cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.3408058
title: Statistics of Primes (and Probably Twin Primes) Satisfy Taylor's Law from Ecology

description: Taylor's law, which originated in ecology, states that, in sets of measurements of population density, the sample variance is approximately proportional to a power of the sample mean. Taylor's law has been verified for many species ranging from bacterial to human. Here, we show that the variance <i>V</i>(<i>x</i>) and the mean <i>M</i>(<i>x</i>) of the primes not exceeding a real number <i>x</i> obey Taylor's law asymptotically for large <i>x</i>. Specifically, <i>V</i>(<i>x</i>) ∼ (1/3)(<i>M</i>(<i>x</i>))<sup>2</sup> as <i>x</i> → ∞. This apparently new fact about primes shows that Taylor's law may arise in the absence of biological processes, and that patterns discovered in biological data can suggest novel questions in number theory. If the Hardy-Littlewood twin primes conjecture is true, then the identical Taylor's law holds also for twin primes. Taylor's law holds in both instances because the primes (and the twin primes, given the conjecture) not exceeding <i>x</i> are asymptotically uniformly distributed on the integers in [2, <i>x</i>]. Hence, asymptotically <i>M</i>(<i>x</i>) ∼ <i>x</i>/2, <i>V</i>(<i>x</i>) ∼ <i>x</i><sup>2</sup>/12. Higher-order moments of the primes (twin primes) not exceeding <i>x</i> satisfy a generalized Taylor's law. The 11,078,937 primes and 813,371 twin primes not exceeding 2 × 10<sup>8</sup> illustrate these results.
DOI: 10.6084/m9.figshare.3408058.v1
title: Statistics of Primes (and Probably Twin Primes) Satisfy Taylor's Law from Ecology

description: Taylor's law, which originated in ecology, states that, in sets of measurements of population density, the sample variance is approximately proportional to a power of the sample mean. Taylor's law has been verified for many species ranging from bacterial to human. Here, we show that the variance <i>V</i>(<i>x</i>) and the mean <i>M</i>(<i>x</i>) of the primes not exceeding a real number <i>x</i> obey Taylor's law asymptotically for large <i>x</i>. Specifically, <i>V</i>(<i>x</i>) ∼ (1/3)(<i>M</i>(<i>x</i>))<sup>2</sup> as <i>x</i> → ∞. This apparently new fact about primes shows that Taylor's law may arise in the absence of biological processes, and that patterns discovered in biological data can suggest novel questions in number theory. If the Hardy-Littlewood twin primes conjecture is true, then the identical Taylor's law holds also for twin primes. Taylor's law holds in both instances because the primes (and the twin primes, given the conjecture) not exceeding <i>x</i> are asymptotically uniformly distributed on the integers in [2, <i>x</i>]. Hence, asymptotically <i>M</i>(<i>x</i>) ∼ <i>x</i>/2, <i>V</i>(<i>x</i>) ∼ <i>x</i><sup>2</sup>/12. Higher-order moments of the primes (twin primes) not exceeding <i>x</i> satisfy a generalized Taylor's law. The 11,078,937 primes and 813,371 twin primes not exceeding 2 × 10<sup>8</sup> illustrate these results.
DOI: 10.6084/m9.figshare.3408055
title: Computation of Two- and Three-Dimensional Confidence Regions With the Likelihood Ratio

description: The asymptotic results pertaining to the distribution of the log-likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two- and three-dimensional regions can be displayed visually to describe the plausible region of the parameters of interest simultaneously. While most advanced statistical textbooks on inference discuss these asymptotic confidence regions, there is no exploration of how to numerically compute these regions for graphical purposes. This article demonstrates the application of a simple trigonometric transformation to compute two- and three-dimensional confidence regions; we transform the Cartesian coordinates of the parameters to create what we call the radial profile log-likelihood. The method is applicable to any distribution with a defined likelihood function, so it is not limited to specific data distributions or model paradigms. We describe the method along with the algorithm, follow with an example of our method, and end with an examination of computation time. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.3408055.v2
title: Computation of Two- and Three-Dimensional Confidence Regions With the Likelihood Ratio

description: The asymptotic results pertaining to the distribution of the log-likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two- and three-dimensional regions can be displayed visually to describe the plausible region of the parameters of interest simultaneously. While most advanced statistical textbooks on inference discuss these asymptotic confidence regions, there is no exploration of how to numerically compute these regions for graphical purposes. This article demonstrates the application of a simple trigonometric transformation to compute two- and three-dimensional confidence regions; we transform the Cartesian coordinates of the parameters to create what we call the radial profile log-likelihood. The method is applicable to any distribution with a defined likelihood function, so it is not limited to specific data distributions or model paradigms. We describe the method along with the algorithm, follow with an example of our method, and end with an examination of computation time. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.3408055.v1
title: <b>Computation of Two and Three Dimensional Confidence Regions with the Likelihood Ratio</b>

description: The asymptotic results pertaining to the distribution of the log likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two and three dimensional regions can be displayed visually in order to describe the plausible region of the parameters of interest simultaneously. While most advanced statistical textbooks on inference discuss these asymptotic confidence regions, there is no exploration of how to numerically compute these regions for graphical purposes. This article demonstrates the application of a simple trigonometric transformation to compute two and three dimensional confidence regions; we transform the Cartesian coordinates of the parameters to create what we call the radial profile log likelihood. The method is applicable to any distribution with a defined likelihood function, so it is not limited to specific data distributions or model paradigms. We describe the method along with the algorithm, follow with an example of our method and end with an examination of computation time.
DOI: 10.6084/m9.figshare.3408052
title: Excel Templates: A Helpful Tool for Teaching Statistics

description: This article describes a free, open-source collection of templates for the popular Excel (2013, and later versions) spreadsheet program. These templates are spreadsheet files that allow easy and intuitive learning and the implementation of practical examples concerning descriptive statistics, random variables, confidence intervals, and hypothesis testing. Although they are designed to be used with Excel, they can also be employed with other free spreadsheet programs (changing some particular formulas). Moreover, we exploit some possibilities of the ActiveX controls of the Excel Developer Menu to perform interactive Gaussian density charts. Finally, it is important to note that they can be often embedded in a web page, so it is not necessary to employ Excel software for their use. These templates have been designed as a useful tool to teach basic statistics and to carry out data analysis even when the students are not familiar with Excel. Additionally, they can be used as a complement to other analytical software packages. They aim to assist students in learning statistics, within an intuitive working environment. Supplementary materials with the Excel templates are available online.
DOI: 10.6084/m9.figshare.3408052.v2
title: Excel Templates: A Helpful Tool for Teaching Statistics

description: This article describes a free, open-source collection of templates for the popular Excel (2013, and later versions) spreadsheet program. These templates are spreadsheet files that allow easy and intuitive learning and the implementation of practical examples concerning descriptive statistics, random variables, confidence intervals, and hypothesis testing. Although they are designed to be used with Excel, they can also be employed with other free spreadsheet programs (changing some particular formulas). Moreover, we exploit some possibilities of the ActiveX controls of the Excel Developer Menu to perform interactive Gaussian density charts. Finally, it is important to note that they can be often embedded in a web page, so it is not necessary to employ Excel software for their use. These templates have been designed as a useful tool to teach basic statistics and to carry out data analysis even when the students are not familiar with Excel. Additionally, they can be used as a complement to other analytical software packages. They aim to assist students in learning statistics, within an intuitive working environment. Supplementary materials with the Excel templates are available online.
DOI: 10.6084/m9.figshare.3408052.v1
title: <b>Excel Templates: A Helpful Tool for Teaching Statistics</b>

description: This paper describes a free, open-source collection of templates for the popular Excel (2013, and later versions) spreadsheet program. These templates are spreadsheet files that allow easy and intuitive learning and the implementation of practical examples concerning descriptive statistics, random variables, confidence intervals, and hypothesis testing. Although they are designed to be used with Excel, they can also be employed with other free spreadsheet programs (changing some particular formulas). Moreover, we exploit some possibilities of the ActiveX controls of the Excel Developer Menu to perform interactive Gaussian density charts. Finally, it is important to note that they can be often embedded in a web page, so it is not necessary to employ Excel software for their use. These templates have been designed as a useful tool to teach basic statistics and to carry out data analysis even when the students are not familiar with Excel. Additionally, they can be used as a complement to other analytical software packages. They aim to assist students in learning statistics, within an intuitive working environment. Supplementary materials with the Excel templates are available online.
DOI: 10.6084/m9.figshare.3408040
title: Nucleosome positioning changes during human embryonic stem cell differentiation

description: Nucleosomes are the basic unit of chromatin. Nucleosome positioning (NP) plays a key role in transcriptional regulation and other biological processes. To better understand NP we used MNase-seq to investigate changes that occur as human embryonic stem cells (hESCs) transition to nascent mesoderm and then to smooth muscle cells (SMCs). Compared to differentiated cell derivatives, nucleosome occupancy at promoters and other notable genic sites, such as exon/intron junctions and adjacent regions, in hESCs shows a stronger correlation with transcript abundance and is less influenced by sequence content. Upon hESC differentiation, genes being silenced, but not genes being activated, display a substantial change in nucleosome occupancy at their promoters. Genome-wide, we detected a shift of NP to regions of higher G+C content as hESCs differentiate to SMCs. Notably, genomic regions with higher nucleosome occupancy harbor twice as many G↔C changes but fewer than half A↔T changes, compared to regions with lower nucleosome occupancy. Finally, our analysis indicates that the hESC genome is not rearranged and has a sequence mutation rate resembling normal human genomes. Our study reveals another unique feature of hESC chromatin, and sheds light on the relationship between nucleosome occupancy and sequence G+C content.
DOI: 10.6084/m9.figshare.3408040.v2
title: Nucleosome positioning changes during human embryonic stem cell differentiation

description: Nucleosomes are the basic unit of chromatin. Nucleosome positioning (NP) plays a key role in transcriptional regulation and other biological processes. To better understand NP we used MNase-seq to investigate changes that occur as human embryonic stem cells (hESCs) transition to nascent mesoderm and then to smooth muscle cells (SMCs). Compared to differentiated cell derivatives, nucleosome occupancy at promoters and other notable genic sites, such as exon/intron junctions and adjacent regions, in hESCs shows a stronger correlation with transcript abundance and is less influenced by sequence content. Upon hESC differentiation, genes being silenced, but not genes being activated, display a substantial change in nucleosome occupancy at their promoters. Genome-wide, we detected a shift of NP to regions of higher G+C content as hESCs differentiate to SMCs. Notably, genomic regions with higher nucleosome occupancy harbor twice as many G↔C changes but fewer than half A↔T changes, compared to regions with lower nucleosome occupancy. Finally, our analysis indicates that the hESC genome is not rearranged and has a sequence mutation rate resembling normal human genomes. Our study reveals another unique feature of hESC chromatin, and sheds light on the relationship between nucleosome occupancy and sequence G+C content.
DOI: 10.6084/m9.figshare.3408040.v1
title: Nucleosome positioning changes during human embryonic stem cell differentiation

description: Nucleosomes are the basic unit of chromatin. Nucleosome positioning (NP) plays a key role in transcriptional regulation and other biological processes. To better understand NP we used MNase-seq to investigate changes that occur as human embryonic stem cells (hESCs) transition to nascent mesoderm and then to smooth muscle cells (SMCs). Compared to differentiated cell derivatives, nucleosome occupancy at promoters and other notable genic sites, such as exon/intron junctions and adjacent regions, in hESCs shows a stronger correlation with transcript abundance and is less influenced by sequence content. Upon hESC differentiation, genes being silenced, but not genes being activated, display a substantial change in nucleosome occupancy at their promoters. Genome-wide, we detected a shift of NP to regions of higher G+C content as hESCs differentiate to SMCs. Notably, genomic regions with higher nucleosome occupancy harbor twice as many G↔C changes but fewer than half A↔T changes, compared to regions with lower nucleosome occupancy. Finally, our analysis indicates that the hESC genome is not rearranged and has a sequence mutation rate resembling normal human genomes. Our study reveals another unique feature of hESC chromatin, and sheds light on the relationship between nucleosome occupancy and sequence G+C content.
DOI: 10.6084/m9.figshare.3408031
title: Photosynthetic efficiency, temperature induction response, carbon isotope discrimination correlate with expression profiling in Indian wheat cultivars

description: In the backdrop of global warming and increase in temperatures, wheat productivity worldwide would be limited. This study was therefore undertaken to analyze the heat stress response in 12 different cultivars of Indian wheat. Three developmental stages were used i.e. germination stage, seedling stage and anthesis stage, to characterize thermotolerant and thermosusceptible cultivars on the basis of different physiological and molecular parameters. Lethal temperature stress on germinating seeds showed a clear reduction in percentage germination. At the seedling stage, higher decrease in Fv/Fm, total chlorophyll content, membrane injury and carbon isotope discrimination was observed in thermosusceptible cultivars. Results similar to seedling stage were obtained at anthesis stage. PSII efficiency of late-sown cultivars and timely-sown cultivars also indicated that thermosusceptible cultivars are more prone to terminal heat stress than thermotolerant cultivars. Heat Susceptibility Index (HSI) was calculated on the basis of physiological parameters. Based on HSI, thermotolerant and thermosusceptible cultivars were identified. HSI revealed comparatively low heat susceptibility in <i>K7903, CBW12</i> and <i>C306</i> and high heat susceptibility in <i>PBW343, HD2329</i> and <i>HD2428</i>. On the basis of HSI, expression analysis of stress induced genes was performed between 2 tolerant cultivars <i>C306</i> and <i>K7903</i> along with 2 susceptible cultivars, <i>HD2329</i> and <i>PBW343</i>. Higher expression of stress induced genes was observed in the 2 thermotolerant cultivars <i>C306</i> and <i>K7903</i> as compared to the 2 thermosusceptible cultivars <i>HD2329</i> and <i>PBW343</i>. Thus further reconfirms that stress inducible genes can be employed for categorizing cultivars into susceptible and tolerant groups.
DOI: 10.6084/m9.figshare.3408031.v2
title: Photosynthetic efficiency, temperature induction response, carbon isotope discrimination correlate with expression profiling in Indian wheat cultivars

description: In the backdrop of global warming and increase in temperatures, wheat productivity worldwide would be limited. This study was therefore undertaken to analyze the heat stress response in 12 different cultivars of Indian wheat. Three developmental stages were used i.e. germination stage, seedling stage and anthesis stage, to characterize thermotolerant and thermosusceptible cultivars on the basis of different physiological and molecular parameters. Lethal temperature stress on germinating seeds showed a clear reduction in percentage germination. At the seedling stage, higher decrease in Fv/Fm, total chlorophyll content, membrane injury and carbon isotope discrimination was observed in thermosusceptible cultivars. Results similar to seedling stage were obtained at anthesis stage. PSII efficiency of late-sown cultivars and timely-sown cultivars also indicated that thermosusceptible cultivars are more prone to terminal heat stress than thermotolerant cultivars. Heat Susceptibility Index (HSI) was calculated on the basis of physiological parameters. Based on HSI, thermotolerant and thermosusceptible cultivars were identified. HSI revealed comparatively low heat susceptibility in <i>K7903, CBW12</i> and <i>C306</i> and high heat susceptibility in <i>PBW343, HD2329</i> and <i>HD2428</i>. On the basis of HSI, expression analysis of stress induced genes was performed between 2 tolerant cultivars <i>C306</i> and <i>K7903</i> along with 2 susceptible cultivars, <i>HD2329</i> and <i>PBW343</i>. Higher expression of stress induced genes was observed in the 2 thermotolerant cultivars <i>C306</i> and <i>K7903</i> as compared to the 2 thermosusceptible cultivars <i>HD2329</i> and <i>PBW343</i>. Thus further reconfirms that stress inducible genes can be employed for categorizing cultivars into susceptible and tolerant groups.
DOI: 10.6084/m9.figshare.3408031.v1
title: Photosynthetic Efficiency, Temperature Induction Response, Carbon Isotope Discrimination correlate with Expression Profiling in Indian wheat cultivars

description: In the backdrop of global warming and increase in temperatures, wheat productivity worldwide would be limited. This study was therefore undertaken to analyze the heat stress response in twelve different cultivars of Indian wheat. Three developmental stages were used i.e. germination stage, seedling stage and anthesis stages, to characterize thermotolerant and thermosusceptible cultivars on the basis of different physiological and molecular parameters. Lethal temperature stress on germinating seeds showed a clear reduction in percentage germination. At the seedling stage, higher decrease in Fv/Fm, total chlorophyll content, membrane injury and carbon isotope discrimination was observed in thermosusceptible cultivars. Results similar to seedling stage were obtained at anthesis stage. PSII efficiency of late-sown cultivars and timely-sown cultivars also indicated that thermosusceptible cultivars are more prone to terminal heat stress than thermotolerant cultivars. Heat Susceptibility Index (HSI) was calculated on the basis of physiological parameters. Based on HSI, thermotolerant and thermosusceptible cultivars were identified. HSI revealed comparatively low heat susceptibility in <i>K7903, CBW12</i> and <i>C306</i> and high heat susceptibility <i>PBW343, HD2329</i> and <i>HD2428</i>. On the basis of HSI, expression analysis of stress induced genes was performed between two tolerant cultivars <i>C306</i> and <i>K7903</i> along with two susceptible cultivars, <i>HD2329</i> and <i>PBW343</i>. Higher expression of stress induced genes was observed in the two thermotolerant cultivars <i>C306</i> and <i>K7903</i> as compared to the two thermosusceptible cultivars <i>HD2329</i> and <i>PBW343</i>. Thus further reconfirms that stress inducible genes can be employed for categorizing cultivars into susceptible and tolerant groups.
DOI: 10.6084/m9.figshare.3408022
title: Aberrant DNA methylation of WNT pathway genes in the development and progression of CIMP-negative colorectal cancer

description: The WNT signaling pathway has an essential role in colorectal carcinogenesis and progression, which involves a cascade of genetic and epigenetic changes. We aimed to analyze DNA methylation affecting the WNT pathway genes in colorectal carcinogenesis in promoter and gene body regions using whole methylome analysis in 9 colorectal cancer, 15 adenoma, and 6 normal tumor adjacent tissue (NAT) samples by methyl capture sequencing. Functional methylation was confirmed on 5-aza-2′-deoxycytidine-treated colorectal cancer cell line datasets. In parallel with the DNA methylation analysis, mutations of WNT pathway genes (<i>APC</i>, β-catenin/<i>CTNNB1</i>) were analyzed by 454 sequencing on GS Junior platform. Most differentially methylated CpG sites were localized in gene body regions (95% of WNT pathway genes). In the promoter regions, 33 of the 160 analyzed WNT pathway genes were differentially methylated in colorectal cancer vs. normal, including hypermethylated <i>AXIN2, CHP1, PRICKLE1, SFRP1, SFRP2, SOX17</i>, and hypomethylated <i>CACYBP, CTNNB1, MYC</i>; 44 genes in adenoma vs. NAT; and 41 genes in colorectal cancer vs. adenoma comparisons. Hypermethylation of <i>AXIN2, DKK1, VANGL1</i>, and <i>WNT5A</i> gene promoters was higher, while those of <i>SOX17, PRICKLE1, DAAM2</i>, and <i>MYC</i> was lower in colon carcinoma compared to adenoma. Inverse correlation between expression and methylation was confirmed in 23 genes, including <i>APC, CHP1, PRICKLE1, PSEN1</i>, and <i>SFRP1</i>. Differential methylation affected both canonical and noncanonical WNT pathway genes in colorectal normal-adenoma-carcinoma sequence. Aberrant DNA methylation appears already in adenomas as an early event of colorectal carcinogenesis.