This overview presents a discussion on several topics of importance shared by the fields of computational mathematics and computational statistics. A brief history of the advancements to the fields of mathematics and ...
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This overview presents a discussion on several topics of importance shared by the fields of computational mathematics and computational statistics. A brief history of the advancements to the fields of mathematics and statistics leading to the modern computational era is provided, along with a discussion of the intersection of topics which comprise the two subjects. The foundational aspects shared by both computational mathematics and computational statistics are explored with elementary discussions suitable to nonexperts and aspiring students of the computational sciences. Finally, a discussion of the role played by computational mathematics and computational statistics in a few selected application areas is explored. (C) 2014 Wiley Periodicals, Inc.
This study developed a Monte Carlo simulation approach to examining the prevalence and incidence of dental decay using Australian children as a test environment. Monte Carlo simulation has been used for a half a centu...
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This study developed a Monte Carlo simulation approach to examining the prevalence and incidence of dental decay using Australian children as a test environment. Monte Carlo simulation has been used for a half a century in particle physics (and elsewhere);put simply, it is the probability for various population-level outcomes seeded randomly to drive the production of individual level data. A total of five runs of the simulation model for all 275,000 12-year-olds in Australia were completed based on 20052006 data. Measured on average decayed/missing/filled teeth (DMFT) and DMFT of highest 10% of sample (Sic10) the runs did not differ from each other by more than 2% and the outcome was within 5% of the reported sampled population data. The simulations rested on the population probabilities that are known to be strongly linked to dental decay, namely, socio-economic status and Indigenous heritage. Testing the simulated population found DMFT of all cases where DMFT <> 0 was 2.3 (n=128,609) and DMFT for Indigenous cases only was 1.9 (n=13,749). In the simulation population the Sic25 was 3.3 (n=68,750). Monte Carlo simulations were created in particle physics as a computational mathematical approach to unknown individual-level effects by resting a simulation on known population-level probabilities. In this study a Monte Carlo simulation approach to childhood dental decay was built, tested and validated.
Computer algebra systems (CAS) are often used programs in universities to support calculations and visualization in teaching mathematical subjects. In this paper we present some examples of dynamic visualizations whic...
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ISBN:
(纸本)9783030504366;9783030504359
Computer algebra systems (CAS) are often used programs in universities to support calculations and visualization in teaching mathematical subjects. In this paper we present some examples of dynamic visualizations which we prepared for students of Warsaw University of Life Sciences using Mathematica. Visualizations for simplex algorithm and Karush-Kuhn-Tucker algorithm are presented. We also describe a didactic experiment for students of the Production Engineering Faculty of Warsaw University of Life Sciences using dynamic visualization of the network flow problem.
The funding initiative ModSim computational mathematics started in 2008. In 2010 there was the, third call for project-proposals. This paper describes the results from the three calls and the comparison with respect t...
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ISBN:
(纸本)9788890372452
The funding initiative ModSim computational mathematics started in 2008. In 2010 there was the, third call for project-proposals. This paper describes the results from the three calls and the comparison with respect to the temporal and financial outcome from the three calls. Also, the topics and contribution of different proposers are shown. Each year the number of proposals increased. The requested funding has increased with the announced available money for funding. At the same time, the size of the funded projects has decreased. Also the request for funding of big companies has increased from 37% to 76%, but their success-rate is lower than for the smaller companies. The sum of the funding asked for was around 19 Mio (sic). In total around 9 Mio (sic) have been announced for the projects and 6.4 Mio (sic) were decided for funding.
The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficien...
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The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm's scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.
Several modern scientific fields rely on computationally intensive mathematical models to study uncertain, complex socio-environmental phenomena such as the spread of a virus, climate change, or the water cycle. Howev...
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Several modern scientific fields rely on computationally intensive mathematical models to study uncertain, complex socio-environmental phenomena such as the spread of a virus, climate change, or the water cycle. However, the degree of epistemic commitment of these fields is unclear. By using machine learning to extract the knowledge claims of around 755,000 abstracts from 14 scientific fields spanning the human and physical sciences, we show that epidemic, integrated assessment, and water modeling display a degree of linguistic assertiveness akin to physics. Water modeling surpasses even the most accurate physical sciences in substantiating knowledge claims with numbers, which are largely produced without accompanying uncertainty and sensitivity analysis. By exploring the balance between doubt and certainty in academic writing, our study reflects on whether the strong conviction and quantification of fields modeling socio-environmental processes, especially water modeling, are epistemically justified.
Evaluating optimal mating combinations in large populations poses significant combinatorial and computational challenges. To address this, we propose a method to optimise mating combinations in composite cattle popula...
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Evaluating optimal mating combinations in large populations poses significant combinatorial and computational challenges. To address this, we propose a method to optimise mating combinations in composite cattle populations, incorporating heterosis and genetic variability. Leveraging integer linear programming, our approach maximises expected offspring merit, outperforming random mating systems. A robust mathematical model and specialised software were developed to implement the method, demonstrating its effectiveness on a real dataset. Notably, results reveal a 14.8% superiority over random mating averages and a 12.4% advantage over random mating maxima. The method's flexibility and adaptability enable constraint inclusion and application to diverse species and genomic data, making it an indispensable tool for enhancing mating selection efficiency and effectiveness in composite beef cattle breeding programmes.
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