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Bestsellers

The Collected Papers of Stephen Smale
The Collected Papers of Stephen Smale

In 3 Volumes
edited by F Cucker and R Wong
Fields Medallists' Lectures
Fields Medallists' Lectures

3th Edition
edited by Sir Michael Atiyah, Daniel Iagolnitzer and Chitat Chongx

 

  • articleNo Access

    Studying the Finiteness of a Tracking Technique with Random Distances and Velocities that Reduces the Collision Time Between a Brownian Particle and a Nanosensor in the Fluid

    The tracking technique that is examined in this study considers the nanosensor’s velocity and distance as independent random variables with known probability density functions (PDFs). The nanosensor moves continuously in both directions from the starting point of the real line (the line’s origin). It oscillates while traveling through the origin (both left and right). We provide an analytical expression for the density of this distance using the Fourier-Laplace representation and a sequence of random points. We can take the tracking distance into account as a function of a discounted effort-reward parameter in order to account for this uncertainty. We provide an analytical demonstration of the effects this parameter has on reducing the expected value of the first collision time between a nanosensor and the particle and confirming the existence of this technique.

  • articleNo Access

    A MULTI-OBJECTIVE RISK-BASED FRAMEWORK FOR MISSION CAPABILITY PLANNING

    In this paper, we propose a risk-based framework for military capability planning. Within this framework, metaheuristic techniques such as Evolutionary Algorithms are used to deal with multi-objectivity of a class of NP-hard resource investment problems, called The Mission Capability Planning Problem, under the presence of risk factors. This problem inherently has at least two conflicting objectives: minimizing the cost of investment in the resources as well as the makespan of the plans. The framework allows the addition of a risk-based objective to the problem in order to support risk assessment during the planning process. In other words, with this framework, a mechanism of progressive risk assessment is introduced to capability planning.

    We analyze the performance of the proposed framework under both scenarios: with and without risk. In the case of no risk, the purpose is to study several optimization-related aspects of the framework such as convergence, trade-off analysis, and its sensitivity to the algorithm parameters; while the second case is to demonstrate the ability of the framework in supporting risk assessment and also robustness analysis.

  • chapterNo Access

    ADAPTIVE PLANNING FOR AIR COMBAT MANEUVERING

    This paper describes Grumman's Rapid Expert Assessment to Counter Threats (REACT) project, designed to aid pilots in air combat decision making. We present a hierarchical design for a planning system which addresses some of the real-time aspects of planning for threat response. This paper concentrates on the lowest level of this hierarchy which is responsible for planning combat maneuvers at low altitude over hilly terrain when the enemy is not in sight. REACT's Lost Line of Sight module attempts to maximize the amount and depth of knowledge which can be utilized in the time available before the system must commit to its next action. It utilizes a hybrid architecture for planning decisions which incorporates multiple knowledge representations and planners based on artificial intelligence, neural networks, and decision theory. This architecture allows planning at different degrees of competence to be performed by concurrently operating planners with differing amounts of knowledge. We describe research on the planning issues in REACT as well as the associated knowledge representation and knowledge acquisition issues. In addition, we describe how work on developing terrain reasoning capability in REACT has suggested guidelines for knowledge base design and data management, system and language specifications, and planner architectures pertinent to real-time coupled systems.