scholarly journals The Proof of Collatz Conjecture

2020 ◽  
Author(s):  
Hongyuan Ye
Keyword(s):  
Big Data ◽  
Negative Integer ◽  
Leaf Node ◽  
Sufficient Condition ◽  
Computer Data ◽  
Collatz Conjecture ◽  
Large Numbers ◽  
Structure Tree ◽  
Mathematical Problems ◽  
Minimum Number

Abstract This paper redefines Collatz conjecture, and proposes strong Collatz conjecture, the strong Collatz conjecture is a sufficient condition for the Collatz conjecture. Based on the computer data structure–tree, we construct the non-negative integer inheritance decimal tree. The nodes on the decimal tree correspond to non-negative integers. We further define the Collatz-leaf node (corresponding to the Collatz-leaf integer) on the decimal tree. The Collatz-leaf nodes satisfy strong Collatz conjecture. Derivation through mathematics, we prove that the Collatz-leaf node (Collatz-leaf integer) has the characteristics of inheritance. With computer large numbers and big data calculation, we conclude that all nodes at depth 800 are Collatz-leaf nodes. So we prove that strong Collatz conjecture is true, the Collatz conjecture must also be true. And for any positive integer N greater than 1, the minimum number of Collatz transform times from N to 1 is log2 N, the maximum number of Collatz transform times is 800 *（N-1）. The non-negative integer inheritance decimal tree proposed and constructed in this paper also can be used for the proof of other mathematical problems.

scholarly journals Computer Data Storage and Management Platform Based on Big Data

2021 ◽  
Vol 2066 (1) ◽  
pp. 012022
Author(s):  
Cheng Luo
Keyword(s):  
Big Data ◽  
Data Management ◽  
Performance Improvement ◽  
Data Storage ◽  
Nonvolatile Memory ◽  
Linear Structure ◽  
Ring Structure ◽  
Computer Data ◽  
Management Platform ◽  
A Performance

Abstract Due to the continuous development of information technology, data has increasingly become the core of the daily operation of enterprises and institutions, the main basis for decision-making development. At the same time, due to the development of network, the storage and management of computer data has attracted more and more attention. Aiming at the common problems of computer data storage and management in practical work, this paper analyzes the object and content of data management, investigates the situation of computer data storage and management in China in recent two years, and interviews and tests the data of programming in this design platform. At the same time, in view of the related problems, the research results are applied to practice. On the basis of big data, the storage and management platform is designed. The research and design adopts a special B+ tree node linear structure of CIRC tree, and the linear node structure is changed into a ring structure, which greatly reduces the number of data persistence instructions and the performance overhead. The results show that compared with the most advanced B+ tree design for nonvolatile memory, crab tree has 3.1 times and 2.5 times performance improvement in reading and writing, respectively. Compared with the previous NV tree designed for nonvolatile memory, it has a performance improvement of 1.5 times, and a performance improvement of 8.4 times compared with the latest fast-fair. In the later stage, the expansion of the platform functions is conducive to the analysis and construction of data related storage and management functions, and further improve the ability of data management.

scholarly journals Indirect predictions with a large number of genotyped animals using the algorithm for proven and young

2020 ◽  
Vol 98 (6) ◽  
Author(s):  
Andre L S Garcia ◽  
Yutaka Masuda ◽  
Shogo Tsuruta ◽  
Stephen Miller ◽  
Ignacy Misztal ◽  
...  
Keyword(s):  
Random Sample ◽  
Best Linear Unbiased Prediction ◽  
Single Step ◽  
Nucleotide Polymorphisms ◽  
Linear Unbiased Prediction ◽  
Single Nucleotide ◽  
Large Numbers ◽  
Minimum Number ◽  
Best Linear Unbiased ◽  
Estimated Breeding Values

Abstract Reliable single-nucleotide polymorphisms (SNP) effects from genomic best linear unbiased prediction BLUP (GBLUP) and single-step GBLUP (ssGBLUP) are needed to calculate indirect predictions (IP) for young genotyped animals and animals not included in official evaluations. Obtaining reliable SNP effects and IP requires a minimum number of animals and when a large number of genotyped animals are available, the algorithm for proven and young (APY) may be needed. Thus, the objectives of this study were to evaluate IP with an increasingly larger number of genotyped animals and to determine the minimum number of animals needed to compute reliable SNP effects and IP. Genotypes and phenotypes for birth weight, weaning weight, and postweaning gain were provided by the American Angus Association. The number of animals with phenotypes was more than 3.8 million. Genotyped animals were assigned to three cumulative year-classes: born until 2013 (N = 114,937), born until 2014 (N = 183,847), and born until 2015 (N = 280,506). A three-trait model was fitted using the APY algorithm with 19,021 core animals under two scenarios: 1) core 2013 (random sample of animals born until 2013) used for all year-classes and 2) core 2014 (random sample of animals born until 2014) used for year-class 2014 and core 2015 (random sample of animals born until 2015) used for year-class 2015. GBLUP used phenotypes from genotyped animals only, whereas ssGBLUP used all available phenotypes. SNP effects were predicted using genomic estimated breeding values (GEBV) from either all genotyped animals or only core animals. The correlations between GEBV from GBLUP and IP obtained using SNP effects from core 2013 were ≥0.99 for animals born in 2013 but as low as 0.07 for animals born in 2014 and 2015. Conversely, the correlations between GEBV from ssGBLUP and IP were ≥0.99 for animals born in all years. IP predictive abilities computed with GEBV from ssGBLUP and SNP predictions based on only core animals were as high as those based on all genotyped animals. The correlations between GEBV and IP from ssGBLUP were ≥0.76, ≥0.90, and ≥0.98 when SNP effects were computed using 2k, 5k, and 15k core animals. Suitable IP based on GEBV from GBLUP can be obtained when SNP predictions are based on an appropriate number of core animals, but a considerable decline in IP accuracy can occur in subsequent years. Conversely, IP from ssGBLUP based on large numbers of phenotypes from non-genotyped animals have persistent accuracy over time.

Building a Rapid Learning Health Care System for Oncology: The Regulatory Framework of CancerLinQ

2014 ◽  
Vol 32 (22) ◽  
pp. 2373-2379 ◽  
Author(s):  
Richard L. Schilsky ◽  
Dina L. Michels ◽  
Amy H. Kearbey ◽  
Peter Paul Yu ◽  
Clifford A. Hudis
Keyword(s):  
Health Care ◽  
Big Data ◽  
Quality Care ◽  
Quality Measurement ◽  
New Drugs ◽  
Large Numbers ◽  
New Information ◽  
American Society ◽  
Clinical Records ◽  
The Cost

Today is a time of unprecedented opportunity and challenge in health care generally and cancer care in particular. An explosion of scientific knowledge, the rapid introduction of new drugs and technologies, and the unprecedented escalation in the cost of health care challenge physicians to quickly assimilate new information and appropriately deploy new advances while also delivering efficient and high-quality care to a rapidly growing and aging patient population. At the same time, big data, with its potential to drive rapid understanding and innovation, promises to transform the health care industry, as it has many others already. CancerLinQ is an initiative of the American Society of Clinical Oncology (ASCO) and its Institute for Quality, developed to build on these opportunities and address these challenges by collecting information from the electronic health records of large numbers of patients with cancer. CancerLinQ is, first and foremost, a quality measurement and reporting system through which oncologists can harness the depth and power of their patients' clinical records and other data to improve the care they deliver. The development and deployment of CancerLinQ raises many important questions about the use of big data in health care. This article focuses on the US federal regulatory pathway by which CancerLinQ will accept patient records and the approach of ASCO toward stewardship of the information.

scholarly journals Collatz conjecture(3X+1)There is a hidden theorem ω1: If α Establishment, necessity (3α+ 1) Established

2021 ◽  
Author(s):  
Xie Ling
Keyword(s):  
Mathematical Logic ◽  
Number Theory ◽  
Human Beings ◽  
Computer Data ◽  
Collatz Conjecture

Abstract From a number theory “Collatz conjecture (3X+1)”, Human beings use a large amount of computer data, so far no counterexample has been found. Does mathematical logic support " Collatz conjecture (3X+1)? Collatz conjecture (3X+1) There is a hidden theorem ω1 : If x holds, it must be (3X+1). In reality, human beings will only (3X+1) deduce that x holds.Example: an integer a, and a = 3b +1, b∈N. If b→3x +1 holds. There must be: a→3x +1 is established.In this way, there is no need to deduce (3b + 1).

scholarly journals Big Data System for Medical Images Analysis

2020 ◽  
Author(s):  
Janusz Bobulski ◽  
Mariusz Kubanek
Keyword(s):  
Big Data ◽  
Medical Images ◽  
Processing System ◽  
Large Data ◽  
Data Systems ◽  
Computer Data ◽  
Fast Processing ◽  
Big Data Systems

Big Data in medicine contains conceivably fast processing of large data volumes, alike new and old in perseverance associate the diagnosis and treatment of patients’ diseases. Backing systems for that kind activities may include pre-programmed rules based on data obtained from the medical interview, and automatic analysis of test diagnostic results will lead to classification of observations to a specific disease entity. The current revolution using Big Data significantly expands the role of computer science in achieving these goals, which is why we propose a computer data processing system using artificial intelligence to analyse and process medical images. We conducted research that confirms the need to use GPUs in Big Data systems that process medical images. The use of this type of processor increases system performance.

scholarly journals An Investigation on the Logical Structure of Mathematics (IV): Compendium for Deductions

1958 ◽  
Vol 13 ◽  
pp. 123-133
Author(s):  
Sigekatu Kuroda
Keyword(s):  
Logical Structure ◽  
Sufficient Condition ◽  
Mechanical Parts ◽  
Mathematical Problems ◽  
Way Of Thinking

In § 1 the usage and conventions which are used in the deductions in UL are explained. In §§ 2-4 some metatheorems concerning the deductions are proved. Namely, in § 2 the order of proof constituents in a proof is investigated; in § 3 the applicability of composite proof constituents are proved on the basis of § 2; in §4 the place of the “ordinarily used” principle of extensionality in a proof is specified. In §5 a sufficient condition of the mechanization of mathematics is given in such a manner that the mechanical and non-mechanical parts in solving mathematical problems are separated in accord with the usual way of thinking in mathematics.

scholarly journals The weak law of large numbers for nonnegative summands

2018 ◽  
Vol 50 (A) ◽  
pp. 241-252
Author(s):  
Eugene Seneta
Keyword(s):  
Branching Process ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Sufficient Condition ◽  
Specific Function ◽  
Slowly Varying Function ◽  
Necessary And Sufficient Condition ◽  
Large Numbers ◽  
Norming Sequence ◽  
Necessary And Sufficient

Abstract Khintchine's (necessary and sufficient) slowly varying function condition for the weak law of large numbers (WLLN) for the sum of n nonnegative, independent and identically distributed random variables is used as an overarching (sufficient) condition for the case that the number of summands is more generally [cn],cn→∞. Either the norming sequence {an},an→∞, or the number of summands sequence {cn}, can be chosen arbitrarily. This theorem generalizes results from a motivating branching process setting in which Khintchine's sufficient condition is automatically satisfied. A second theorem shows that Khintchine's condition is necessary for the generalized WLLN when it holds with cn→∞ and an→∞. Theorem 3, which is known, gives a necessary and sufficient condition for Khintchine's WLLN to hold with cn=n and an a specific function of n; it is extended to general cn subject to a growth restriction in Theorem 4. Section 6 returns to the branching process setting.

Sign in / Sign up

Export Citation Format

Share Document