A Quantum Calculus Formulation of Dynamic Programming and Ordered Derivatives

Much recent research activity has focused on the theory and application of quantum calculus. This branch of mathematics continues to find new and useful applications and there is much promise left for investigation into this field. We present a formulation of dynamic programming grounded in the quantum calculus. Our results include the standard dynamic programming induction algorithm which can be interpreted as the Hamilton-Jacobi-Bellman equation in the quantum calculus. Furthermore, we show that approximate dynamic programming in quantum calculus is tenable by laying the groundwork for the backpropagation algorithm common in neural network training. In particular, we prove that the chain rule for ordered derivatives, fundamental to backpropagation, is valid in quantum calculus. In doing this we have connected two major fields of research

Maximum Likelihood Methods in Biology Revisited with Tools of Computational Intelligence

We investigate the problem of identification of genes correlated with the occurrence of diseases in a given population. The classical method of parametric linkage analysis is combined with newer tools and results are achieved on a model problem. This traditional method has advantages over non-parametric methods, but these advantages have been difficult to realize due to their high computational cost. We study a class of Evolutionary Algorithms from the Computational Intelligence literature which are designed to cut such costs considerably for optimization problems. We outline the details of this algorithm, called Particle Swarm Optimization, and present all the equations and parameter values we used to accomplish our optimization. We view this study as a launching point for a wider investigation into the leveraging of computational intelligence tools in the study of complex biological systems

Decision Theory on Dynamic Domains Nabla Derivatives and the Hamilton-Jacobi-Bellman Equation

The time scales calculus, which includes the study of the nabla derivatives, is an emerging key topic due to many multidisciplinary applications. We extend this calculus to Approximate Dynamic Programming. In particular, we investigate application of the nabla derivative, one of the fundamental dynamic derivatives of time scales. We present a nabla-derivative based derivation and proof of the Hamilton-Jacobi-Bellman equation, the solution of which is the fundamental problem in the field of dynamic programming. By drawing together the calculus of time scales and the applied area of stochastic control via Approximate Dynamic Programming, we connect two major fields of research

Hamilton-Jacobi-Bellman Equations and Approximate Dynamic Programming on Time Scales

The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research

Adaptive Multi-Vehicle Area Coverage Optimization System and Method

A mission planning system for determining an optimum use of a plurality of vehicles in searching a predefined geographic area (PGA). A discretizer subsystem may be used for sensing the capabilities of each vehicle to produce a point set defining a number of points within the PGA that the vehicles must traverse to completely search the PGA. A task allocator subsystem may determine an optimum division of the PGA into different subregions to be handled by specific ones of the vehicles, thus to minimize an overall time needed to search the PGA. A path optimizer subsystem may determine an optimum path through a particular vehicle\u27s assigned subregion to minimize the time needed for each specific vehicle to traverse its associated subregion

Vehicle Base Station

A system to load and unload material from a vehicle comprises a vehicle base station and an assembly to autonomously load and unload material from the vehicle

Coordinated Machine Learning and Decision Support for Situation Awareness

For applications such as force protection, an effective decision maker needs to maintain an unambiguous grasp of the environment. Opportunities exist to leverage computational mechanisms for the adaptive fusion of diverse information sources. The current research employs neural networks and Markov chains to process information from sources including sensors, weather data, and law enforcement. Furthermore, the system operator\u27s input is used as a point of reference for the machine learning algorithms. More detailed features of the approach are provided, along with an example force protection scenario

Real Time Mission Planning

The different advantageous embodiments provide a system comprising a number of computers, a graphical user interface, first program code stored on the computer, and second program code stored on the computer. The graphical user interface is executed by a computer in the number of computers. The computer is configured to run the first program code to define a mission using a number of mission elements. The computer is configured to run the second program code to generate instructions for a number of assets to execute the mission and monitor the number of assets during execution of the mission

Real Time Mission Planning

The different advantageous embodiments provide a system comprising a number of computers, a graphical user interface, first program code stored on the computer, and second program code stored on the computer. The graphical user interface is executed by a computer in the number of computers. The computer is configured to run the first program code to define a mission using a number of mission elements. The computer is configured to run the second program code to generate instructions for a number of assets to execute the mission and monitor the number of assets during execution of the mission