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The prediction of future values of time series is a challenging task in many fields. In particular, making prediction based on short-term data is believed to be difficult. Here, we propose a method to predict systems' low-dimensional dynamics from high-dimensional but short-term data. Intuitively, it can be considered as a transformation from the inter-variable information of the observed high-dimensional data into the corresponding low-dimensional but long-term data, thereby equivalent to prediction of time series data. Technically, this method can be viewed as an inverse implementation of delayed embedding reconstruction. Both methods and algorithms are developed. To demonstrate the effectiveness of the theoretical result, benchmark examples and real-world problems from various fields are studied.

This study was conducted to understand the cellular proliferative effect of Photobiomodulation Therapy (PBMT) on thawed dental pulp stem cells (DPSCs) stored for 2 years. For this purpose, cells were exposed to PBMT for short period of time to evaluate the most appropriate PBMT parameter for stimulating cellular proliferation that can be used for future tissue engineering therapies. Fully characterized DPSCs were seperated into three groups according to the laser energy densities (5J/cm² or 7J/cm²) applied and a group was served as control in which cells did not receive any laser irradiation. The cells in laser-irradiated groups were further divided into two subgroups according to the period of application (24h and 0h) and exposed to Gallium–Aluminum–Arsenide diode laser irradiation. Cell viability and the proliferation rate of the cells were analyzed with the 3-[4,5-dimethylthiazol-2-yl]-2,5 diphenyl tetrazolium bromide (MTT) assay, any PBMT related cellular cytotoxicity were determined by performing a lactate dehydrogenase assay (LDH) and statistical analysis of data were performed. The percentage of proliferation seemed to increase upon laser therapy in both different doses of irradiation (5J/cm² and 7J/cm²). DPSCs showed significantly higher proliferation rate upon 7J/cm² irradiation in both 0h and 24h when compared to control groups. However, DPSCs irradiated with 5J/cm² dose induced relatively lower proliferation rate when compared to 7J/cm² dose of irradiation. According to the LDH data, PBMT exposure did not show any significant cytotoxicity at both energy densities in all different time periods. PBMT at 7J/cm² should be an effective parameter to stimulate proliferation of long-term cryopreserved DPSCs in a short term time period. Photobiomodulation therapy may be an upcoming tool for future tissue enngineering and regenerative dentistry applications.