projection methods
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The self-organizing maps portraying has been proven to be a powerful approach for analysis of transcriptomic, genomic, epigenetic, single-cell, and pathway-level data as well as for “multi-omic” integrative analyses. However, the SOM method has a major disadvantage: it requires the retraining of the entire dataset once a new sample is added, which can be resource- and time-demanding. It also shifts the gene landscape, thus complicating the interpretation and comparison of results. To overcome this issue, we have developed two approaches of transfer learning that allow for extending SOM space with new samples, meanwhile preserving its intrinsic structure. The extension SOM (exSOM) approach is based on adding secondary data to the existing SOM space by “meta-gene adaptation”, while supervised SOM portrayal (supSOM) adds support vector machine regression model on top of the original SOM algorithm to “predict” the portrait of a new sample. Both methods have been shown to accurately combine existing and new data. With simulated data, exSOM outperforms supSOM for accuracy, while supSOM significantly reduces the computing time and outperforms exSOM for this parameter. Analysis of real datasets demonstrated the validity of the projection methods with independent datasets mapped on existing SOM space. Moreover, both methods well handle the projection of samples with new characteristics that were not present in training datasets.

The purpose of this research is to find out the comparison of forecasting calculations using the moving average and trend projection methods as a means measuring tool in production planning at UD. Jaya Abadi Probolinggo Regency. The type of research used is quantitative descriptive. Population and sample in this research is UD production data. Jaya Abadi Probolinggo Regerency from 2018 to March 2021. Data  analysis using the moving average and trend projection methods which aim to predict future production or the next period. The results showed that the value of  MAD (Mean Absolute Deviation)  and the MSE (Mean Square Error) moving average values are  higher than  the MAD  and the MSE trend projection, so the company you should use trend projection because when viewed  from the results of the comparision of  MAD and MSE, this method has a smaller error rate than the moving average method. So it can be concluded that the trend projection method can be used in planning bread production  at UD. Jaya Abadi Probolinggo Regency

The traditional method of studying plate motion still cannot be used to obtain plate motion trajectory quantitatively. In this paper, we proposed a new method to quantitative determine plate motion trajectory. Depending on the paleomagnetic data of lithosphere plate and the stereographic projection principle. We selected the Wulff net as the basic projection net, improved and transformed the traditional stereographic projection methods. Projecting the paleomagnetic data (magnetic declination, palaeolatitude and geomagnetic pole coordinate) of the lithosphere plate into the improved stereographic projection net, we can get the analysis results of lithosphere plate stereographic projection. In our study, we took the Indian plate as an example, projected the paleomagnetic data (from Cretaceous) into the stereographic projection net, got the analysis results of motion trajectory of the Indian plate from Cretaceous. This method can be applied to quantify lithospheric plate motion trajectory.

Background: Accurate projections of the future number of people with chronic diseases are necessary for effective resource allocation and health care planning in response to changes in disease burden. Aim: To introduce and compare different projection methods to estimate the number of people with diagnosed type 2 diabetes (T2D) in Germany in 2040. Methods: We compare three methods to project the number of males with T2D in Germany in 2040. Method 1) simply combines the sex- and age-specific prevalence of T2D in 2010 with future population distributions projected by the German Federal Statistical Office (FSO). Methods 2) and 3) additionally account for the incidence of T2D and mortality rates using partial differential equations (PDEs). Method 2) models the prevalence of T2D employing a scalar PDE which incorporates incidence and mortality rates. Subsequently, the estimated prevalence is applied to the population projection of the FSO. Method 3) uses a two-dimensional system of PDEs and estimates future case numbers directly while future mortality of people with and without T2D is modelled independently from the projection of the FSO. Results: Method 1) projects 3.6 million male people with diagnosed T2D in Germany in 2040. Compared to 2.8 million males in 2010, this equals an increase by 29%. Methods 2) and 3) project 5.9 million (+104% compared to 2010) and 6.0 million (+116%) male T2D patients, respectively. Conclusions: The results of the three methods differ substantially. It appears that ignoring temporal trends in incidence and mortality may result in misleading projections of the future number of people with chronic diseases. Hence, it is essential to include these rates as is done by method 2) and 3).

AbstractWe introduce a dynamical system to the problem of finding zeros of the sum of two maximally monotone operators. We investigate the existence, uniqueness and extendability of solutions to this dynamical system in a Hilbert space. We prove that the trajectories of the proposed dynamical system converge strongly to a primal–dual solution of the considered problem. Under explicit time discretization of the dynamical system we obtain the best approximation algorithm for solving coupled monotone inclusion problem.

AbstractCarbon ion radiotherapy is a sophisticated radiation treatment modality because of its superiority in achieving precise dosage distribution and high biological effectiveness. However, there exist beam range uncertainties that affect treatment efficiency. This problem can be resolved if the clinical beam could be monitored precisely in real-time, such as by imaging the prompt gamma emission from the target. In this study, we performed real-time detection and imaging of 718 keV prompt gamma emissions using a Si/CdTe Compton camera. We conducted experiments on graphite phantoms using clinical carbon ion beams of 290 MeV/u energy. Compton images were reconstructed using simple back-projection methods from the energy events of 718 keV prompt gamma emissions. The peak intensity position in reconstructed 718 keV prompt gamma images was few millimeters below the Bragg peak position. Moreover, the dual- and triple-energy window images for all positions of phantoms were not affected by scattered gammas, and their peak intensity positions were approximately similar to those observed in the reconstructed 718 keV prompt gamma images. In conclusion, the findings of the current study demonstrate the feasibility of using our Compton camera for real-time beam monitoring of carbon ion beams under clinical beam intensity.