Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Datasets on the statistical properties of the first 3000 squared positive integers.

ABSTRACT: The data in this article are as a result of a quest to uncover alternative research routes of deepening researchers' understanding of integers apart from the traditional number theory approach. Hence, the article contains the statistical properties of the digits sum of the first 3000 squared positive integers. The data describes the various statistical tools applied to reveal different statistical and random nature of the digits sum of the first 3000 squared positive integers. Digits sum here implies the sum of all the digits that make up the individual integer.

SUBMITTER: Okagbue HI

PROVIDER: S-EPMC5647521 | biostudies-literature | 2017 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Datasets on the statistical properties of the first 3000 squared positive integers.

Okagbue Hilary I HI Adamu Muminu O MO Oguntunde Pelumi E PE Opanuga Abiodun A AA Adebiyi Ayodele A AA Bishop Sheila A SA

Data in brief 20171006

The data in this article are as a result of a quest to uncover alternative research routes of deepening researchers' understanding of integers apart from the traditional number theory approach. Hence, the article contains the statistical properties of the digits sum of the first 3000 squared positive integers. The data describes the various statistical tools applied to reveal different statistical and random nature of the digits sum of the first 3000 squared positive integers. Digits sum here im ...[more]

PMID: 29062870

Similar Datasets

Datasets on the statistical and algebraic properties of primitive Pythagorean triples.

Project description:The data in this article was obtained from the algebraic and statistical analysis of the first 331 primitive Pythagorean triples. The ordered sample is a subset of the larger Pythagorean triples. A primitive Pythagorean triple consists of three integers a, b and c such that; [Formula: see text]. A primitive Pythagorean triple is one which the greatest common divisor (gcd), that is; [Formula: see text] or a, b and c are coprime, and pairwise coprime. The dataset describe the various algebraic and statistical manipulations of the integers a, b and c that constitute the primitive Pythagorean triples. The correlation between the integers at each analysis was included. The data analysis of the non-normal nature of the integers was also included in this article. The data is open to criticism, adaptation and detailed extended analysis.

| S-EPMC5596336 | biostudies-literature

Scaling statistical multiple sequence alignment to large datasets.

Project description:BackgroundMultiple sequence alignment is an important task in bioinformatics, and alignments of large datasets containing hundreds or thousands of sequences are increasingly of interest. While many alignment methods exist, the most accurate alignments are likely to be based on stochastic models where sequences evolve down a tree with substitutions, insertions, and deletions. While some methods have been developed to estimate alignments under these stochastic models, only the Bayesian method BAli-Phy has been able to run on even moderately large datasets, containing 100 or so sequences. A technique to extend BAli-Phy to enable alignments of thousands of sequences could potentially improve alignment and phylogenetic tree accuracy on large-scale data beyond the best-known methods today.ResultsWe use simulated data with up to 10,000 sequences representing a variety of model conditions, including some that are significantly divergent from the statistical models used in BAli-Phy and elsewhere. We give a method for incorporating BAli-Phy into PASTA and UPP, two strategies for enabling alignment methods to scale to large datasets, and give alignment and tree accuracy results measured against the ground truth from simulations. Comparable results are also given for other methods capable of aligning this many sequences.ConclusionsExtensions of BAli-Phy using PASTA and UPP produce significantly more accurate alignments and phylogenetic trees than the current leading methods.

| S-EPMC5123300 | biostudies-literature

On the statistical properties of family-based association tests in datasets containing both pedigrees and unrelated case-control samples.

Project description:A common approach to genetic mapping of loci for complex diseases is to perform a genome-wide association study (GWAS) by analyzing a vast number of SNP markers in cohorts of unrelated cases and controls. A direct motivation for the case-control design is that unrelated, affected individuals can be easier to collect than large families with multiple affected persons in the Western world. Despite its higher potential power, investigators have not actively pursued family ascertainment in part because of a dearth of methods for analyzing such correlated data on a large scale. We examine the statistical properties of several commonly used family-based association tests, as to their performance using real-life mixtures of families and singletons taken from our own migraine and schizophrenia studies, as well as population-based data for a complex trait simulated with the evolutionary phenogenetic simulator, ForSim. In virtually every situation, the full likelihood-based methods in the PSEUDOMARKER program outperformed those implemented in FBAT, GENEHUNTER TDT, PLINK (family-based options), HRR/HHRR, QTDT, TRANSMIT, UNPHASED, MENDEL, and LAMP. We further show that GWAS is much more powerful when family samples are used rather than unrelateds, on a genotype-by-genotype basis.

| S-EPMC3260916 | biostudies-literature

Statistical Inference Models for Image Datasets with Systematic Variations.

Project description:Statistical analysis of longitudinal or cross sectional brain imaging data to identify effects of neurodegenerative diseases is a fundamental task in various studies in neuroscience. However, when there are systematic variations in the images due to parameter changes such as changes in the scanner protocol, hardware changes, or when combining data from multi-site studies, the statistical analysis becomes problematic. Motivated by this scenario, the goal of this paper is to develop a unified statistical solution to the problem of systematic variations in statistical image analysis. Based in part on recent literature in harmonic analysis on diffusion maps, we propose an algorithm which compares operators that are resilient to the systematic variations. These operators are derived from the empirical measurements of the image data and provide an efficient surrogate to capturing the actual changes across images. We also establish a connection between our method to the design of wavelets in non-Euclidean space. To evaluate the proposed ideas, we present various experimental results on detecting changes in simulations as well as show how the method offers improved statistical power in the analysis of real longitudinal PIB-PET imaging data acquired from participants at risk for Alzheimer's disease (AD).

| S-EPMC4792194 | biostudies-literature

Design-based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator.

Project description:Nearest neighbor spatial interpolation for mapping continuous populations and finite populations of areas or units is approached from a design-based perspective, that is, populations are fixed, and uncertainty stems from the sampling scheme adopted to select locations. We derive conditions for design-based pointwise and uniform consistency of the nearest neighbor interpolators. We prove that consistency holds under certain schemes that are widely applied in environmental and forest surveys. Furthermore, we propose a pseudopopulation bootstrap estimator of the root mean squared errors of the interpolated values. Finally, a simulation study is performed to assess the theoretical results.

| S-EPMC10078774 | biostudies-literature

Datasets on the elastic and mechanical properties of hydroxyapatite: A first principle investigation, experiments, and pedagogical perspective.

Project description:The purpose of this data article is to report the quantum mechanical analysis by generalized gradient approximation (GGA) exchange-correlation functional using density functional theory (DFT). The predictions were based on the elastic constants and mechanical properties of stoichiometric hydroxyapatite (HAp) crystal. The elastic stiffness constants in hexagonal symmetry were obtained by fitting the Hookes' law for the energy-strain and stress-stain relations. Some of the theoretical datasets were compared to measured mechanical properties of produced HAp pellets obtained through micro and nanoindentation experiments. The datasets show considerable anisotropy in the stress-strain behaviour and are discussed in the context of the mechanical properties of HAp which are useful for tissue engineering. We also provide a pedagogical snapshot on the use of the datasets herein to teach and interpret DFT based atomistic simulations in a typical blended online teaching set-up for engineering students using a new pedagogy, CACPLA (Communicate, Active, Collaborate, Practice, Learning and Assessment).

| S-EPMC10068552 | biostudies-literature

Optimal strategy for linkage of datasets containing a statistical linkage key and datasets with full personal identifiers.

Project description:BackgroundLinkage of aged care and hospitalisation data provides valuable information on patterns of health service utilisation among aged care service recipients. Many aged care datasets in Australia contain a Statistical Linkage Key (SLK-581) instead of full personal identifiers. We linked hospital and death records using a full probabilistic strategy, the SLK-581, and three combined strategies; and compared results for each strategy.MethodsLinkage of Admitted Patient Data for 2000-01 to 2008-09 and Registry of Births, Deaths and Marriages death registration data for 2008-09 for New South Wales, Australia, was carried out using probabilistic methods and compared to links created using four strategies incorporating a SLK-581. The Basic SLK-581 strategy used the SLK-581 alone. The Most Recent SLK-581, Most Frequent SLK-581, and Any Match SLK-581 strategies leveraged probabilistic links between hospital records drawn from the Centre for Health Record Linkage Master Linkage Key. Rates of hospitalisations among people who died were calculated for each strategy and a range of health conditions.ResultsCompared to full probabilistic linkage, the basic SLK-581 strategy produced substantial rates of missed links that increased over the study period and produced underestimates of hospitalisation rates that varied by health condition. The Most Recent SLK-581, Most Frequent SLK-581, and Any Match SLK-581 strategies resulted in substantially lower rates of underestimation than the Basic SLK-581. The Any Match SLK-581 strategy gave results closest to full probabilistic linkage.ConclusionsHospitalisation rates prior to death are substantially underestimated by linkage using a SLK-581 alone. Linkage rates can be increased by combining deterministic methods with probabilistically created links across hospital records.

| S-EPMC4236530 | biostudies-literature

Generalized R-squared for detecting dependence.

Project description:Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared statistic is almost identical to the square of the Pearson correlation coefficient, R-squared, for linear relationships with constant error variance, and has the intuitive meaning of the piecewise R-squared between the variables. It is particularly effective in handling nonlinearity and heteroscedastic errors. We propose two estimators of G-squared and show their consistency. Simulations demonstrate that G-squared estimators are among the most powerful test statistics compared with several state-of-the-art methods.

| S-EPMC5793683 | biostudies-literature

Statistical properties of sketching algorithms.

Project description:Sketching is a probabilistic data compression technique that has been largely developed by the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a smaller surrogate dataset. Typically, inference proceeds on the compressed dataset. Sketching algorithms generally use random projections to compress the original dataset, and this stochastic generation process makes them amenable to statistical analysis. We argue that the sketched data can be modelled as a random sample, thus placing this family of data compression methods firmly within an inferential framework. In particular, we focus on the Gaussian, Hadamard and Clarkson-Woodruff sketches and their use in single-pass sketching algorithms for linear regression with huge samples. We explore the statistical properties of sketched regression algorithms and derive new distributional results for a large class of sketching estimators. A key result is a conditional central limit theorem for data-oblivious sketches. An important finding is that the best choice of sketching algorithm in terms of mean squared error is related to the signal-to-noise ratio in the source dataset. Finally, we demonstrate the theory and the limits of its applicability on two datasets.

| S-EPMC7612324 | biostudies-literature

Statistical Shape Analysis of Large Datasets Based on Diffeomorphic Iterative Centroids.

Project description:In this paper, we propose an approach for template-based shape analysis of large datasets, using diffeomorphic centroids as atlas shapes. Diffeomorphic centroid methods fit in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework and use kernel metrics on currents to quantify surface dissimilarities. The statistical analysis is based on a Kernel Principal Component Analysis (Kernel PCA) performed on the set of initial momentum vectors which parametrize the deformations. We tested the approach on different datasets of hippocampal shapes extracted from brain magnetic resonance imaging (MRI), compared three different centroid methods and a variational template estimation. The largest dataset is composed of 1,000 surfaces, and we are able to analyse this dataset in 26 h using a diffeomorphic centroid. Our experiments demonstrate that computing diffeomorphic centroids in place of standard variational templates leads to similar shape analysis results and saves around 70% of computation time. Furthermore, the approach is able to adequately capture the variability of hippocampal shapes with a reasonable number of dimensions, and to predict anatomical features of the hippocampus, only present in 17% of the population, in healthy subjects.

| S-EPMC6241313 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data