2,343,080 research outputs found

    Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case

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    In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of the Langevin SDE used in finite dimensional sampling. Here the theory is developed for conditioned Gaussian processes for which the resulting SPDE is linear. Applications include the Kalman-Bucy filter/smoother. A companion paper studies the nonlinear case, building on the linear analysis provided here

    Time-Optimal Path Tracking via Reachability Analysis

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    Given a geometric path, the Time-Optimal Path Tracking problem consists in finding the control strategy to traverse the path time-optimally while regulating tracking errors. A simple yet effective approach to this problem is to decompose the controller into two components: (i)~a path controller, which modulates the parameterization of the desired path in an online manner, yielding a reference trajectory; and (ii)~a tracking controller, which takes the reference trajectory and outputs joint torques for tracking. However, there is one major difficulty: the path controller might not find any feasible reference trajectory that can be tracked by the tracking controller because of torque bounds. In turn, this results in degraded tracking performances. Here, we propose a new path controller that is guaranteed to find feasible reference trajectories by accounting for possible future perturbations. The main technical tool underlying the proposed controller is Reachability Analysis, a new method for analyzing path parameterization problems. Simulations show that the proposed controller outperforms existing methods.Comment: 6 pages, 3 figures, ICRA 201

    Solving integral equations in η→3π\eta\to 3\pi

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    A dispersive analysis of η→3π\eta\to 3\pi decays has been performed in the past by many authors. The numerical analysis of the pertinent integral equations is hampered by two technical difficulties: i) The angular averages of the amplitudes need to be performed along a complicated path in the complex plane. ii) The averaged amplitudes develop singularities along the path of integration in the dispersive representation of the full amplitudes. It is a delicate affair to handle these singularities properly, and independent checks of the obtained solutions are demanding and time consuming. In the present article, we propose a solution method that avoids these difficulties. It is based on a simple deformation of the path of integration in the dispersive representation (not in the angular average). Numerical solutions are then obtained rather straightforwardly. We expect that the method also works for ω→3π\omega\to 3\pi.Comment: 11 pages, 10 Figures. Version accepted for publication in EPJC. The ancillary files contain an updated set of fundamental solutions. The numerical differences to the former set are tiny, see the READMEv2 file for detail

    At Last! An Explicit Solution for the Ramsey Saddle Path

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    I derive an explicit solution for the saddle path in a Ramsey growth model. The existence of a closed form expression greatly simplifies the analysis of how the parameters of the utility function affects investments and growth.Ramsey growth model

    Exaptation and emergence as mechanisms to cross fitness valleys during evolution: an example using simulated homing behaviour

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    Evolution is often considered a gradual hill climbing process, slowly increasing the fitness of organisms. I investigate the evolution of homing behaviour in simulated intertidal limpets. In order to evolve path integration as a homing mechanism, a temporary reduction in an organism’s fitness is required – since high developmental costs occur before a successful homing strategy evolves. Simple hill-climbing algorithms, therefore, only rarely result in the evolution of a functional homing behaviour. The inclusion of a second behaviour (trail-following) greatly increases the frequency of success of evolution of a path integration strategy. Initially an emergent homing behaviour is formed combining path integration with trail following. This also demonstrates evolution through exaptation, since the original role of trail following is likely to be unrelated to homing. Analysis of the fitness landscapes of homing in the presence of trail-following behaviour shows a high variability of fitness, which results in the formation of ‘stepping-stones’ of high fitness across fitness valleys. By using these stepping-stones, simple hill-climbing algorithms can reach the global maximum fitness value

    An Economic Life in Vain − Path Dependence and East Germanyñs Pre- and Post-Unification Economic Stagnation

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    20 years after unification, the East German twin’s economic position is relatively stagnant compared to most of the West German productivity and income variables. The strong initial takeoff until the mid-end 1990s ended at a level of 70% to 80% of the western reference. In this paper, two interdependent hypotheses are put to the test: (i) that the communist economy prior to unification was on a stagnating path contrary to what standard analyses show; (ii) that strong elements of path dependence exist and that the switch from plan to market offset the pre-unification stagnation but was not able to repair structural deficits inherited from the past. In fact, looking into West German long-term data, an extremely stable development path can be found that extends from the 19th century to the present. Thus, the analysis of the East German development path is both economically relevant and politically interesting if economic policies are to be formulated.East Germany, time series, income, institution, product, unification, economic growth, convergence
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