Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment

This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path integral control framework, which forms the backbone of the proposed method, re-writes the Hamilton-Jacobi-Bellman equation as a statistical inference problem; the resulting inference problem is solved by a sampling procedure that computes the distribution of controlled trajectories around the trajectory by the passive dynamics. For motion control of robots in a highly cluttered environment, however, this sampling can easily be trapped in a local minimum unless the sample size is very large, since the global optimality of local minima depends on the degree of uncertainty. Thus, a homology-embedded sampling-based planner that identifies many (potentially) local-minimum trajectories in different homology classes is developed to aid the sampling process. In combination with a receding-horizon fashion of the optimal control the proposed method produces a dynamically feasible and collision-free motion plans without being trapped in a local minimum. Numerical examples on a synthetic toy problem and on quadrotor control in a complex obstacle field demonstrate the validity of the proposed method.Comment: arXiv admin note: text overlap with arXiv:1510.0534

Monolingual or Bilingual Approach: The Effectiveness of Teaching Methods in Second Language Classroom

Previous studies (Slavin & Cheung, 2005; Purkarthofer & Mossakowski, 2011) have argued that bilingual instruction provides an advantage over English-only instruction in second language (SL) learning and English learners in bilingual condition feel more satisfied with the teaching method. However, there is a discrepancy between language policy and practice. This study investigates which method of the two (bilingual vs. monolingual instruction) is more effective and satisfying ELL students. Experimental research focused on the perspectives of future educators was conducted to answer this question. The participants were selected from graduate and undergraduate students who are enrolled in the college of education at a large public university. The purpose of selecting participants from students majoring in education was for them, as future educators, to experience the different methods of second language instruction and to investigate their opinions about these two teaching methods. The participants were randomly assigned into two different classes and learned Korean vocabulary lesson on definitions and pronunciation. After they were exposed to each different teaching method, the students were tested on what they learned. The first part was on the performance of phonics and the second part of the test measured the performance of vocabulary comprehension. Afterward a survey was conducted to determine their method of preference as they considered applying this experience to their future work teaching English to ELLs. The results indicate that the bilingual method is more effective and the participants under bilingual conditions preferred their method significantly to the monolingual instruction. The monolingual instruction group presented negative perception of using only target language in second language instruction. This study can provide an effective teaching method to future educators and contribute to the development of SL teachers training and SL education

Nematic and chiral orders for planar spins on triangular lattice

We propose a variant of the antiferromagnetic XY model on the triangular lattice to study the interplay between the chiral and nematic orders in addition to the magnetic order. The model has a significant bi-quadratic interaction of the planar spins. When the bi-quadratic exchange energy dominates, a large temperature window is shown to exist over which the nematic and the chiral orders co-exist without the magnetic order, thus defining a chiral-nematic state. The phase diagram of the model and some of its critical properties are derived by means of the Monte Carlo simulation.Comment: minor change

Dynamical mean-field theory of Hubbard-Holstein model at half-filling: Zero temperature metal-insulator and insulator-insulator transitions

We study the Hubbard-Holstein model, which includes both the electron-electron and electron-phonon interactions characterized by $U$ and $g$, respectively, employing the dynamical mean-field theory combined with Wilson's numerical renormalization group technique. A zero temperature phase diagram of metal-insulator and insulator-insulator transitions at half-filling is mapped out which exhibits the interplay between $U$ and $g$. As $U$ ($g$) is increased, a metal to Mott-Hubbard insulator (bipolaron insulator) transition occurs, and the two insulating states are distinct and can not be adiabatically connected. The nature of and transitions between the three states are discussed.Comment: 5 pages, 4 figures. Submitted to Physical Review Letter