Complex energies of the coherent longitudinal optical phonon-plasmon coupled mode according to dynamic mode decomposition analysis.

In a dissipative quantum system, we report the dynamic mode decomposition (DMD) analysis of damped oscillation signals. We used a reflection-type pump-probe method to observe time-domain signals, including the coupled modes of long-lived longitudinal optical phonons and quickly damped plasmons (LOPC) at various pump powers. The Fourier transformed spectra of the observed damped oscillation signals show broad and asymmetric modes, making it difficult to evaluate their frequencies and damping rates. We then used DMD to analyze the damped oscillation signals by precisely determining their frequencies and damping rates. We successfully identified the LOPC modes. The obtained frequencies and damping rates were shown to depend on the pump power, which implies photoexcited carrier density. We compared the pump-power dependence of the frequencies and damping rates of the LOPC modes with the carrier density dependence of the complex eigen-energies of the coupled modes by using the non-Hermitian phenomenological effective Hamiltonian. Good agreement was obtained between the observed and calculated dependences, demonstrating that DMD is an effective alternative to Fourier analysis which often fails to estimate effective damping rates.

Collective dynamics of repeated inference in variational autoencoder rapidly find cluster structure.

Deep neural networks are good at extracting low-dimensional subspaces (latent spaces) that represent the essential features inside a high-dimensional dataset. Deep generative models represented by variational autoencoders (VAEs) can generate and infer high-quality datasets, such as images. In particular, VAEs can eliminate the noise contained in an image by repeating the mapping between latent and data space. To clarify the mechanism of such denoising, we numerically analyzed how the activity pattern of trained networks changes in the latent space during inference. We considered the time development of the activity pattern for specific data as one trajectory in the latent space and investigated the collective behavior of these inference trajectories for many data. Our study revealed that when a cluster structure exists in the dataset, the trajectory rapidly approaches the center of the cluster. This behavior was qualitatively consistent with the concept retrieval reported in associative memory models. Additionally, the larger the noise contained in the data, the closer the trajectory was to a more global cluster. It was demonstrated that by increasing the number of the latent variables, the trend of the approach a cluster center can be enhanced, and the generalization ability of the VAE can be improved.

Efficient predictors for the decline of activities of daily living in patients with hip fracture one year after surgery: A multicenter prospective cohort study.

BACKGROUND: Previous studies have examined when activities of daily living (ADL) recovery more than six months after surgery can be predicted, and how much accuracy the predictors have. OBJECTIVE: The purpose of this study was to determine the predictors of ADL decline and evaluate their accuracies one year post-operation for hip-fracture patients. METHODS: We studied patients who underwent hip fracture surgery and were able to walk independently pre-operatively. The predictors of ADL declined one year post-operation, as analyzed using data of the basic medical attributes of the patients, including pain, 30-s chair-stand test, dementia [using the Revised Hasegawa Dementia Scale (HDS-R)], and walking/mobility style [using Barthel Index (BI)]. Using a receiver operating curve (ROC) curve, the cut-off value for each significant predictor was determined in the logistic regression analysis. To calculate the cut-off values and diagnostic performances of each of the extraction factors. RESULTS: The data of 36 patients were collected over a period of one year. The prior probability of ADL decline at one year post-operation was 44.4%. The results of logistic regression analyses showed that the score of HDS-R at admission and the walking/mobility BI score at three weeks post-operation were significant predictors of the one year post-operative decline in ADL. The results of the ROC analyses showed that the cut-off value of the HDS-R score at admission was < 23 points. The posterior probability increased to 62.0%. In contrast, the cut-off value of the walking/mobility BI score was 0 points. The posterior probability increased to 91.0%. CONCLUSION: The ADL decline of the patients who underwent hip fracture surgery at one year after surgery can be predicted at three weeks post-operation.

Normal mode analysis of a relaxation process with Bayesian inference.

Measurements of relaxation processes are essential in many fields, including nonlinear optics. Relaxation processes provide many insights into atomic/molecular structures and the kinetics and mechanisms of chemical reactions. For the analysis of these processes, the extraction of modes that are specific to the phenomenon of interest (normal modes) is unavoidable. In this study we propose a framework to systematically extract normal modes from the viewpoint of model selection with Bayesian inference. Our approach consists of a well-known method called sparsity-promoting dynamic mode decomposition, which decomposes a mixture of damped oscillations, and the Bayesian model selection framework. We numerically verify the performance of our proposed method by using coherent phonon signals of a bismuth polycrystal and virtual data as typical examples of relaxation processes. Our method succeeds in extracting the normal modes even from experimental data with strong backgrounds. Moreover, the selected set of modes is robust to observation noise, and our method can estimate the level of observation noise. From these observations, our method is applicable to normal mode analysis, especially for data with strong backgrounds.