Grouting in Consideration of Predominant Direction of Joints in Rock Masses

We conducted a grouting test in rock mass having steep joints with predominant direction, assuming blanket grouting for embankment dams. Vertical holes and inclined holes designed in consideration of the predominant direction of the joints were used as grouting holes, and the hole spacing was determined such that the number of grouting holes per unit area on a joint was the same for both cases. As a result, both tests saw a similar improvement despite the fact that the test using inclined holes had wider hole spacing than the test using vertical holes on the ground surface. We can also reduce the total drilling length of grouting holes if we use inclined holes instead of vertical holes, the hole spacing of which is determined in this manner, and thus we have demonstrated the usefulness of grouting that considers the predominant direction of joints in rock mass

Deep Learning-Based Average Consensus

In this study, we analyzed the problem of accelerating the linear average consensus algorithm for complex networks. We propose a data-driven approach to tuning the weights of temporal (i.e., time-varying) networks using deep learning techniques. Given a finite-time window, the proposed approach first unfolds the linear average consensus protocol to obtain a feedforward signal-flow graph, which is regarded as a neural network. The edge weights of the obtained neural network are then trained using standard deep learning techniques to minimize consensus error over a given finite-time window. Through this training process, we obtain a set of optimized time-varying weights, which yield faster consensus for a complex network. We also demonstrate that the proposed approach can be extended for infinite-time window problems. Numerical experiments revealed that our approach can achieve a significantly smaller consensus error compared to baseline strategies

Constructing Goeritz matrix from Dehn coloring matrix

Associated to a knot diagram, Goeritz introduced an integral matrix, which is now called a Goeritz matrix. It was shown by Traldi that the solution space of the equations with Goeritz matrix (precisely, unreduced Goeritz matrix called in his paper) as a coefficient matrix is isomorphic to the linear space consisting of the Dehn colorings for a knot. In this paper, we give a construction of a Goeritz matrix from a Dehn coloring matrix, from which Dehn colorings are induced. Moreover, if the knot diagram is prime, we give a purely algebraic construction of a Goeritz matrix from a Dehn coloring matrix.Comment: 10 pages, 6 figure