Extrapolated High-Order Propagators for Path Integral Monte Carlo Simulations

We present a new class of high-order imaginary time propagators for path-integral Monte Carlo simulations by subtracting lower order propagators. By requiring all terms of the extrapolated propagator be sampled uniformly, the subtraction only affects the potential part of the path integral. The negligible violation of positivity of the resulting path integral at small time steps has no discernable affect on the accuracy of our method. Thus in principle arbitrarily high order algorithms can be devised for path-integral Monte Carlo simulations. We verify this claim is by showing that fourth, sixth, and eighth order convergence can indeed be achieved in solving for the ground state of strongly interacting quantum many-body systems such as bulk liquid $^4$He.Comment: 9 pages and 3 figures. Submitted to J. Chem. Phy

Artificial Intelligence in the Path Planning Optimization of Mobile Agent Navigation

AbstractMany difficult problem solving require computational intelligence. One of the major directions in artificial intelligence consists in the development of efficient computational intelligence algorithms, like: evolutionary algorithms, and neural networks. Systems, that operate in isolation or cooperate with each other, like mobile robots could use computational intelligence algorithms for different problems/tasks solving, however in their behavior could emerge an intelligence called system's intelligence, intelligence of a system. The traveling salesman problem TSP has a large application area. It is a well-known business problem. Maximum benefits TSP, price collecting TSP have a large number of economic applications. TSP is also used in the transport logic Raja, 2012. It also has a wide range of applicability in the mobile robotic agent path planning optimization. In this paper a mobile robotic agent's path planning will be discussed, using unsupervised neural networks for the TSP solving, and from the TSP results the finding of a closely optimal path between two points in the agent's working area. In the paper a modification of the criteria function of the winner neuron selection will also be presented. At the end of the paper measurement results will be presented

A new perspective on the complexity of interior point methods for linear programming

In a dynamical systems paradigm, many optimization algorithms are equivalent to applying forward Euler method to the system of ordinary differential equations defined by the vector field of the search directions. Thus the stiffness of such vector fields will play an essential role in the complexity of these methods. We first exemplify this point with a theoretical result for general linesearch methods for unconstrained optimization, which we further employ to investigating the complexity of a primal short-step path-following interior point method for linear programming. Our analysis involves showing that the Newton vector field associated to the primal logarithmic barrier is nonstiff in a sufficiently small and shrinking neighbourhood of its minimizer. Thus, by confining the iterates to these neighbourhoods of the primal central path, our algorithm has a nonstiff vector field of search directions, and we can give a worst-case bound on its iteration complexity. Furthermore, due to the generality of our vector field setting, we can perform a similar (global) iteration complexity analysis when the Newton direction of the interior point method is computed only approximately, using some direct method for solving linear systems of equations

Autonomous Recharging and Flight Mission Planning for Battery-operated Autonomous Drones

Autonomous drones (also known as unmanned aerial vehicles) are increasingly popular for diverse applications of light-weight delivery and as substitutions of manned operations in remote locations. The computing systems for drones are becoming a new venue for research in cyber-physical systems. Autonomous drones require integrated intelligent decision systems to control and manage their flight missions in the absence of human operators. One of the most crucial aspects of drone mission control and management is related to the optimization of battery lifetime. Typical drones are powered by on-board batteries, with limited capacity. But drones are expected to carry out long missions. Thus, a fully automated management system that can optimize the operations of battery-operated autonomous drones to extend their operation time is highly desirable. This paper presents several contributions to automated management systems for battery-operated drones: (1) We conduct empirical studies to model the battery performance of drones, considering various flight scenarios. (2) We study a joint problem of flight mission planning and recharging optimization for drones with an objective to complete a tour mission for a set of sites of interest in the shortest time. This problem captures diverse applications of delivery and remote operations by drones. (3) We present algorithms for solving the problem of flight mission planning and recharging optimization. We implemented our algorithms in a drone management system, which supports real-time flight path tracking and re-computation in dynamic environments. We evaluated the results of our algorithms using data from empirical studies. (4) To allow fully autonomous recharging of drones, we also develop a robotic charging system prototype that can recharge drones autonomously by our drone management system

Convexity properties of the condition number II

In our previous paper [SIMAX 31 n.3 1491-1506(2010)], we studied the condition metric in the space of maximal rank matrices. Here, we show that this condition metric induces a Lipschitz-Riemann structure on that space. After investigating geodesics in such a nonsmooth structure, we show that the inverse of the smallest singular value of a matrix is a log-convex function along geodesics (Theorem 1). We also show that a similar result holds for the solution variety of linear systems (Theorem 31). Some of our intermediate results, such as Theorem 12, on the second covariant derivative or Hessian of a function with symmetries on a manifold, and Theorem 29 on piecewise self-convex functions, are of independent interest. Those results were motivated by our investigations on the com- plexity of path-following algorithms for solving polynomial systems.Comment: Revised versio