Separatrix modes in weakly deformed microdisk cavities

Optical modes in deformed dielectric microdisk cavities often show an unexpected localization along unstable periodic ray orbits. We reveal a new mechanism for this kind of localization in weakly deformed cavities. In such systems the ray dynamics is nearly integrable and its phase space contains small island chains. When increasing the deformation the enlarging islands incorporate more and more modes. Each time a mode comes close to the border of an island chain (separatrix) the mode exhibits a strong localization near the corresponding unstable periodic orbit. Using an EBK quantization scheme taking into account the Fresnel coefficients we derive a frequency condition for the localization. Observing far field intensity patterns and tunneling distances, reveals small differences in the emission properties. © 2017 Optical Society of America.1

On the limit of the sequence {Cm(D)}m=1∞\left\{ C^m(D) \right\}_{m=1}^{\infty} for a multipartite tournament DD

For an integer $k \ge 2$, let $A$ be a Boolean block matrix with blocks $A_{ij}$ for $1 \le i,j \le k$ such that $A_{ii}$ is a zero matrix and $A_{ij}+A_{ji}^T$ is a matrix with all elements $1$ but not both corresponding elements of $A_{ij}$ and $A_{ji}^T$ equal to $1$ for $i \neq j$. Jung~{\em et al.} [Competition periods of multipartite tournaments. {\it Linear and Multilinear Algebra}, https://doi.org/10.1080/03081087.2022.2038057] studied the matrix sequence $\{A^m(A^T)^m\}_{m=1}^{\infty}$. This paper, which is a natural extension of the above paper and was initiated by the observation that $\{A^m(A^T)^m\}_{m=1}^{\infty}$ converges if $A$ has no zero rows, computes the limit of the matrix sequence $\{A^m(A^T)^m\}_{m=1}^{\infty}$ if $A$ has no zero rows. To this end, we take a graph theoretical approach: noting that $A$ is the adjacency matrix of a multipartite tournament $D$, we compute the limit of the graph sequence $\left\{ C^m(D) \right\}_{m=1}^{\infty}$ when $D$ has no sinks

Chirality of a resonance in the absence of backscatterings

Chirality of a resonance localized on an islands chain is studied in a deformed Reuleaux triangular-shaped microcavity, where clockwise and counter clockwise traveling rays are classically separated. A resonance localized on a period-5 islands chain exhibits chiral emission due to the asymmetric cavity shape. Chirality is experimentally proved in a InGaAsP multiquantum-well semiconductor laser by showing that the experimental emission characteristics well coincide with the wave dynamical ones. (C) 2017 Optical Society of America1

A Predictive Model with Data Scaling Methodologies for Forecasting Spare Parts Demand in Military Logistics

This study addresses the challenge of accurately forecasting demand for maintenance-related spare parts of the K-X tank, influenced by high uncertainty and external factors. Deep learning models with RobustScaler demonstrate significant improvements, achieving an accuracy of 86.90% compared to previous methods. RobustScaler outperforms other scaling models, enhancing machine learning performance across time series and data mining. By collecting eight years’ worth of demand data and utilising various consumption data items, this study develops accurate forecasting models that contribute to the advancement of spare parts demand forecasting. The results highlight the effectiveness of the proposed approach, showcasing its superiority in accuracy, precision, recall, and F1-Score. RobustScaler particularly excels in time series analysis, further emphasizing its potential for enhancing machine learning performance on diverse datasets. This study provides innovative techniques and insights, demonstrating the effectiveness of deep learning and data scaling methodologies in improving forecasting accuracy for maintenance spare parts demand