The perfection ratio of a number is a concept that is related to perfect numbers and how closely a given number approximates the ideal perfection ratio, which is 2.0.

Perfect Numbers:

A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding the number itself. For example: • 6 is a perfect number because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6 . • 28 is another perfect number because its divisors are 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28 .

Perfection Ratio:

The perfection ratio of a number n is a measure of how close the sum of its divisors (excluding the number itself) is to the number. It is defined as:

\text{Perfection Ratio} = \frac{\text{Sum of Proper Divisors of } n}{n}

•  If the perfection ratio is 2.0, the number is considered perfect.
•  If the perfection ratio is greater than 2.0, the number is abundant (i.e., the sum of its proper divisors exceeds the number itself).
•  If the perfection ratio is less than 2.0, the number is deficient (i.e., the sum of its proper divisors is less than the number itself).

Examples:

1. Perfect Number Example:
•  For n = 6 :
•  Proper divisors: 1, 2, 3 
•  Sum of proper divisors: 1 + 2 + 3 = 6 
•  Perfection ratio: \frac{6}{6} = 1.0 
•  Since the perfection ratio is 2.0 for a perfect number, we see the idea of perfect numbers where the sum of divisors divides evenly.

1. Near-Perfect Numbers

• Definition: A near-perfect number is a number for which the sum of its proper divisors is close to the number itself but not exactly equal.
• Example: Consider the number 24. Its proper divisors are 1, 2, 3, 4, 6, 8, and 12. The sum is 36, which is larger than 24, making it almost perfect in the sense that the sum of its divisors is significant but not equal to the number.

2. Almost-Perfect Numbers

• Definition: An almost-perfect number is a number where the sum of its proper divisors equals the number minus one.
• Example: The number 16 is an almost-perfect number. Its proper divisors are 1, 2, 4, and 8, which sum to 15 (16 - 1).

3. Abundant Numbers

• Definition: A number is abundant if the sum of its proper divisors is greater than the number itself.
• Example: The number 12 is abundant because its proper divisors (1, 2, 3, 4, and 6) sum to 16, which is greater than 12.

4. Deficient Numbers

• Definition: A number is deficient if the sum of its proper divisors is less than the number itself.
• Example: The number 8 is deficient because its proper divisors (1, 2, and 4) sum to 7, which is less than 8.

5. Semiperfect Numbers

• Definition: A semiperfect number is a number that is equal to the sum of some (or all) of its proper divisors.
• Example: The number 12 is semiperfect because 12 = 6 + 4 + 2 (some of its proper divisors).

Relevance to the Heat Map

• Density Analysis: By analyzing the heat map further, we might observe concentrations at other specific perfection ratios besides 2. These could indicate near-perfect, almost-perfect, abundant, deficient, or semiperfect numbers.
• Patterns and Trends: Identifying where these numbers cluster can help us understand the distribution and frequency of numbers with these properties within your dataset.

The model contains a fixed effect for period and a random effect for district (n = 15).

This is a sample dataset for the Biodemography Workshop. Within this dataset, input files related to demographic statistics will be considered, specifically population by gender and by Nuts2 in Italy, as well as shapefiles for map creation. The variables to be analyzed include the ratio between male and female, and vice versa. The final output consists of two maps. The data source is Istat, which provides these with a CC BY license: 1-https://demo.istat.it/app/?i=POS&l=it 2-https://www.istat.it/it/archivio/222527 To conduct the analysis, the open-source software R-Studio was used. The data management methodology will also be outlined in a Data Management Plan, written using Overleaf, in which we will provide more detailed information.

Graph and download economic data for Retailers: Inventories to Sales Ratio (RETAILIRSA) from Jan 1992 to Aug 2025 about ratio, inventories, sales, retail, and USA.

In order to understand the provenance of lead in the surface water, groundwater, soils, and shallow pore water within and near the Middleton Municipal Airport–Morey Field (C29) in Middleton, WI, a subset of samples were sent to the Wisconsin State Lab of Hygiene for analysis. The results of these analyses are included in this data release and include both low-level lead concentrations and lead isotope ratios. Also included in this data release are lead isotope ratios from a number of environmental and historical reference samples that help contextualize the lead isotope ratios found within and near the Middleton Municipal Airport.

The model contains a fixed effect for treatment and a random effect for pens (n = 24) nested within rooms (n = 2).

This dataset provides calculated age of air (AoA) and the argon/nitrogen (Ar/N2) ratio (per meg) from stratospheric flask samples and simultaneous high-frequency measurements of nitrous oxide (N2O), carbon dioxide (CO2), ozone (O3), methane (CH4), and carbon monoxide (CO) compiled from three airborne projects. The trace gases were used to identify 235 flask samples with stratospheric influence collected by the Medusa Whole Air Sampler and to calculate AoA using a new N2O-AoA relationship developed using a Markov Chain Monte Carlo algorithm. The data span a wide range of latitudes poleward of 40 degrees in both the Northern and Southern Hemispheres and cover the period 2009-01-10 to 2018-05-21.

We compare percentages present in the true labels of the real data and the predicted labels. Analogously, we measure the ratio of samples with positive label present in the synthetic generated data and predicted labels for datasets generated using distinct synthesizer techniques. Predictions(R) represents ratio of positive prediction labels of an experiment where model trained on synthetic data was evaluated on real data, and Predictions(S) ratio of positive prediction labels of an experiment where model trained on synthetic data was evaluated on synthetic data.

YouTube Video and Channel Analysis

YouTube Video and Channel Statistics

By VISHWANATH SESHAGIRI [source]

About this dataset

This dataset contains valuable information about YouTube videos and channels, including various metrics related to views, likes, dislikes, comments, and other related statistics. The dataset consists of 9 direct features and 13 indirect features. The direct features include the ratio of comments on a video to the number of views on the video (comments/views), the total number of subscribers of the channel (subscriberCount), the ratio of likes on a video to the number of subscribers of the channel (likes/subscriber), the total number of views on the channel (channelViewCount), and several other informative ratios such as views/elapsedtime, totalviews/channelelapsedtime, comments/subscriber, views/subscribers, dislikes/subscriber.

The dataset also includes indirect features that are derived from YouTube's API. These indirect features provide additional insights into videos and channels by considering factors such as dislikes/views ratio, channelCommentCount (total number of comments on the channel), likes/dislikes ratio, totviews/totsubs ratio (total views on a video to total subscribers of a channel), and more.

The objective behind analyzing this dataset is to establish statistical relationships between videos and channels within YouTube. Furthermore, this analysis aims to form a topic tree based on these statistical relations.

For further exploration or utilization purposes beyond this dataset description document itself, you can refer to relevant repositories such as the GitHub repository associated with this dataset where you might find useful resources that complement or expand upon what is available in this dataset.

Overall,this comprehensive collection provides diverse insights into YouTube video and channel metadata for conducting statistical analyses in order to better understand viewer engagement patterns varies parameters across different channels. With its range from basic counts like subscriber counts,counting no.of viewership per minute , timing vs viewership rate ,text related user responses etc.,this detailed Youtube Dataset will assist in making informed decisions regarding channel optimization,more effective targeting and creation of content that will appeal to the target audience

How to use the dataset

This dataset provides valuable information about YouTube videos and their corresponding channels. With this data, you can perform statistical analysis to gain insights into various aspects of YouTube video and channel performance. Here is a guide on how to effectively use this dataset for your analysis:

• Understanding the Columns:
  • totalviews/channelelapsedtime: The ratio of total views of a video to the elapsed time of the channel.
  • channelViewCount: The total number of views on the channel.
  • likes/subscriber: The ratio of likes on a video to the number of subscribers of the channel.
  • views/subscribers: The ratio of views on a video to the number of subscribers of the channel.
  • subscriberCount: The total number of subscribers of the channel.
  • dislikes/views: The ratio

Research Ideas

• Predicting the popularity of YouTube videos: By analyzing the various ratios and metrics in this dataset, such as comments/views, likes/subscriber, and views/subscribers, one can build predictive models to estimate the popularity or engagement level of YouTube videos. This can help content creators or businesses understand which types of videos are likely to be successful and tailor their content accordingly.
• Analyzing channel performance: The dataset provides information about the total number of views on a channel (channelViewCount), the number of subscribers (subscriberCount), and other related statistics. By examining metrics like views/elapsedtime and totalviews/channelelapsedtime, one can assess how well a channel is performing over time. This analysis can help content creators identify trends or patterns in their viewership and make informed decisions about their video strategies.
• Understanding audience engagement: Ratios like comments/subscriber, likes/dislikes, dislikes/subscriber provide insights into how engaged a channel's subscribers are with its content. By examining these ratios across multiple videos or channels, one can identify trends in audience behavior and preferences. For example, a high ratio of comments/subscriber may indicate strong community participation and active discussion around the videos posted by a particular YouTuber or channel

Acknowledgements

If you use this dataset in y...

DEPTH, sediment/rock [m] is given in mcd. On 2018-06-22 it was noted, that the Ca/Sr ratio was erroneously denoted as Ca/Si ratio in this dataset. This has been corrected.

The Atlantic Tradewind Ocean-Atmosphere Mesoscale Interaction Campaign (ATOMIC) was a field campaign held January-February 2020 in the tropical North Atlantic east of Barbados. The campaign, the U.S. complement to the European field campaign called EUREC4A, was aimed at better understanding cloud and air-sea interaction processes. ATOMIC included measurements from a NOAA WP-3D Orion "Hurricane Hunter" aircraft, NOAA Ship Ronald H. Brown, and unpiloted vehicles launched from Barbados and from NOAA Ship Ronald H. Brown. This dataset consists of rain and seawater isotope ratio data in netCDF files.

About this dataset

Context

The dataset tabulates the population of Rufus by gender across 18 age groups. It lists the male and female population in each age group along with the gender ratio for Rufus. The dataset can be utilized to understand the population distribution of Rufus by gender and age. For example, using this dataset, we can identify the largest age group for both Men and Women in Rufus. Additionally, it can be used to see how the gender ratio changes from birth to senior most age group and male to female ratio across each age group for Rufus.

Key observations

Largest age group (population): Male # 10-14 years (23) | Female # 65-69 years (14). Source: U.S. Census Bureau American Community Survey (ACS) 2019-2023 5-Year Estimates.

Content

When available, the data consists of estimates from the U.S. Census Bureau American Community Survey (ACS) 2019-2023 5-Year Estimates.

Age groups:

• Under 5 years
• 5 to 9 years
• 10 to 14 years
• 15 to 19 years
• 20 to 24 years
• 25 to 29 years
• 30 to 34 years
• 35 to 39 years
• 40 to 44 years
• 45 to 49 years
• 50 to 54 years
• 55 to 59 years
• 60 to 64 years
• 65 to 69 years
• 70 to 74 years
• 75 to 79 years
• 80 to 84 years
• 85 years and over

Scope of gender :

Please note that American Community Survey asks a question about the respondents current sex, but not about gender, sexual orientation, or sex at birth. The question is intended to capture data for biological sex, not gender. Respondents are supposed to respond with the answer as either of Male or Female. Our research and this dataset mirrors the data reported as Male and Female for gender distribution analysis.

Variables / Data Columns

• Age Group: This column displays the age group for the Rufus population analysis. Total expected values are 18 and are define above in the age groups section.
• Population (Male): The male population in the Rufus is shown in the following column.
• Population (Female): The female population in the Rufus is shown in the following column.
• Gender Ratio: Also known as the sex ratio, this column displays the number of males per 100 females in Rufus for each age group.

Good to know

Margin of Error

Data in the dataset are based on the estimates and are subject to sampling variability and thus a margin of error. Neilsberg Research recommends using caution when presening these estimates in your research.

Custom data

If you do need custom data for any of your research project, report or presentation, you can contact our research staff at research@neilsberg.com for a feasibility of a custom tabulation on a fee-for-service basis.

Inspiration

Neilsberg Research Team curates, analyze and publishes demographics and economic data from a variety of public and proprietary sources, each of which often includes multiple surveys and programs. The large majority of Neilsberg Research aggregated datasets and insights is made available for free download at https://www.neilsberg.com/research/.

Recommended for further research

This dataset is a part of the main dataset for Rufus Population by Gender. You can refer the same here

Annual global maps of foliar δ15N during 1984-2022, produced based on the method described in detail in Yang et al. (in review) . The maps could inform the improvement of nitrogen cycle models and the assessments of the impacts of environmental changes.

The annual maps are accompanied by the standard deviation of the predictions of the 500 trees of the random forest model. There are addition analysis using Monte Carlo method to quantify the prediction uncertainty in the PredictionUncertainty folder.

Lineage: The method to derive the data is described in detail in Yang et al. (in review), with code provided in Yang et al (2024).

Briefly, the Landsat spectra were linked to ground based δ15N data with a random forest model.

We used surface reflectance from all six spectral bands of Landsat 5 and 8 from 1984-2022. Landsat data in croplands, urban areas, permanent water, ice, or bare ground were removed.

Each ground-based δ15N was matched to a peak-growing season Landsat retrieval with highest green vegetation cover. A random forest model was then fitted to the ground-based δ15N and Landsat spectra. We used multiple validation methods to avoid overfitting and autocorrelation. The maps are generated using the random forest model and the Landsat spectra of the 30m centroid of each 0.1 degree pixel globally. The full description of the method and the evaluation can be found in Yang et al. (in review). In future this collection may be updated with finer resolution data layers.

FILE DESCRIPTION The d15N_01 folder contains the maps of predicted d15N of the 30m centroid of each 0.1 degree grid cell. The SD folder contains the standard deviation of the predictions of all 500 trees of the random forest model.

REFERENCES Yang et al. (in review) Mapping the multidecadal trends of terrestrial plant nitrogen stable isotope ratios globally. Yang et al. (2024) A framework to estimate nitrogen stable isotope ratio from satellite spectra. https://data.csiro.au/collection/csiro:62621

This dataset is about: (Table 1) Stable carbon isotope ratios of water samples from Site GeoB1202-1.

This data set contains directly determined complex Poisson's ratio from axial and transversal strain measurements. Here, the axial and transverse strains were measured locally with strain gauges (K-CXY3-0060-3-350-O, HBK, Darmstadt, Germany) on cylindric polymethyl methacrylate (PMMA, EH-Design, Wörrstadt, Germany) samples with a diameter of d = 30 mm. Dynamic mechanical analysis (DMA) was performed with the piezoelectric actuator (8P-035.20P, Physik Instrumente, Karlsruhe, Germany) driven by the high power amplifier (E-482, Physik Instrumente, Karlsruhe, Germany). Small strain amplitudes excitation in the frequency range from 0.1 Hz to 1000 Hz are performed. To ensure the oscillation around a strain amplitude, a static preload is applied by a universal testing machine (RM50, Schenk, Germany). Transversal and axial strain is then measured on the PMMA sample with strain gauges in compression mode. The material response in the time domain is transformed to the frequency domain using the Fast Fourier Transform. This gives the axial and transverse amplitude as well as the axial and transverse phase shift. With the variable from the frequency domain, the complex Poisson's ratio is calculated in post-processing. The data set contains the calculated complex Poisson's ratio of three measured PMMA samples.

CO and associated 13C:
At the same sites (Niwot Ridge, Colorado and Montan'a de Oro, California) where we collect air samples to analyze for CH4 data, we also measure CO mixing ratios and 13CO isotope ratios (e.g., Tyler et al., 1999; DB1022, CDIAC archives). Atmospheric CO mixing ratio measurements begin with the first dates of sample collection at Niwot Ridge and Montan'a de Oro while measurements of d13C -CO begin in late 1999 (NWT) and early 2000 (MDO). Hydroxyl radicals (OH), the most important oxidizing agent in the atmosphere, react with CO rather quickly, giving a CO lifetime of the order of a few months, to produce CO2 [Levy, 1971; Logan et al., 1981; Levine et al., 1985]. Thus, knowledge of the sources and sinks of tropospheric CO is vital to understanding and quantifying the distribution of OH concentrations in the atmosphere. Admittedly, 14C and d18O-CO, which we do not currently measure, provide at least as much information as the d13C -CO data. However, the simultaneous measurements of CH4 and CO for mixing and 13C isotope ratio (as well as CO2 data which we also collect) help us to screen samples for outliers not representative of well-mixed background surface air.

Site descriptions, sample collection procedures, and most mixing ratio and isotope ratio analytical techniques are described in our sample archives for atmospheric CH4, appearing as the abstch4.txt file in the CDIAC DB1022 data base. Small differences or additions relevant to the CO data are noted below.

CO2 and associated 13C and 18O:
At the same sites above where we collect air samples to analyze for CH4 and CO data, we also measure CO2 mixing and d13C and d18O isotope ratios (e.g., Tyler et al., 1999; DB1022, CDIAC archives). Atmospheric CO2 measurements of mixing and stable isotope ratio begin with January 1999 at both Niwot Ridge (NWT) and Montana de Oro while (MDO). Measurements of d13C in atmospheric CO2 have long been used to help interpret the global CO2 budget [e.g., Keeling, 1958 and 1961; Mook et al., 1983; Keeling et al., 1984; Quay et al., 1992; Tans et al., 1993], while d18O measurements in atmospheric CO2 have added an important component to the interpretation of CO2 fluxes more recently [e.g., Ciais et al., 1997; Flanagan et al., 1997; Miller et al., 1999].

The d13C of atmospheric CO2 is an indicator of either plant photosynthesis or air-sea exchange of CO2. This is because terrestrial plants preferentially fix 12C in photosynthesis, thereby leaving remaining CO2 relatively 13C heavy, while the dissolution and evaporation of CO2 to and from ocean waters is practically non-fractionating isotopically. In addition, the burning of fossil fuel has significantly increased the CO2 content of the atmosphere, with a corresponding decrease in the d13C signal toward more negative values. On the other hand, the d18O of atmospheric CO2 is a marker to constrain separately the gross uptake (photosynthesis) and release (respiration) of carbon by terrestrial biota. This is because CO2 can exchange an 18O atom with two isotopically distinct reservoirs, i.e., either evaporating leaf water during photosynthesis or soil moisture during respiration. However, the simultaneous measurements of CH4 and CO for mixing and 13C isotope ratio (as well as CO2 data which we also collect) help us to screen samples for outliers not representative of well-mixed background surface air.

Site descriptions, sample collection procedures, and most mixing ratio and isotope ratio analytical techniques have been described in our sample archives for atmospheric CH4 appearing in the CDIAC database. Small differences or additions to these are noted below.

CH4 and associated 2H and 13C:
We report mixing ratios and dD and d13C measurements of atmospheric CH4 from air samples collected bi-weekly from fixed surface sites in the United States. Our fixed surface sites are located at the mid-continental site Niwot Ridge, CO (41 degrees N, 105 degrees W) and a Pacific coastal site receiving strong westerlies, Montan'a de Oro, CA (35 degrees N, 121 degrees W). Data from multiyear approximately bi-weekly sampling provide information relating seasonal cycling of CH4 sources and sinks in background air, record long term trends in CH4 mixing and isotope ratio related to the atmospheric CH4 loading, and may indicate regional CH4 sources. Our continuous record of CH4 mixing ratio and d13C-CH4 from Niwot Ridge extends from 1995 to 2001 while that of Montan'a de Oro extends from 1996 to 2001. A more recently initiated time series of measurements of dD-CH4 were begun during 1998 at Niwot Ridge and during 2000 at Montan'a de Oro. We are archiving these data to make them available for modeling and advanced calculations by other atmospheric researchers. The air sample collections con... Visit https://dataone.org/datasets/ess-dive-b5ec5320ba470ca-20180716T221141140826 for complete metadata about this dataset.

The H2O concentration and H2O/Ce ratio in olivine-hosted melt inclusions are high (H2O up to 1410 ppm; H2O/Ce up to 77) in lunar sample 74220 but lower (H2O up to 430 ppm; H2O/Ce up to 9.4) in all other lunar samples studied before this work. This difference is absent for other volatiles (F, S, and Cl) in melt inclusions in 74220 and other lunar samples. Because H2O (or H) is a critical volatile component with significant ramifications on the origin and evolution of the Moon, it is important to understand what causes such a large gap in H2O/Ce ratio between 74220 and other lunar samples. Two explanations have been advanced. One is that volcanic product in sample 74220 has the highest cooling rate and thus best preserved H2O in melt inclusions compared to melt inclusions in other samples. The other explanation is that sample 74220 is a localized heterogeneity enriched in some volatiles. To distinguish the two possibilities, here we present new data from three rapidly cooled lunar samples: olivine-hosted glassy melt inclusions (OHMIs) in 74220 regolith and 79135 regolith breccia, and pyroxene-hosted glassy melt inclusions (PHMIs) in 15597 pigeonite basalts. If the gap is due to the difference in cooling rates, samples with cooling rates between 74220 and other studied lunar samples should have preserved intermediate H2O concentrations and H2O/Ce ratios. Our results show that melt inclusions in 79135 and 15597 contain high H2O concentrations (up to 969 ppm in 79135 and up to 793 ppm in 15597) and high H2O/Ce ratios (up to 21 in 79135 and up to 13 in 15997). Combined with literature data, we confirm that H2O/Ce ratios of different lunar samples are positively correlated to the cooling rates and independent of the type of mare basalts. Our work bridges the big gap in H2O/Ce ratio among 74220 and other lunar samples. We hence reinforce the interpretation that the lunar sample with the highest cooling rate best represents pre-eruptive volatiles in lunar basalts due to the least degassing. H2O, F, P, S and Cl concentrations in the lunar primitive mantle are also estimated in this work. ;*** 2024-03-19: In addition to the files in the previous version, this updated deposit contains more data files as the supplementary files of the paper. For example, we added a summary excel file containing data that are used for figures in the paper, and an excel file contains data in the tables of the paper for easy use by readers. See ReadMe.txt for changes.

CERN-LHC. The ratio between the prompt psi(2S) and J/psi yields, reconstructed via their decays into muon pairs, is measured in lead-lead and proton-proton collisions at a centre-of-mass energy per nucleon-nucleon pair of 2.76 TeV. The analysis is based on lead-lead and proton-proton data samples collected by CMS at the LHC, corresponding to integrated luminosities of 150 mub^-1 and 5.4 pb^-1, respectively. The double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, is computed in three lead-lead collision centrality bins and two kinematic ranges: one at midrapidity, |y|<1.6, covering the transverse momentum range 6.5<pT<30 GeV/c, and the other at forward rapidity, 1.6<|y|<2.4, extending to lower pT values, 3<pT<30 GeV/c. The centrality-integrated double ratio changes from 0.45 +/- 0.13 (stat) +/- 0.07 (syst) in the first range to 1.67 +- 0.34 (stat) +- 0.27 (syst) in the second. This difference is most pronounced in the most central collisions.

From examining plantation records from St Domingue (present-day Haiti), between the years 1721 and 1797, it was found that there were 133 males for every 100 females, based on numerous sources that give details of more than 13.3 thousand slaves. Such records were rare in the Caribbean, particularly before the 18th century; as this data comes from plantation records, and not from shipping records, it gives a more accurate depiction of the slave gender ratios in the New World, where male slaves had a higher mortality rate during seasoning (i.e. the period of adjustment to the new climate).

By investigating the regional breakdowns, historians have been able to identify a number of trends relating to the capture of slaves in Africa and the survival rates in the New World. For example, ethnic groups located further inland in Africa, such as the Hausa* and Nupe peoples of present-day northern-Nigeria, had a very high gender ratio, as the slaves were more likely to have been captured in battle or in a raid. In contrast, there was a higher rate of female slaves from the Ewe-Fon societies of the so-called Slave Coast, as their location and long-established connection with the slave trade meant that the number of potential male slaves had already been depleted by the late 18th century, and the older male slaves were less likely to survive seasoning.

This research examined the effect of the Current Ratio, Return on Equity, and Debt to Equity Ratio on Stock Returns in Kompas 100 Companies Listed on the Indonesia Stock Exchange in the 2015-2019 period. The sampling technique used in this study was purposive sampling. The samples obtained were 30 companies from 100 companies. The type of data used in this research is secondary data, and the method of analysis uses multiple linear regression analysis. Based on the data analysis done, the variable Return on Equity has a positive and significant effect on stock returns. The Current Ratio has a negative and insignificant effect on stock returns, and the Debt to Equity Ratio has a negative and insignificant effect on stock returns. The current ratio, return on equity, and debt to equity ratio simultaneously does not affect stock returns.