Abstract: A system and method model a time series from missing data by imputing missing values, denoising measured but noisy values, and forecasting future values of a single time series. A time series of potentially noisy, partially-measured values of a physical process is represented as a non-overlapping matrix. For several classes of common model functions, it can be proved that the resulting matrix has a low rank or approximately low rank, allowing a matrix estimation technique, for example singular value thresholding, to be efficiently applied. Applying such a technique produces a mean matrix that estimates latent values, of the physical process at times or intervals corresponding to measurements, with less error than previously known methods. These latent values have been denoised (if noisy) and imputed (if missing). Linear regression of the estimated latent values permits forecasting with an error that decreases as more measurements are made.

Abstract: A computer-implemented method includes: identifying, from first and second data, interventions common to a target unit and one or more of a plurality of donor units as filtered donor units, the first data corresponding to the target unit under one or more interventions, the second data corresponding to the plurality of donor units each under one or more interventions; identifying, from the first data, third data corresponding to the target unit under the common interventions; identifying, from the second data, fourth data corresponding to the filtered donor units under the common interventions; identifying, from the second data, fifth data corresponding to the filtered donor units under a subject intervention; generating, from the third and fourth data, a learned model representing to a relationship between the target unit and the filtered donor units; applying the learned model to the fifth data to generate the synthetic data; and outputting the synthetic data.

Abstract: A system and method model a time series from missing data by imputing missing values, denoising measured but noisy values, and forecasting future values of a single time series. A time series of potentially noisy, partially-measured values of a physical process is represented as a non-overlapping matrix. For several classes of common model functions, it can be proved that the resulting matrix has a low rank or approximately low rank, allowing a matrix estimation technique, for example singular value thresholding, to be efficiently applied. Applying such a technique produces a mean matrix that estimates latent values, of the physical process at times or intervals corresponding to measurements, with less error than previously known methods. These latent values have been denoised (if noisy) and imputed (if missing). Linear regression of the estimated latent values permits forecasting with an error that decreases as more measurements are made.

Abstract: A system and method model a time series from missing data by imputing missing values, denoising measured but noisy values, and forecasting future values of a single time series. A time series of potentially noisy, partially-measured values of a physical process is represented as a non-overlapping matrix. For several classes of common model functions, it can be proved that the resulting matrix has a low rank or approximately low rank, allowing a matrix estimation technique, for example singular value thresholding, to be efficiently applied. Applying such a technique produces a mean matrix that estimates latent values, of the physical process at times or intervals corresponding to measurements, with less error than previously known methods. These latent values have been denoised (if noisy) and imputed (if missing). Linear regression of the estimated latent values permits forecasting with an error that decreases as more measurements are made.

Abstract: A foldable device may include a foldable layer and a hinge mechanism. The hinge mechanism may include a plurality of hinge segments, arranged in a plurality of rows, and with adjacent hinge segments being movably coupled so as to guide a folding and an unfolding motion of the foldable layer.

Abstract: A system and method model a time series from missing data by imputing missing values, denoising measured but noisy values, and forecasting future values of a single time series. A time series of potentially noisy, partially-measured values of a physical process is represented as a non-overlapping matrix. For several classes of common model functions, it can be proved that the resulting matrix has a low rank or approximately low rank, allowing a matrix estimation technique, for example singular value thresholding, to be efficiently applied. Applying such a technique produces a mean matrix that estimates latent values, of the physical process at times or intervals corresponding to measurements, with less error than previously known methods. These latent values have been denoised (if noisy) and imputed (if missing). Linear regression of the estimated latent values permits forecasting with an error that decreases as more measurements are made.

Abstract: A portable water purifying bottle comprises: an upper cover, having a water output port; a filter core component, disposed inside the upper cover, and located below the water output port; and a plastic cup sleeve, sleeved into a lower portion of the upper cover. The portable water purifying bottle is simple in design, the plastic cup sleeve made of silicone for storing water is retractable for easy carrying, thus fulfilling the needs of outdoor user. Further, the portable water purifying bottle is able to provide water output at fast speed to save time, while its appearance is compact and pleasing, hereby having a good prospect in the market.

Abstract: A faucet water output structure includes an L shape housing including a short tube and a long tube, wherein one end of the short tube is connected to one of the long tube, and on a wall of other end of the long tube is provided with an opening; a first water passage channel and a second water passage channel, both of which are located inside the L shape housing; and a first water route interface and a second water route interface, wherein, on the first water route interface is sleeved a water output end of the first water passage channel and a water input end of the second water passage channel, and on the second water route interface is sleeved a water input end of the first water passage channel and a water output end of the second water passage channel.

Abstract: A front release buckle includes a buckle body, which has a top receiving chamber and a bottom opening, a sliding hook coupled to the top receiving chamber and movable relative to the buckle body between a first position to close the bottom opening of the buckle body for enabling the buckle body to be fastened to a mounting member at an article and a second position to open the bottom opening, and a spring member mounted in the top receiving chamber and stopped between a part of the buckle body and a part of the sliding hook to support the sliding hook in the close position.