This paper is aimed at the illustration of how a recently proposed logarithm based high dimensional model representation (HDMR) works on the functions which have different structures. The main focus of the paper is on...
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This paper is aimed at the illustration of how a recently proposed logarithm based high dimensional model representation (HDMR) works on the functions which have different structures. The main focus of the paper is on the dominantly multiplicative functions. Since the logarithm converts multiplicativity to additivity what we expect from this new representation is the sufficiency of less number of these new HDMR components than the number of components of plain High Dimensional Model Representation which works well for dominantly additive functions. In implementations we use MuPAD Computer Algebra System to have any desired precision in calculations and to use its symbolic programming nature. We do not use continuous functions instead we take discrete data about the function under consideration. However these data is produced from continuous functions for illustrative purposes. The comparison of the given function values and the values evaluated by truncated Logarithm Based HDMR.
As populations age, understanding cognitive decline and age-related diseases like dementia has become increasingly important. “SuperAgers,” individuals over 65 with cognitive abilities similar to those in their 40s,...
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As populations age, understanding cognitive decline and age-related diseases like dementia has become increasingly important. “SuperAgers,” individuals over 65 with cognitive abilities similar to those in their 40s, provide a unique perspective on cognitive reserve. This study analyzed 55 blood biomarkers, including cellular components and metabolism/inflammation-related factors, in 39 SuperAgers and 42 typical agers. While conventional statistical analyses identified significant differences in only four biomarkers, advanced feature selection and machine learning techniques revealed a broader set of 15 key biomarkers associated with SuperAger status. A predictive model built using these biomarkers achieved an accuracy of 76% in cognitive domain prediction. To address the limitation of small sample sizes, data augmentation leveraging large language models improved the model’s robustness. Shapley Additive exPlanations (SHAP) provided interpretability, revealing the impact of specific blood factors on cognitive function. These findings suggest that certain blood biomarkers are not only associated with cognitive performance but may also serve as indicators of cognitive reserve. By utilizing simple blood tests, this research presents a clinically significant method for predicting cognitive function and identifying SuperAger status in healthy elderly individuals, offering a foundation for future studies on the biological mechanisms underpinning cognitive resilience.
A parallel implementation for linear set of equations of the form Ax = b is presented in this paper. In this implementation, instead of the traditional direct solution of Ax = b, conjugate gradient method is used. The...
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A parallel implementation for linear set of equations of the form Ax = b is presented in this paper. In this implementation, instead of the traditional direct solution of Ax = b, conjugate gradient method is used. The conjugate gradient method is accelerated with an approximate inverse matrix preconditioner obtained from a linear combination of matrix-valued Chebyshev polynomials. This implementation is tested on a Sun SMP machine. Since conjugate gradient method and preconditioner contain mainly matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.
High Dimensional Model Representation (HDMR) presents the possibility to measure how constant, how constant, how univariate, how bivariate (and so on) a given uniform discrete multivariate data or the multivariate fun...
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High Dimensional Model Representation (HDMR) presents the possibility to measure how constant, how constant, how univariate, how bivariate (and so on) a given uniform discrete multivariate data or the multivariate function under consideration of HDMR is. Amongst these measurements the most important one is the one for univariance since univariance means additive separability which is the best thing to facilitate the computations in computers. In this paper we define the HDMR's univariance level for a given discrete data. We discuss the possibility of increasing univariance by using certain mappings although the details will not be explicitly given. The basic tool to this end is the recently developed Logarithmic High Dimensional Model Representation and related issues.
E-Learning activities are growing around the world, accompanied by a proliferation of data, learning objects (LO) and tools. This imposes new challenges as, for example, how to find available artifacts. This work aims...
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Presidential actions on Jan 20, 2025, by President Donald Trump, including executive orders, have delayed access to or led to the removal of crucial public health data sources in the USA. The continuous collection and...
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This paper proposes a method to estimate the posture of an athlete moving on a vast field in a sporting event using a pan-tilt-zoom camera. In order to estimate the posture of an athlete on a sports field from a dynam...
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Understanding historical wildfire variations and their environmental driving mechanisms is key to predicting and mitigating wildfires. However, current knowledge of climatic responses and regional contributions to the...
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Understanding historical wildfire variations and their environmental driving mechanisms is key to predicting and mitigating wildfires. However, current knowledge of climatic responses and regional contributions to the interannual variability (IAV) of global burned area remains limited. Using recent satellite-derived wildfire products and simulations from version v1.0 of the land component of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM land model [ELM] v1) driven by three different climate forcings, we investigated the burned area IAV and its climatic sensitivity globally and across nine biomes from 1997 to 2018. We found that 1) the ELM simulations generally agreed with the satellite observations in terms of the burned area IAV magnitudes, regional contributions, and covariations with climate factors, confirming the robustness of the ELM to the usage of different climate forcing sources;2) tropical savannas, tropical forests, and semi-arid grasslands near deserts were primary contributors to the global burned area IAV, collectively accounting for 71.7%–99.7% of the global wildfire IAV estimated by both the satellite observations and ELM simulations;3) precipitation was a major fire suppressing factor and dominated the global and regional burned area IAVs, and temperature and shortwave solar radiation were mostly positively related with burned area IAVs;and 4) noticeable local discrepancies between the ELM and remote-sensing results occurred in semi-arid grasslands, croplands, boreal forests, and wetlands, likely caused by uncertainties in the current ELM fire scheme and the imperfectly derived satellite observations. Our findings revealed the spatiotemporal diversity of wildfire variations, regional contributions and climatic responses, and provided new metrics for wildfire modeling, facilitating the wildfire prediction and management.
Digital image inpainting is the process by which corrupted or defective areas in an image are systematically corrected. New digital image inpainting techniques have been developed in recent years, leading to numerous ...
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Digital image inpainting is the process by which corrupted or defective areas in an image are systematically corrected. New digital image inpainting techniques have been developed in recent years, leading to numerous successful applications, particularly in the area of image restoration. We propose a new image inpainting algorithm based on wavelet sparse representation, and extend its applicability as a new approach for gap-filling in micrometeorological data. Our approach consists of treating the incomplete data set as a structured image that has a sparse representation in the wavelet domain. Therefore, an l_1 minimization problem is formulated in order to characterize the sparsest solution associated with the complete data set. A numerical experimentation on a real micrometeorological data set is conducted, demonstrating the effectiveness of the proposed approach.
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