Streamflow forecasting is essential for hydrological engineering. In accordance with the advancement of computer aids in this field, various machine learning (ML) models have been explored to solve this highly non-stationary, stochastic, and nonlinear problem. In the current research, a newly explored version of an ML model called the long short-term memory (LSTM) was investigated for streamflow prediction using historical data for forecasting for a particular period. For a case study located in a tropical environment, the Kelantan river in the northeast region of the Malaysia Peninsula was selected. The modelling was performed according to several perspectives: (i) The feasibility of applying the developed LSTM model to streamflow prediction was verified, and the performance of the developed LSTM model was compared with the classic backpropagation neural network model; (ii) In the experimental process of applying the LSTM model to the prediction of streamflow, the influence of the training set size on the performance of the developed LSTM model was tested; (iii) The effect of the time interval between the training set and the testing set on the performance of the developed LSTM model was tested; (iv) The effect of the time span of the prediction data on the performance of the developed LSTM model was tested. The experimental data show that not only does the developed LSTM model have obvious advantages in processing steady streamflow data in the dry season but it also shows good ability to capture data features in the rapidly fluctuant streamflow data in the rainy season.

The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can efficiently encode all homotopy path classes between any two points. Thereafter, the optimal path planning task consists of two steps: (i) search for the homotopy path class that may contain the optimal path, and (ii) obtain the shortest homotopy path in this class. Furthermore, an optimal path planning algorithm called CDT-RRT* (Rapidly-exploring Random Tree Star based on Convex Division Topology) is proposed. We designed an efficient sampling formula for CDT-RRT*, which gives it a tendency to actively explore unknown homotopy classes, and incorporated the principles of the Elastic Band algorithm to obtain the shortest path in each class. Through a series of experiments, it was determined that the performance of the proposed algorithm is comparable with state-of-the-art path planning algorithms. Hence, the application significance of the developed homotopy invariant in the field of path planning was verified.

The impact of the precision and direction of motion of a two-dimensional (2D) diffractive optical element (DOE) based on binary pseudo-random sequences on speckle suppression efficiency is investigated experimentally. The experimental data show a large speckle suppression efficiency and agree qualitatively with the theoretical results. The experimental results confirm that the wavelength range for the speckle suppression of a two-level 2D DOE based on binary random sequences is narrower than the visible range. The experimental data confirm the theoretical prediction that the wavelength range for the speckle suppression for a double-sided one-dimensional (1D) DOE is wider than the visible range. The large speckle suppression coefficient $k>16$ and a speckle contrast below 2.6% are obtained in the entire visible range by using one two-sided 1D $M$-sequence-based DOE with code length $N=15$. The proposed method has potential applications in laser projection display systems.