Optimal trajectory generation with DMOC versus NTG : application to an underwater glider and a JPL aerobot.

Optimal trajectory generation is an essential part for robotic explorers to execute the total exploration of deep oceans or outer space planets while curiosity of human and technology advancements of society both require robots to search for unknown territories efficiently and safely. As one of state-of-the-art optimal trajectory generation methodologies, Nonlinear Trajectory Generation (NTG) combines with B-spline, nonlinear programming, differential flatness technique to generate optimal trajectories for modelled mechanical systems. While Discrete Mechanics and Optimal Control (DMOC) is a newly proposed optimal control method for mechanical systems, it is based on direct discretization of Lagrange-d\u27Alembert principle. In this dissertation, NTG is utilized to generate trajectories for an underwater glider with a 3D B-spline ocean current model. The optimal trajectories are corresponding well with the Lagrangian Coherent Structures (LCS). Then NTG is utilized to generate 3D opportunistic trajectories for a JPL (Jet Propulsion Laboratory) Aerobot by taking advantage of wind velocity. Since both DMOC and NTG are methods which can generate optimal trajectories for mechanical systems, their differences in theory and application are investigated. In a simple ocean current example and a more complex ocean current model, DMOC with discrete Euler-Lagrange constraints generates local optimal solutions with different initial guesses while NTG is also generating similar solutions with more computation time and comparable energy consumption. DMOC is much easier to implement than NTG because in order to generate good solutions in NTG, its variables need to be correctly defined as B-spline variables with rightly-chosen orders. Finally, the MARIT (Multiple Air Robotics Indoor Testbed) is established with a Vicon 8i motion capture system. Six Mcam 2 cameras connected with a datastation are able to track real-time coordinates of a draganflyer helicopter. This motion capture system establishes a good foundation for future NTG and DMOC algorithms verifications

Comparative Study on the Senior Secondary School Mathematics Curricula Development in Ethiopia and Australia

The main objective of this study is to compare the process of the senior secondary school mathematics curricula development in Ethiopia and Australia. The study was investigated qualitatively with document analysis and semi-structured interview research methods. The documents were collected from Federal Democratic Republic of Ethiopia Ministry of Education website and Australian curriculum website. The documents were analyzed and supported by interviews. The study was conducted based on four themes needs assessment, developing/writing the curriculum, implementation, and monitoring and evaluation. The study revealed both similarities and differences. The considerable differences in the senior secondary school mathematics curriculum development process are (1) emphasis given to international research results and contemporary issues on mathematics education as inputs for curriculum development (2) the underlying principle of content standard organizations (3) trialing the curriculum before implementation initiated, and (4) monitoring and evaluation strategies. Even though substantial differences exist, the similarities are (1) conducting needs assessment and (2) the adoption of the constructivism approach. Depending on the findings of the study, the suggested recommendations were presented under conclusion section. Keywords: Ethiopia, Australia, comparative study, senior secondary school curriculum, curriculum developmen

Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations

Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector $\boldsymbol x = (x_1,\dots,x_d)$ such that for each node $v$ in a social network, $v$ could be activated as a seed of diffusion with probability $h_v(\boldsymbol x)$, where $h_v$ is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix $\boldsymbol x$ with constraint $\sum_i x_i \le k$ where $k$ is a budget constraint, such that the total number of activated nodes after the diffusion process, called influence spread and denoted as $g(\boldsymbol x)$, is maximized. In this paper, we extend CIM to consider budget saving, that is, each strategy mix $\boldsymbol x$ has a cost $c(\boldsymbol x)$ where $c$ is a convex cost function, we want to maximize the balanced sum $g(\boldsymbol x) + \lambda(k - c(\boldsymbol x))$ where $\lambda$ is a balance parameter, subject to the constraint of $c(\boldsymbol x) \le k$. We denote this problem as CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular or concave, and thus neither the greedy algorithm nor the standard result on gradient method could be directly applied. Our key innovation is the combination of the gradient method with reverse influence sampling to design algorithms that solve CIM-BS: For the general case, we give an algorithm that achieves $\left(\frac{1}{2}-\varepsilon\right)$-approximation, and for the case of independent strategy activations, we present an algorithm that achieves $\left(1-\frac{1}{e}-\varepsilon\right)$ approximation.Comment: To appear in AAAI-20, 43 page

Test-Time Compensated Representation Learning for Extreme Traffic Forecasting

Traffic forecasting is a challenging task due to the complex spatio-temporal correlations among traffic series. In this paper, we identify an underexplored problem in multivariate traffic series prediction: extreme events. Road congestion and rush hours can result in low correlation in vehicle speeds at various intersections during adjacent time periods. Existing methods generally predict future series based on recent observations and entirely discard training data during the testing phase, rendering them unreliable for forecasting highly nonlinear multivariate time series. To tackle this issue, we propose a test-time compensated representation learning framework comprising a spatio-temporal decomposed data bank and a multi-head spatial transformer model (CompFormer). The former component explicitly separates all training data along the temporal dimension according to periodicity characteristics, while the latter component establishes a connection between recent observations and historical series in the data bank through a spatial attention matrix. This enables the CompFormer to transfer robust features to overcome anomalous events while using fewer computational resources. Our modules can be flexibly integrated with existing forecasting methods through end-to-end training, and we demonstrate their effectiveness on the METR-LA and PEMS-BAY benchmarks. Extensive experimental results show that our method is particularly important in extreme events, and can achieve significant improvements over six strong baselines, with an overall improvement of up to 28.2%.Comment: 13 pages, 10 figures, 5 table

Normalizing Flow with Variational Latent Representation

Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal distribution, has difficulty in handling data distributions with multiple relatively isolated modes. To overcome this issue, we propose a new framework based on variational latent representation to improve the practical performance of NF. The idea is to replace the standard normal latent variable with a more general latent representation, jointly learned via Variational Bayes. For example, by taking the latent representation as a discrete sequence, our framework can learn a Transformer model that generates the latent sequence and an NF model that generates continuous data distribution conditioned on the sequence. The resulting method is significantly more powerful than the standard normalization flow approach for generating data distributions with multiple modes. Extensive experiments have shown the advantages of NF with variational latent representation.Comment: 24 pages, 7 figure