6,568 research outputs found

    Betti number signatures of homogeneous Poisson point processes

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    The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: B_0 is the number of connected components and B_k effectively counts the number of k-dimensional holes. Although they are appealing natural descriptors of shape, the higher-order Betti numbers are more difficult to compute than other measures and so have not previously been studied per se in the context of stochastic geometry or statistical physics. As a mathematically tractable model, we consider the expected Betti numbers per unit volume of Poisson-centred spheres with radius alpha. We present results from simulations and derive analytic expressions for the low intensity, small radius limits of Betti numbers in one, two, and three dimensions. The algorithms and analysis depend on alpha-shapes, a construction from computational geometry that deserves to be more widely known in the physics community.Comment: Submitted to PRE. 11 pages, 10 figure

    Tactile Interactions with a Humanoid Robot : Novel Play Scenario Implementations with Children with Autism

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    Acknowledgments: This work has been partially supported by the European Commission under contract number FP7-231500-ROBOSKIN. Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.The work presented in this paper was part of our investigation in the ROBOSKIN project. The project has developed new robot capabilities based on the tactile feedback provided by novel robotic skin, with the aim to provide cognitive mechanisms to improve human-robot interaction capabilities. This article presents two novel tactile play scenarios developed for robot-assisted play for children with autism. The play scenarios were developed against specific educational and therapeutic objectives that were discussed with teachers and therapists. These objectives were classified with reference to the ICF-CY, the International Classification of Functioning – version for Children and Youth. The article presents a detailed description of the play scenarios, and case study examples of their implementation in HRI studies with children with autism and the humanoid robot KASPAR.Peer reviewedFinal Published versio

    Pseudorehearsal in value function approximation

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    Catastrophic forgetting is of special importance in reinforcement learning, as the data distribution is generally non-stationary over time. We study and compare several pseudorehearsal approaches for Q-learning with function approximation in a pole balancing task. We have found that pseudorehearsal seems to assist learning even in such very simple problems, given proper initialization of the rehearsal parameters

    Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

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    The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective 1D Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matterwave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the purely classical simulation, suggesting that observing such exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.Comment: Close to the published versio

    Bayesian Exponential Random Graph Models with Nodal Random Effects

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    We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Two data examples and a small simulation study illustrate our mixed model approach and the corresponding model selection.Comment: 23 pages, 9 figures, 3 table

    A Pilot Study with a Novel Setup for Collaborative Play of the Humanoid Robot KASPAR with children with autism

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    This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.This article describes a pilot study in which a novel experimental setup, involving an autonomous humanoid robot, KASPAR, participating in a collaborative, dyadic video game, was implemented and tested with children with autism, all of whom had impairments in playing socially and communicating with others. The children alternated between playing the collaborative video game with a neurotypical adult and playing the same game with the humanoid robot, being exposed to each condition twice. The equipment and experimental setup were designed to observe whether the children would engage in more collaborative behaviours while playing the video game and interacting with the adult than performing the same activities with the humanoid robot. The article describes the development of the experimental setup and its first evaluation in a small-scale exploratory pilot study. The purpose of the study was to gain experience with the operational limits of the robot as well as the dyadic video game, to determine what changes should be made to the systems, and to gain experience with analyzing the data from this study in order to conduct a more extensive evaluation in the future. Based on our observations of the childrens’ experiences in playing the cooperative game, we determined that while the children enjoyed both playing the game and interacting with the robot, the game should be made simpler to play as well as more explicitly collaborative in its mechanics. Also, the robot should be more explicit in its speech as well as more structured in its interactions. Results show that the children found the activity to be more entertaining, appeared more engaged in playing, and displayed better collaborative behaviours with their partners (For the purposes of this article, ‘partner’ refers to the human/robotic agent which interacts with the children with autism. We are not using the term’s other meanings that refer to specific relationships or emotional involvement between two individuals.) in the second sessions of playing with human adults than during their first sessions. One way of explaining these findings is that the children’s intermediary play session with the humanoid robot impacted their subsequent play session with the human adult. However, another longer and more thorough study would have to be conducted in order to better re-interpret these findings. Furthermore, although the children with autism were more interested in and entertained by the robotic partner, the children showed more examples of collaborative play and cooperation while playing with the human adult.Peer reviewe

    Optically trapped atom interferometry using the clock transition of large Rb-87 Bose-Einstein condensates

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    We present a Ramsey-type atom interferometer operating with an optically trapped sample of 10^6 Bose-condensed Rb-87 atoms. The optical trap allows us to couple the |F =1, mF =0>\rightarrow |F =2, mF =0> clock states using a single photon 6.8GHz microwave transition, while state selective readout is achieved with absorption imaging. Interference fringes with contrast approaching 100% are observed for short evolution times. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the atomic projection noise limit on 10^6 condensate atoms. We discuss the technical and fundamental noise sources that limit our current system, and outline the improvements that can be made. Our results indicate that, with further experimental refinements, it will be possible to produce and measure the output of a sub-shot-noise limited, large atom number BEC-based interferometer. In an addendum to the original paper, we attribute our inability to observe quantum projection noise to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross-Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions account for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 \times 10^4 atoms, we observe a coherence time of {\tau} = (1.0+0.5-0.3) s.Comment: 22 pages, 6 figures Addendum: 11 pages, 6 figure
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