciplinary boundaries, Integrated Assessment usually involves interdisciplinary research. However, what distinguishes Integrated Assessment from interdisciplinary research is its policy dimension, aiming to inform decision-makers on the complexity of real world problems. Unfortunately, the body of existing disciplinary knowledge is often insufficient for the construction of an accurate representation of real world problems. Integrated Assessment offers a systematic approach to identification of the gaps in disciplinary knowledge that have often frustrated policy analysis in the past. Thus, Integrated Assessment has increasingly been the source of critical questions and new directions of research in the disciplinary sciences. Integrated Assessment is particularly useful for analysis of real world problems that are complex, operate at different levels in time and space, are immersed in uncertainty and for which the stakes are high. Because there are no simple solutions to these complex problems facing humankind, Integrated Assessment aims at conveying innovative and sometimes counterintuitive insights into the issues at hand rather than ready-made solutions. Portraying and translating real world problems can be done from a plurality of perspectives. There is no one “right” way to represent and analyse the world, therefore a diversity of methods and approaches to Integrated Assessment are needed, ranging from model-based methods to participatory methods [22,29]. Generally, these methods are, in varying degrees, in their relative infancy. The currently most widely used method of performing Integrated Assessment is modelling. Integrated Assessment models are frameworks to organize and structure various pieces of recent scientific disciplinary knowledge. A key issue in Integrated Assessment (IA) modelling is uncertainty due to various reasons. First of all IA modelling is confronted with the inherent uncertainty and lack of knowledge that the disciplinary sciences face. Secondly, IA models have to deal with a variety of types and sources of uncertainty that have to be structured and combined in one way or another. And finally, IA models are prone to a cumulation of uncertainties, because of their ambition to cover the whole cause–effect chain of a particular real world problem. This all makes uncertainty one of the most problematic but also one of the most challenging issues in the field of IA modelling. This paper therefore focuses on the laborious relation between uncertainty and IA modelling. After a description of what IA models are and where they can be used for, the issue of uncertainty is raised and how IA models struggle with it. One possible way out is presented in terms of a pluralistic approach towards the management of uncertainties in IA modelling.

Around the Sun in a Graphing Calculator

The topics of polar equations and parametric equations are found in almost all precalculus and calculus textbooks. They furnish important a lgebraic representations of real-world problems. For example, polar equations are used to describe the e lliptical orbit of planets around the sun (Kepler's first law), and parametric equations are frequently used to describe the trajectory of moving objects. These topics are seldom given more than superficial treatment in high school and college precalculus and calculus courses because of the difficulty of obtaining appropriate graphical representations.