Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo integration using techniques from the high-dimensional statistics literature by allowing the dimension of the integral to increase. In doing so, we derive nonasymptotic bounds for the relative and absolute error of the approximation for some general classes of functions through concentration inequalities. We provide concrete examples in which the magnitude of the number of points sampled needed to guarantee a consistent estimate varies between polynomial to exponential, and show that in theory arbitrarily fast or slow rates are possible. This demonstrates that the behavior of Monte Carlo integration in high dimensions is not uniform. Through our methods we also obtain nonasymptotic confidence intervals which are valid regardless of the number of points sampled.

Example data sets and computer code for the book chapter titled "Missing Data in the Analysis of Multilevel and Dependent Data" submitted for publication in the second edition of "Dependent Data in Social Science Research" (Stemmler et al., 2015). This repository includes the computer code (".R") and the data sets from both example analyses (Examples 1 and 2). The data sets are available in two file formats (binary ".rda" for use in R; plain-text ".dat").

The data sets contain simulated data from 23,376 (Example 1) and 23,072 (Example 2) individuals from 2,000 groups on four variables:

ID = group identifier (1-2000) x = numeric (Level 1) y = numeric (Level 1) w = binary (Level 2)

In all data sets, missing values are coded as "NA".

Sheet 1 (Raw-Data): The raw data of the study is provided, presenting the tagging results for the used measures described in the paper. For each subject, it includes multiple columns: A. a sequential student ID B an ID that defines a random group label and the notation C. the used notation: user Story or use Cases D. the case they were assigned to: IFA, Sim, or Hos E. the subject's exam grade (total points out of 100). Empty cells mean that the subject did not take the first exam F. a categorical representation of the grade L/M/H, where H is greater or equal to 80, M is between 65 included and 80 excluded, L otherwise G. the total number of classes in the student's conceptual model H. the total number of relationships in the student's conceptual model I. the total number of classes in the expert's conceptual model J. the total number of relationships in the expert's conceptual model K-O. the total number of encountered situations of alignment, wrong representation, system-oriented, omitted, missing (see tagging scheme below) P. the researchers' judgement on how well the derivation process explanation was explained by the student: well explained (a systematic mapping that can be easily reproduced), partially explained (vague indication of the mapping ), or not present.

Tagging scheme:
Aligned (AL) - A concept is represented as a class in both models, either

with the same name or using synonyms or clearly linkable names; Wrongly represented (WR) - A class in the domain expert model is incorrectly represented in the student model, either (i) via an attribute, method, or relationship rather than class, or (ii) using a generic term (e.g., user'' instead ofurban planner''); System-oriented (SO) - A class in CM-Stud that denotes a technical implementation aspect, e.g., access control. Classes that represent legacy system or the system under design (portal, simulator) are legitimate; Omitted (OM) - A class in CM-Expert that does not appear in any way in CM-Stud; Missing (MI) - A class in CM-Stud that does not appear in any way in CM-Expert.

All the calculations and information provided in the following sheets

originate from that raw data.

Sheet 2 (Descriptive-Stats): Shows a summary of statistics from the data collection,

including the number of subjects per case, per notation, per process derivation rigor category, and per exam grade category.

Sheet 3 (Size-Ratio):

The number of classes within the student model divided by the number of classes within the expert model is calculated (describing the size ratio). We provide box plots to allow a visual comparison of the shape of the distribution, its central value, and its variability for each group (by case, notation, process, and exam grade) . The primary focus in this study is on the number of classes. However, we also provided the size ratio for the number of relationships between student and expert model.

Sheet 4 (Overall):

Provides an overview of all subjects regarding the encountered situations, completeness, and correctness, respectively. Correctness is defined as the ratio of classes in a student model that is fully aligned with the classes in the corresponding expert model. It is calculated by dividing the number of aligned concepts (AL) by the sum of the number of aligned concepts (AL), omitted concepts (OM), system-oriented concepts (SO), and wrong representations (WR). Completeness on the other hand, is defined as the ratio of classes in a student model that are correctly or incorrectly represented over the number of classes in the expert model. Completeness is calculated by dividing the sum of aligned concepts (AL) and wrong representations (WR) by the sum of the number of aligned concepts (AL), wrong representations (WR) and omitted concepts (OM). The overview is complemented with general diverging stacked bar charts that illustrate correctness and completeness.

For sheet 4 as well as for the following four sheets, diverging stacked bar

charts are provided to visualize the effect of each of the independent and mediated variables. The charts are based on the relative numbers of encountered situations for each student. In addition, a "Buffer" is calculated witch solely serves the purpose of constructing the diverging stacked bar charts in Excel. Finally, at the bottom of each sheet, the significance (T-test) and effect size (Hedges' g) for both completeness and correctness are provided. Hedges' g was calculated with an online tool: https://www.psychometrica.de/effect_size.html. The independent and moderating variables can be found as follows:

Sheet 5 (By-Notation):

Model correctness and model completeness is compared by notation - UC, US.

Sheet 6 (By-Case):

Model correctness and model completeness is compared by case - SIM, HOS, IFA.

Sheet 7 (By-Process):

Model correctness and model completeness is compared by how well the derivation process is explained - well explained, partially explained, not present.

Sheet 8 (By-Grade):

Model correctness and model completeness is compared by the exam grades, converted to categorical values High, Low , and Medium.

1) Data Introduction • The Sample Sales Data is a retail sales dataset of 2,823 orders and 25 columns that includes a variety of sales-related data, including order numbers, product information, quantity, unit price, sales, order date, order status, customer and delivery information.

2) Data Utilization (1) Sample Sales Data has characteristics that: • This dataset consists of numerical (sales, quantity, unit price, etc.), categorical (product, country, city, customer name, transaction size, etc.), and date (order date) variables, with missing values in some columns (STATE, ADDRESSLINE2, POSTALCODE, etc.). (2) Sample Sales Data can be used to: • Analysis of sales trends and performance by product: Key variables such as order date, product line, and country can be used to visualize and analyze monthly and yearly sales trends, the proportion of sales by product line, and top sales by country and region. • Segmentation and marketing strategies: Segmentation of customer groups based on customer information, transaction size, and regional data, and use them to design targeted marketing and customized promotion strategies.

This is a sample of data from a MAYA numerical relativity simulation, primarily for use with the tutorials for the mayawaves python package. This simulation is of binary black holes with a mass ratio of 5 and precessing spins.

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We present a simple, spreadsheet-based method to determine the statistical significance of the difference between any two arbitrary curves. This modified Chi-squared method addresses two scenarios: A single measurement at each point with known standard deviation, or multiple measurements at each point averaged to produce a mean and standard error. The method includes an essential correction for the deviation from normality in measurements with small sample size, which are typical in biomedical sciences. Statistical significance is determined without regard to the functionality of the curves, or the signs of the differences. Numerical simulations are used to validate the procedure. Example experimental data are used to demonstrate its application. An Excel spreadsheet is provided for performing the calculations for either scenario.

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This GIS layer provides detailed information from Pellegrino and Hubbard (1983). It shows the sample locations and provides a summary of the total number of species found at each station (species_richness).

The considerations in this report A Skateboard are part of the example collection which can be found in http://www3.math.tu-berlin.de/multiphysics/Examples/. The aim is to investigate different formulations, i.e., regularized formulations or also index reduced formulations, of the model equations in combination with different numerical solvers with respect to its applicability, efficiency, accuracy, and robustness.

The US Consumer Phone file contains phone numbers, mobile and landline, tied to an individual in the Consumer Database. The fields available include the phone number, phone type, mobile carrier, and Do Not Call registry status.

All phone numbers can be processed and cleansed using telecom carrier data. The telecom data, including phone and texting activity, porting instances, carrier scoring, spam, and known fraud activity, comprise a proprietary Phone Quality Level (PQL), which is a data-science derived score to ensure the highest levels of deliverability at a fraction of the cost compared to competitors.

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Note - all Consumer packages can include necessary PII (address, email, phone, DOB, etc.) for merging, linking, and activation of the data.

BIGDBM Privacy Policy: https://bigdbm.com/privacy.html

Although it is a widespread phenomenon in nature, turbulence in fluids (gases, liquids) is still very poorly understood. One area of research involves analyzing data from academic flow simulations. To make progress, the scientific community needs a large amount of reliable data in various configurations. Turbulent flows near solid flat or curved walls are very interesting examples. The database is composed of the 3D raw data (velocity, pressure, time derivative of velocity) and statistics (mean, Reynolds stresses, length scales) of a direct numerical simulations of moderate adverse pressure gradient (decelerating) turbulent boundary layer on a flat plate at Reynolds number up to Reθ = 8000 .

To create the dataset, the top 10 countries leading in the incidence of COVID-19 in the world were selected as of October 22, 2020 (on the eve of the second full of pandemics), which are presented in the Global 500 ranking for 2020: USA, India, Brazil, Russia, Spain, France and Mexico. For each of these countries, no more than 10 of the largest transnational corporations included in the Global 500 rating for 2020 and 2019 were selected separately. The arithmetic averages were calculated and the change (increase) in indicators such as profitability and profitability of enterprises, their ranking position (competitiveness), asset value and number of employees. The arithmetic mean values of these indicators for all countries of the sample were found, characterizing the situation in international entrepreneurship as a whole in the context of the COVID-19 crisis in 2020 on the eve of the second wave of the pandemic. The data is collected in a general Microsoft Excel table. Dataset is a unique database that combines COVID-19 statistics and entrepreneurship statistics. The dataset is flexible data that can be supplemented with data from other countries and newer statistics on the COVID-19 pandemic. Due to the fact that the data in the dataset are not ready-made numbers, but formulas, when adding and / or changing the values in the original table at the beginning of the dataset, most of the subsequent tables will be automatically recalculated and the graphs will be updated. This allows the dataset to be used not just as an array of data, but as an analytical tool for automating scientific research on the impact of the COVID-19 pandemic and crisis on international entrepreneurship. The dataset includes not only tabular data, but also charts that provide data visualization. The dataset contains not only actual, but also forecast data on morbidity and mortality from COVID-19 for the period of the second wave of the pandemic in 2020. The forecasts are presented in the form of a normal distribution of predicted values and the probability of their occurrence in practice. This allows for a broad scenario analysis of the impact of the COVID-19 pandemic and crisis on international entrepreneurship, substituting various predicted morbidity and mortality rates in risk assessment tables and obtaining automatically calculated consequences (changes) on the characteristics of international entrepreneurship. It is also possible to substitute the actual values identified in the process and following the results of the second wave of the pandemic to check the reliability of pre-made forecasts and conduct a plan-fact analysis. The dataset contains not only the numerical values of the initial and predicted values of the set of studied indicators, but also their qualitative interpretation, reflecting the presence and level of risks of a pandemic and COVID-19 crisis for international entrepreneurship.

VAPOR is the Visualization and Analysis Platform for Ocean, Atmosphere, and Solar Researchers. VAPOR provides an interactive 3D visualization environment that can also produce animations and still frame images. VAPOR runs on most UNIX and Windows systems equipped with modern 3D graphics cards. VAPOR is a product of the National Center for Atmospheric Research's Computational and Information Systems Lab. Support for VAPOR is provided by the U.S. National Science Foundation and by the Korea Institute of Science and Technology Information This dataset contains sample files of model outputs from numerical simulations that VAPOR is capable of directly reading. They are not related to each other aside from being sample data for VAPOR.
To unpack the tar.gz files on Linux/OSX, issue the command tar -xzvf [myFile].tar.gz on the file you've downloaded. On Windows, a program like 7-zip can perform that operation. Once unpacked, the files can be directly imported into VAPOR, or converted to VDC. For more information see the "Getting Data Into VAPOR" Related Link below.

The considerations in this report Slider Crank are part of the example collection which can be found in http://www3.math.tu-berlin.de/multiphysics/Examples/. The aim is to investigate different formulations, i.e., regularized formulations or also index reduced formulations, of the model equations in combination with different numerical solvers with respect to its applicability, efficiency, accuracy, and robustness.

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 complete dataset used in the analysis comprises 36 samples, each described by 11 numeric features and 1 target. The attributes considered were caspase 3/7 activity, Mitotracker red CMXRos area and intensity (3 h and 24 h incubations with both compounds), Mitosox oxidation (3 h incubation with the referred compounds) and oxidation rate, DCFDA fluorescence (3 h and 24 h incubations with either compound) and oxidation rate, and DQ BSA hydrolysis. The target of each instance corresponds to one of the 9 possible classes (4 samples per class): Control, 6.25, 12.5, 25 and 50 µM for 6-OHDA and 0.03, 0.06, 0.125 and 0.25 µM for rotenone. The dataset is balanced, it does not contain any missing values and data was standardized across features. The small number of samples prevented a full and strong statistical analysis of the results. Nevertheless, it allowed the identification of relevant hidden patterns and trends.

Exploratory data analysis, information gain, hierarchical clustering, and supervised predictive modeling were performed using Orange Data Mining version 3.25.1 [41]. Hierarchical clustering was performed using the Euclidean distance metric and weighted linkage. Cluster maps were plotted to relate the features with higher mutual information (in rows) with instances (in columns), with the color of each cell representing the normalized level of a particular feature in a specific instance. The information is grouped both in rows and in columns by a two-way hierarchical clustering method using the Euclidean distances and average linkage. Stratified cross-validation was used to train the supervised decision tree. A set of preliminary empirical experiments were performed to choose the best parameters for each algorithm, and we verified that, within moderate variations, there were no significant changes in the outcome. The following settings were adopted for the decision tree algorithm: minimum number of samples in leaves: 2; minimum number of samples required to split an internal node: 5; stop splitting when majority reaches: 95%; criterion: gain ratio. The performance of the supervised model was assessed using accuracy, precision, recall, F-measure and area under the ROC curve (AUC) metrics.

The assignment of a symbolic representation to a specific numerosity is a fundamental requirement for humans solving complex mathematical calculations used in diverse applications such as algebra, accounting, physics, and everyday commerce. Here we show that honeybees are able to learn to match a sign to a numerosity, or a numerosity to a sign and subsequently transfer this knowledge to novel numerosity stimuli changed in colour properties, shape, and configuration. While honeybees learnt the associations between two quantities (two; three) and two signs (N-shape; inverted T-shape), they failed at reversing their specific task of sign-to-numerosity-matching to numerosity-to-sign-matching and vice-versa (i.e. a honeybee that learnt to match a sign to a number of elements was not able to invert this learning to match the numerosity of elements to a sign). Thus, while bees could learn the association between a symbol and numerosity, it was linked to the specific task and bees could not spo...

This repository includes the data associated to the numerical examples in the 'Applications of an isogeometric indirect boundary element method and the importance of accurate geometrical representation in acoustic problems' article submitted to the Engineering Analysis with Boundary Elements Elsevier journal. The data comprise of the CAD models, NURBS models to be solved by the isogeometric boundary element method (IGiBEM) with the proposed method in the article, meshes to be solved indirect boundary element method (iBEM) with LMS Virtual.Lab 13.7v, and the results of the numerical examples: 1) vibrating cube, 2) car hood and 3) loudspeaker. The IGiBEM software is under private license of KU Leuven and Siemens Industry Software NV, therefore, it is not shared in this repository.

Prediction comparison for model based on the Lorenz system.