This dataset consists of mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.

## Example questions

 Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.
 Answer: 4
 
 Question: Calculate -841880142.544 + 411127.
 Answer: -841469015.544
 
 Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).
 Answer: 54*a - 30

It contains 2 million (question, answer) pairs per module, with questions limited to 160 characters in length, and answers to 30 characters in length. Note the training data for each question type is split into "train-easy", "train-medium", and "train-hard". This allows training models via a curriculum. The data can also be mixed together uniformly from these training datasets to obtain the results reported in the paper. Categories:

• algebra (linear equations, polynomial roots, sequences)
• arithmetic (pairwise operations and mixed expressions, surds)
• calculus (differentiation)
• comparison (closest numbers, pairwise comparisons, sorting)
• measurement (conversion, working with time)
• numbers (base conversion, remainders, common divisors and multiples, primality, place value, rounding numbers)
• polynomials (addition, simplification, composition, evaluating, expansion)
• probability (sampling without replacement)

MathInstruct Dataset: Hybrid Math Instruction Tuning

A curated dataset for math instruction tuning models

By TIGER-Lab (From Huggingface) [source]

About this dataset

MathInstruct is a comprehensive and meticulously curated dataset specifically designed to facilitate the development and evaluation of models for math instruction tuning. This dataset consists of a total of 13 different math rationale datasets, out of which six have been exclusively curated for this project, ensuring a diverse range of instructional materials. The main objective behind creating this dataset is to provide researchers with an easily accessible and manageable resource that aids in enhancing the effectiveness and precision of math instruction.

One noteworthy feature of MathInstruct is its lightweight nature, making it highly convenient for researchers to utilize without any hassle. With carefully selected columns such as source, source, output, output, users can readily identify the origin or reference material from where the math instruction was obtained. Additionally, they can also refer to the expected output or solution corresponding to each specific math problem or exercise.

Overall, MathInstruct offers immense potential in refining hybrid math instruction by facilitating meticulous model development and rigorous evaluation processes. Researchers can leverage this diverse dataset to gain deeper insights into effective teaching methodologies while exploring innovative approaches towards enhancing mathematical learning experiences

How to use the dataset

Title: How to Use the MathInstruct Dataset for Hybrid Math Instruction Tuning

Introduction: The MathInstruct dataset is a comprehensive collection of math instruction examples, designed to assist in developing and evaluating models for math instruction tuning. This guide will provide an overview of the dataset and explain how to make effective use of it.

• Understanding the Dataset Structure: The dataset consists of a file named train.csv. This CSV file contains the training data, which includes various columns such as source and output. The source column represents the source of math instruction (textbook, online resource, or teacher), while the output column represents expected output or solution to a particular math problem or exercise.

• Accessing the Dataset: To access the MathInstruct dataset, you can download it from Kaggle's website. Once downloaded, you can read and manipulate the data using programming languages like Python with libraries such as pandas.

• Exploring the Columns: a) Source Column: The source column provides information about where each math instruction comes from. It may include references to specific textbooks, online resources, or even teachers who provided instructional material. b) Output Column: The output column specifies what students are expected to achieve as a result of each math instruction. It contains solutions or expected outputs for different math problems or exercises.

• Utilizing Source Information: By analyzing the different sources mentioned in this dataset, researchers can understand which instructional materials are more effective in teaching specific topics within mathematics. They can also identify common strategies used by teachers across multiple sources.

• Analyzing Expected Outputs: Researchers can study variations in expected outputs for similar types of problems across different sources. This analysis may help identify differences in approaches across textbooks/resources and enrich our understanding of various teaching methods.

• Model Development and Evaluation: Researchers can utilize this dataset to develop machine learning models that automatically assess whether a given math instruction leads to the expected output. By training models on this data, one can create automated systems that provide feedback on math problems or suggest alternative instruction sources.

• Scaling the Dataset: Due to its lightweight nature, the MathInstruct dataset is easily accessible and manageable. Researchers can scale up their training data by combining it with other instructional datasets or expand it further by labeling more examples based on similar guidelines.

Conclusion: The MathInstruct dataset serves as a valuable resource for developing and evaluating models related to math instruction tuning. By analyzing the source information and expected outputs, researchers can gain insights into effective teaching methods and build automated assessment

Research Ideas

• Model development: This dataset can be used for developing and training models for math instruction...

Mathematics database.

This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.

Original paper: Analysing Mathematical Reasoning Abilities of Neural Models (Saxton, Grefenstette, Hill, Kohli).

Example usage:

train_examples, val_examples = tfds.load(
  'math_dataset/arithmetic_mul',
  split=['train', 'test'],
  as_supervised=True)

To use this dataset:

import tensorflow_datasets as tfds

ds = tfds.load('math_dataset', split='train')
for ex in ds.take(4):
 print(ex)

See the guide for more informations on tensorflow_datasets.

Math Formula Retrieval

Math Formula Pair Classification Dataset

By ddrg (From Huggingface) [source]

About this dataset

With a total of six columns, including formula1, formula2, label (binary format), formula1, formula2, and label, the dataset provides all the necessary information for conducting comprehensive analysis and evaluation.

The train.csv file contains a subset of the dataset specifically curated for training purposes. It includes an extensive range of math formula pairs along with their corresponding labels and unique ID names. This allows researchers and data scientists to construct models that can predict whether two given formulas fall within the same category or not.

On the other hand, test.csv serves as an evaluation set. It consists of additional pairs of math formulas accompanied by their respective labels and unique IDs. By evaluating model performance on this test set after training it on train.csv data, researchers can assess how well their models generalize to unseen instances.

By leveraging this informative dataset, researchers can unlock new possibilities in mathematics-related fields such as pattern recognition algorithms development or enhancing educational tools that involve automatic identification and categorization tasks based on mathematical formulas

How to use the dataset

Introduction

Dataset Description

train.csv

The train.csv file contains a set of labeled math formula pairs along with their corresponding labels and formula name IDs. It consists of the following columns: - formula1: The first mathematical formula in the pair (text). - formula2: The second mathematical formula in the pair (text). - label: The classification label indicating whether the pair of formulas belong to the same category or not (binary). A label value of 1 indicates that both formulas belong to the same category, while a label value of 0 indicates different categories.

test.csv

The purpose of the test.csv file is to provide a set of formula pairs along with their labels and formula name IDs for testing and evaluation purposes. It has an identical structure to train.csv, containing columns like formula1, formula2, label, etc.

Task

The main task using this dataset is binary classification, where your objective is to predict whether two mathematical formulas belong to the same category or not based on their textual representation. You can use various machine learning algorithms such as logistic regression, decision trees, random forests, or neural networks for training models on this dataset.

Exploring & Analyzing Data

Before building your model, it's crucial to explore and analyze your data. Here are some steps you can take:

• Load both CSV files (train.csv and test.csv) into your preferred data analysis framework or programming language (e.g., Python with libraries like pandas).
• Examine the dataset's structure, including the number of rows, columns, and data types.
• Check for missing values in the dataset and handle them accordingly.
• Visualize the distribution of labels to understand whether it is balanced or imbalanced.

Model Building

Once you have analyzed and preprocessed your dataset, you can start building your classification model using various machine learning algorithms:

• Split your train.csv data into training and validation sets for model evaluation during training.
• Choose a suitable

Research Ideas

• Math Formula Similarity: This dataset can be used to develop a model that classifies whether two mathematical formulas are similar or not. This can be useful in various applications such as plagiarism detection, identifying duplicate formulas in databases, or suggesting similar formulas based on user input.
• Formula Categorization: The dataset can be used to train a model that categorizes mathematical formulas into different classes or categories. For example, the model can classify formulas into algebraic expressions, trigonometric equations, calculus problems, or geometric theorems. This categorization can help organize and search through large collections of mathematical formulas.
• Formula Recommendation: Using this dataset, one could build a recommendation system that suggests related math formulas based on user input. By analyzing the similarities between different formula pairs and their corresponding labels, the system could provide recommendations for relevant mathematical concepts that users may need while solving problems or studying specific topics in mathematics

Acknowle...

Study information

The sample included in this dataset represents five children who participated in a number line intervention study. Originally six children were included in the study, but one of them fulfilled the criterion for exclusion after missing several consecutive sessions. Thus, their data is not included in the dataset.

All participants were currently attending Year 1 of primary school at an independent school in New South Wales, Australia. For children to be able to eligible to participate they had to present with low mathematics achievement by performing at or below the 25th percentile in the Maths Problem Solving and/or Numerical Operations subtests from the Wechsler Individual Achievement Test III (WIAT III A & NZ, Wechsler, 2016). Participants were excluded from participating if, as reported by their parents, they have any other diagnosed disorders such as attention deficit hyperactivity disorder, autism spectrum disorder, intellectual disability, developmental language disorder, cerebral palsy or uncorrected sensory disorders.

The study followed a multiple baseline case series design, with a baseline phase, a treatment phase, and a post-treatment phase. The baseline phase varied between two and three measurement points, the treatment phase varied between four and seven measurement points, and all participants had 1 post-treatment measurement point.

The number of measurement points were distributed across participants as follows:

Participant 1 – 3 baseline, 6 treatment, 1 post-treatment

Participant 3 – 2 baseline, 7 treatment, 1 post-treatment

Participant 5 – 2 baseline, 5 treatment, 1 post-treatment

Participant 6 – 3 baseline, 4 treatment, 1 post-treatment

Participant 7 – 2 baseline, 5 treatment, 1 post-treatment

In each session across all three phases children were assessed in their performance on a number line estimation task, a single-digit computation task, a multi-digit computation task, a dot comparison task and a number comparison task. Furthermore, during the treatment phase, all children completed the intervention task after these assessments. The order of the assessment tasks varied randomly between sessions.

Measures

Number Line Estimation. Children completed a computerised bounded number line task (0-100). The number line is presented in the middle of the screen, and the target number is presented above the start point of the number line to avoid signalling the midpoint (Dackermann et al., 2018). Target numbers included two non-overlapping sets (trained and untrained) of 30 items each. Untrained items were assessed on all phases of the study. Trained items were assessed independent of the intervention during baseline and post-treatment phases, and performance on the intervention is used to index performance on the trained set during the treatment phase. Within each set, numbers were equally distributed throughout the number range, with three items within each ten (0-10, 11-20, 21-30, etc.). Target numbers were presented in random order. Participants did not receive performance-based feedback. Accuracy is indexed by percent absolute error (PAE) [(number estimated - target number)/ scale of number line] x100.

Single-Digit Computation. The task included ten additions with single-digit addends (1-9) and single-digit results (2-9). The order was counterbalanced so that half of the additions present the lowest addend first (e.g., 3 + 5) and half of the additions present the highest addend first (e.g., 6 + 3). This task also included ten subtractions with single-digit minuends (3-9), subtrahends (1-6) and differences (1-6). The items were presented horizontally on the screen accompanied by a sound and participants were required to give a verbal response. Participants did not receive performance-based feedback. Performance on this task was indexed by item-based accuracy.

Multi-digit computational estimation. The task included eight additions and eight subtractions presented with double-digit numbers and three response options. None of the response options represent the correct result. Participants were asked to select the option that was closest to the correct result. In half of the items the calculation involved two double-digit numbers, and in the other half one double and one single digit number. The distance between the correct response option and the exact result of the calculation was two for half of the trials and three for the other half. The calculation was presented vertically on the screen with the three options shown below. The calculations remained on the screen until participants responded by clicking on one of the options on the screen. Participants did not receive performance-based feedback. Performance on this task is measured by item-based accuracy.

Dot Comparison and Number Comparison. Both tasks included the same 20 items, which were presented twice, counterbalancing left and right presentation. Magnitudes to be compared were between 5 and 99, with four items for each of the following ratios: .91, .83, .77, .71, .67. Both quantities were presented horizontally side by side, and participants were instructed to press one of two keys (F or J), as quickly as possible, to indicate the largest one. Items were presented in random order and participants did not receive performance-based feedback. In the non-symbolic comparison task (dot comparison) the two sets of dots remained on the screen for a maximum of two seconds (to prevent counting). Overall area and convex hull for both sets of dots is kept constant following Guillaume et al. (2020). In the symbolic comparison task (Arabic numbers), the numbers remained on the screen until a response was given. Performance on both tasks was indexed by accuracy.

The Number Line Intervention

During the intervention sessions, participants estimated the position of 30 Arabic numbers in a 0-100 bounded number line. As a form of feedback, within each item, the participants’ estimate remained visible, and the correct position of the target number appeared on the number line. When the estimate’s PAE was lower than 2.5, a message appeared on the screen that read “Excellent job”, when PAE was between 2.5 and 5 the message read “Well done, so close! and when PAE was higher than 5 the message read “Good try!” Numbers were presented in random order.

Variables in the dataset

Age = age in ‘years, months’ at the start of the study

Sex = female/male/non-binary or third gender/prefer not to say (as reported by parents)

Math_Problem_Solving_raw = Raw score on the Math Problem Solving subtest from the WIAT III (WIAT III A & NZ, Wechsler, 2016).

Math_Problem_Solving_Percentile = Percentile equivalent on the Math Problem Solving subtest from the WIAT III (WIAT III A & NZ, Wechsler, 2016).

Num_Ops_Raw = Raw score on the Numerical Operations subtest from the WIAT III (WIAT III A & NZ, Wechsler, 2016).

Math_Problem_Solving_Percentile = Percentile equivalent on the Numerical Operations subtest from the WIAT III (WIAT III A & NZ, Wechsler, 2016).

The remaining variables refer to participants’ performance on the study tasks. Each variable name is composed by three sections. The first one refers to the phase and session. For example, Base1 refers to the first measurement point of the baseline phase, Treat1 to the first measurement point on the treatment phase, and post1 to the first measurement point on the post-treatment phase.

The second part of the variable name refers to the task, as follows:

DC = dot comparison

SDC = single-digit computation

NLE_UT = number line estimation (untrained set)

NLE_T= number line estimation (trained set)

CE = multidigit computational estimation

NC = number comparison

The final part of the variable name refers to the type of measure being used (i.e., acc = total correct responses and pae = percent absolute error).

Thus, variable Base2_NC_acc corresponds to accuracy on the number comparison task during the second measurement point of the baseline phase and Treat3_NLE_UT_pae refers to the percent absolute error on the untrained set of the number line task during the third session of the Treatment phase.

Dataset Card for NuminaMath 1.5

  Dataset Summary

This is the second iteration of the popular NuminaMath dataset, bringing high quality post-training data for approximately 900k competition-level math problems. Each solution is formatted in a Chain of Thought (CoT) manner. The sources of the dataset range from Chinese high school math exercises to US and international mathematics olympiad competition problems. The data were primarily collected from online exam paper PDFs… See the full description on the dataset page: https://huggingface.co/datasets/AI-MO/NuminaMath-1.5.

Welcome to the Spanish Chain of Thought prompt-response dataset, a meticulously curated collection containing 3000 comprehensive prompt and response pairs. This dataset is an invaluable resource for training Language Models (LMs) to generate well-reasoned answers and minimize inaccuracies. Its primary utility lies in enhancing LLMs' reasoning skills for solving arithmetic, common sense, symbolic reasoning, and complex problems.

Dataset Content

This COT dataset comprises a diverse set of instructions and questions paired with corresponding answers and rationales in the Spanish language. These prompts and completions cover a broad range of topics and questions, including mathematical concepts, common sense reasoning, complex problem-solving, scientific inquiries, puzzles, and more.

Each prompt is meticulously accompanied by a response and rationale, providing essential information and insights to enhance the language model training process. These prompts, completions, and rationales were manually curated by native Spanish people, drawing references from various sources, including open-source datasets, news articles, websites, and other reliable references.

Our chain-of-thought prompt-completion dataset includes various prompt types, such as instructional prompts, continuations, and in-context learning (zero-shot, few-shot) prompts. Additionally, the dataset contains prompts and completions enriched with various forms of rich text, such as lists, tables, code snippets, JSON, and more, with proper markdown format.

Prompt Diversity

To ensure a wide-ranging dataset, we have included prompts from a plethora of topics related to mathematics, common sense reasoning, and symbolic reasoning. These topics encompass arithmetic, percentages, ratios, geometry, analogies, spatial reasoning, temporal reasoning, logic puzzles, patterns, and sequences, among others.

These prompts vary in complexity, spanning easy, medium, and hard levels. Various question types are included, such as multiple-choice, direct queries, and true/false assessments.

Response Formats

To accommodate diverse learning experiences, our dataset incorporates different types of answers depending on the prompt and provides step-by-step rationales. The detailed rationale aids the language model in building reasoning process for complex questions.

These responses encompass text strings, numerical values, and date and time formats, enhancing the language model's ability to generate reliable, coherent, and contextually appropriate answers.

Data Format and Annotation Details

This fully labeled Spanish Chain of Thought Prompt Completion Dataset is available in JSON and CSV formats. It includes annotation details such as a unique ID, prompt, prompt type, prompt complexity, prompt category, domain, response, rationale, response type, and rich text presence.

Quality and Accuracy

Our dataset upholds the highest standards of quality and accuracy. Each prompt undergoes meticulous validation, and the corresponding responses and rationales are thoroughly verified. We prioritize inclusivity, ensuring that the dataset incorporates prompts and completions representing diverse perspectives and writing styles, maintaining an unbiased and discrimination-free stance.

The Spanish version is grammatically accurate without any spelling or grammatical errors. No copyrighted, toxic, or harmful content is used during the construction of this dataset.

Continuous Updates and Customization

The entire dataset was prepared with the assistance of human curators from the FutureBeeAI crowd community. Ongoing efforts are made to add more assets to this dataset, ensuring its growth and relevance. Additionally, FutureBeeAI offers the ability to gather custom chain of thought prompt completion data tailored to specific needs, providing flexibility and customization options.

License

The dataset, created by FutureBeeAI, is now available for commercial use. Researchers, data scientists, and developers can leverage this fully labeled and ready-to-deploy Spanish Chain of Thought Prompt Completion Dataset to enhance the rationale and accurate response generation capabilities of their generative AI models and explore new approaches to NLP tasks.

Welcome to the English Chain of Thought prompt-response dataset, a meticulously curated collection containing 3000 comprehensive prompt and response pairs. This dataset is an invaluable resource for training Language Models (LMs) to generate well-reasoned answers and minimize inaccuracies. Its primary utility lies in enhancing LLMs' reasoning skills for solving arithmetic, common sense, symbolic reasoning, and complex problems.

Dataset Content

This COT dataset comprises a diverse set of instructions and questions paired with corresponding answers and rationales in the English language. These prompts and completions cover a broad range of topics and questions, including mathematical concepts, common sense reasoning, complex problem-solving, scientific inquiries, puzzles, and more.

Each prompt is meticulously accompanied by a response and rationale, providing essential information and insights to enhance the language model training process. These prompts, completions, and rationales were manually curated by native English people, drawing references from various sources, including open-source datasets, news articles, websites, and other reliable references.

Our chain-of-thought prompt-completion dataset includes various prompt types, such as instructional prompts, continuations, and in-context learning (zero-shot, few-shot) prompts. Additionally, the dataset contains prompts and completions enriched with various forms of rich text, such as lists, tables, code snippets, JSON, and more, with proper markdown format.

Prompt Diversity

To ensure a wide-ranging dataset, we have included prompts from a plethora of topics related to mathematics, common sense reasoning, and symbolic reasoning. These topics encompass arithmetic, percentages, ratios, geometry, analogies, spatial reasoning, temporal reasoning, logic puzzles, patterns, and sequences, among others.

These prompts vary in complexity, spanning easy, medium, and hard levels. Various question types are included, such as multiple-choice, direct queries, and true/false assessments.

Response Formats

To accommodate diverse learning experiences, our dataset incorporates different types of answers depending on the prompt and provides step-by-step rationales. The detailed rationale aids the language model in building reasoning process for complex questions.

These responses encompass text strings, numerical values, and date and time formats, enhancing the language model's ability to generate reliable, coherent, and contextually appropriate answers.

Data Format and Annotation Details

This fully labeled English Chain of Thought Prompt Completion Dataset is available in JSON and CSV formats. It includes annotation details such as a unique ID, prompt, prompt type, prompt complexity, prompt category, domain, response, rationale, response type, and rich text presence.

Quality and Accuracy

Our dataset upholds the highest standards of quality and accuracy. Each prompt undergoes meticulous validation, and the corresponding responses and rationales are thoroughly verified. We prioritize inclusivity, ensuring that the dataset incorporates prompts and completions representing diverse perspectives and writing styles, maintaining an unbiased and discrimination-free stance.

The English version is grammatically accurate without any spelling or grammatical errors. No copyrighted, toxic, or harmful content is used during the construction of this dataset.

Continuous Updates and Customization

The entire dataset was prepared with the assistance of human curators from the FutureBeeAI crowd community. Ongoing efforts are made to add more assets to this dataset, ensuring its growth and relevance. Additionally, FutureBeeAI offers the ability to gather custom chain of thought prompt completion data tailored to specific needs, providing flexibility and customization options.

License

The dataset, created by FutureBeeAI, is now available for commercial use. Researchers, data scientists, and developers can leverage this fully labeled and ready-to-deploy English Chain of Thought Prompt Completion Dataset to enhance the rationale and accurate response generation capabilities of their generative AI models and explore new approaches to NLP tasks.

Welcome to the Urdu Chain of Thought prompt-response dataset, a meticulously curated collection containing 3000 comprehensive prompt and response pairs. This dataset is an invaluable resource for training Language Models (LMs) to generate well-reasoned answers and minimize inaccuracies. Its primary utility lies in enhancing LLMs' reasoning skills for solving arithmetic, common sense, symbolic reasoning, and complex problems.

Dataset Content

This COT dataset comprises a diverse set of instructions and questions paired with corresponding answers and rationales in the Urdu language. These prompts and completions cover a broad range of topics and questions, including mathematical concepts, common sense reasoning, complex problem-solving, scientific inquiries, puzzles, and more.

Each prompt is meticulously accompanied by a response and rationale, providing essential information and insights to enhance the language model training process. These prompts, completions, and rationales were manually curated by native Urdu people, drawing references from various sources, including open-source datasets, news articles, websites, and other reliable references.

Our chain-of-thought prompt-completion dataset includes various prompt types, such as instructional prompts, continuations, and in-context learning (zero-shot, few-shot) prompts. Additionally, the dataset contains prompts and completions enriched with various forms of rich text, such as lists, tables, code snippets, JSON, and more, with proper markdown format.

Prompt Diversity

To ensure a wide-ranging dataset, we have included prompts from a plethora of topics related to mathematics, common sense reasoning, and symbolic reasoning. These topics encompass arithmetic, percentages, ratios, geometry, analogies, spatial reasoning, temporal reasoning, logic puzzles, patterns, and sequences, among others.

These prompts vary in complexity, spanning easy, medium, and hard levels. Various question types are included, such as multiple-choice, direct queries, and true/false assessments.

Response Formats

To accommodate diverse learning experiences, our dataset incorporates different types of answers depending on the prompt and provides step-by-step rationales. The detailed rationale aids the language model in building reasoning process for complex questions.

These responses encompass text strings, numerical values, and date and time formats, enhancing the language model's ability to generate reliable, coherent, and contextually appropriate answers.

Data Format and Annotation Details

This fully labeled Urdu Chain of Thought Prompt Completion Dataset is available in JSON and CSV formats. It includes annotation details such as a unique ID, prompt, prompt type, prompt complexity, prompt category, domain, response, rationale, response type, and rich text presence.

Quality and Accuracy

Our dataset upholds the highest standards of quality and accuracy. Each prompt undergoes meticulous validation, and the corresponding responses and rationales are thoroughly verified. We prioritize inclusivity, ensuring that the dataset incorporates prompts and completions representing diverse perspectives and writing styles, maintaining an unbiased and discrimination-free stance.

The Urdu version is grammatically accurate without any spelling or grammatical errors. No copyrighted, toxic, or harmful content is used during the construction of this dataset.

Continuous Updates and Customization

The entire dataset was prepared with the assistance of human curators from the FutureBeeAI crowd community. Ongoing efforts are made to add more assets to this dataset, ensuring its growth and relevance. Additionally, FutureBeeAI offers the ability to gather custom chain of thought prompt completion data tailored to specific needs, providing flexibility and customization options.

License

The dataset, created by FutureBeeAI, is now available for commercial use. Researchers, data scientists, and developers can leverage this fully labeled and ready-to-deploy Urdu Chain of Thought Prompt Completion Dataset to enhance the rationale and accurate response generation capabilities of their generative AI models and explore new approaches to NLP tasks.

We include a description of the data sets in the meta-data as well as sample code and results from a simulated data set. This dataset is not publicly accessible because: EPA cannot release personally identifiable information regarding living individuals, according to the Privacy Act and the Freedom of Information Act (FOIA). This dataset contains information about human research subjects. Because there is potential to identify individual participants and disclose personal information, either alone or in combination with other datasets, individual level data are not appropriate to post for public access. Restricted access may be granted to authorized persons by contacting the party listed. It can be accessed through the following means: The R code is available on line here: https://github.com/warrenjl/SpGPCW. Format: Abstract The data used in the application section of the manuscript consist of geocoded birth records from the North Carolina State Center for Health Statistics, 2005-2008. In the simulation study section of the manuscript, we simulate synthetic data that closely match some of the key features of the birth certificate data while maintaining confidentiality of any actual pregnant women. Availability Due to the highly sensitive and identifying information contained in the birth certificate data (including latitude/longitude and address of residence at delivery), we are unable to make the data from the application section publicly available. However, we will make one of the simulated datasets available for any reader interested in applying the method to realistic simulated birth records data. This will also allow the user to become familiar with the required inputs of the model, how the data should be structured, and what type of output is obtained. While we cannot provide the application data here, access to the North Carolina birth records can be requested through the North Carolina State Center for Health Statistics and requires an appropriate data use agreement. Description Permissions: These are simulated data without any identifying information or informative birth-level covariates. We also standardize the pollution exposures on each week by subtracting off the median exposure amount on a given week and dividing by the interquartile range (IQR) (as in the actual application to the true NC birth records data). The dataset that we provide includes weekly average pregnancy exposures that have already been standardized in this way while the medians and IQRs are not given. This further protects identifiability of the spatial locations used in the analysis. File format: R workspace file. Metadata (including data dictionary) • y: Vector of binary responses (1: preterm birth, 0: control) • x: Matrix of covariates; one row for each simulated individual • z: Matrix of standardized pollution exposures • n: Number of simulated individuals • m: Number of exposure time periods (e.g., weeks of pregnancy) • p: Number of columns in the covariate design matrix • alpha_true: Vector of “true” critical window locations/magnitudes (i.e., the ground truth that we want to estimate). This dataset is associated with the following publication: Warren, J., W. Kong, T. Luben, and H. Chang. Critical Window Variable Selection: Estimating the Impact of Air Pollution on Very Preterm Birth. Biostatistics. Oxford University Press, OXFORD, UK, 1-30, (2019).

Technological advances have steadily increased the detail of animal tracking datasets, yet fundamental data limitations exist for many species that cause substantial biases in home‐range estimation. Specifically, the effective sample size of a range estimate is proportional to the number of observed range crossings, not the number of sampled locations. Currently, the most accurate home‐range estimators condition on an autocorrelation model, for which the standard estimation frame‐works are based on likelihood functions, even though these methods are known to underestimate variance—and therefore ranging area—when effective sample sizes are small. Residual maximum likelihood (REML) is a widely used method for reducing bias in maximum‐likelihood (ML) variance estimation at small sample sizes. Unfortunately, we find that REML is too unstable for practical application to continuous‐time movement models. When the effective sample size N is decreased to N ≤ urn:x-wiley:2041210X:media:mee313270:mee313270-math-0001(10), which is common in tracking applications, REML undergoes a sudden divergence in variance estimation. To avoid this issue, while retaining REML’s first‐order bias correction, we derive a family of estimators that leverage REML to make a perturbative correction to ML. We also derive AIC values for REML and our estimators, including cases where model structures differ, which is not generally understood to be possible. Using both simulated data and GPS data from lowland tapir (Tapirus terrestris), we show how our perturbative estimators are more accurate than traditional ML and REML methods. Specifically, when urn:x-wiley:2041210X:media:mee313270:mee313270-math-0002(5) home‐range crossings are observed, REML is unreliable by orders of magnitude, ML home ranges are ~30% underestimated, and our perturbative estimators yield home ranges that are only ~10% underestimated. A parametric bootstrap can then reduce the ML and perturbative home‐range underestimation to ~10% and ~3%, respectively. Home‐range estimation is one of the primary reasons for collecting animal tracking data, and small effective sample sizes are a more common problem than is currently realized. The methods introduced here allow for more accurate movement‐model and home‐range estimation at small effective sample sizes, and thus fill an important role for animal movement analysis. Given REML’s widespread use, our methods may also be useful in other contexts where effective sample sizes are small.

Motivation

The goal of introducing the Rescaled CIFAR-10 dataset is to provide a dataset that contains scale variations (up to a factor of 4), to evaluate the ability of networks to generalise to scales not present in the training data.

The Rescaled CIFAR-10 dataset was introduced in the paper:

[1] A. Perzanowski and T. Lindeberg (2025) "Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations”, Journal of Mathematical Imaging and Vision, 67(29), https://doi.org/10.1007/s10851-025-01245-x.

with a pre-print available at arXiv:

[2] Perzanowski and Lindeberg (2024) "Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations”, arXiv preprint arXiv:2409.11140.

Importantly, the Rescaled CIFAR-10 dataset contains substantially more natural textures and patterns than the MNIST Large Scale dataset, introduced in:

[3] Y. Jansson and T. Lindeberg (2022) "Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales", Journal of Mathematical Imaging and Vision, 64(5): 506-536, https://doi.org/10.1007/s10851-022-01082-2

and is therefore significantly more challenging.

Access and rights

The Rescaled CIFAR-10 dataset is provided on the condition that you provide proper citation for the original CIFAR-10 dataset:

[4] Krizhevsky, A. and Hinton, G. (2009). Learning multiple layers of features from tiny images. Tech. rep., University of Toronto.

and also for this new rescaled version, using the reference [1] above.

The data set is made available on request. If you would be interested in trying out this data set, please make a request in the system below, and we will grant you access as soon as possible.

The dataset

The Rescaled CIFAR-10 dataset is generated by rescaling 32×32 RGB images of animals and vehicles from the original CIFAR-10 dataset [4]. The scale variations are up to a factor of 4. In order to have all test images have the same resolution, mirror extension is used to extend the images to size 64x64. The imresize() function in Matlab was used for the rescaling, with default anti-aliasing turned on, and bicubic interpolation overshoot removed by clipping to the [0, 255] range. The details of how the dataset was created can be found in [1].

There are 10 distinct classes in the dataset: “airplane”, “automobile”, “bird”, “cat”, “deer”, “dog”, “frog”, “horse”, “ship” and “truck”. In the dataset, these are represented by integer labels in the range [0, 9].

The dataset is split into 40 000 training samples, 10 000 validation samples and 10 000 testing samples. The training dataset is generated using the initial 40 000 samples from the original CIFAR-10 training set. The validation dataset, on the other hand, is formed from the final 10 000 image batch of that same training set. For testing, all test datasets are built from the 10 000 images contained in the original CIFAR-10 test set.

The h5 files containing the dataset

The training dataset file (~5.9 GB) for scale 1, which also contains the corresponding validation and test data for the same scale, is:

cifar10_with_scale_variations_tr40000_vl10000_te10000_outsize64-64_scte1p000_scte1p000.h5

Additionally, for the Rescaled CIFAR-10 dataset, there are 9 datasets (~1 GB each) for testing scale generalisation at scales not present in the training set. Each of these datasets is rescaled using a different image scaling factor, 2^k/4, with k being integers in the range [-4, 4]:

cifar10_with_scale_variations_te10000_outsize64-64_scte0p500.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte0p595.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte0p707.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte0p841.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte1p000.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte1p189.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte1p414.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte1p682.h5
cifar10_with_scale_variations_te10000_outsize64-64_scte2p000.h5

These dataset files were used for the experiments presented in Figures 9, 10, 15, 16, 20 and 24 in [1].

Instructions for loading the data set

The datasets are saved in HDF5 format, with the partitions in the respective h5 files named as
('/x_train', '/x_val', '/x_test', '/y_train', '/y_test', '/y_val'); which ones exist depends on which data split is used.

The training dataset can be loaded in Python as:

with h5py.File(`

x_train = np.array( f["/x_train"], dtype=np.float32)
x_val = np.array( f["/x_val"], dtype=np.float32)
x_test = np.array( f["/x_test"], dtype=np.float32)
y_train = np.array( f["/y_train"], dtype=np.int32)
y_val = np.array( f["/y_val"], dtype=np.int32)
y_test = np.array( f["/y_test"], dtype=np.int32)

We also need to permute the data, since Pytorch uses the format [num_samples, channels, width, height], while the data is saved as [num_samples, width, height, channels]:

x_train = np.transpose(x_train, (0, 3, 1, 2))
x_val = np.transpose(x_val, (0, 3, 1, 2))
x_test = np.transpose(x_test, (0, 3, 1, 2))

The test datasets can be loaded in Python as:

with h5py.File(`

x_test = np.array( f["/x_test"], dtype=np.float32)
y_test = np.array( f["/y_test"], dtype=np.int32)

The test datasets can be loaded in Matlab as:

x_test = h5read(`

The images are stored as [num_samples, x_dim, y_dim, channels] in HDF5 files. The pixel intensity values are not normalised, and are in a [0, 255] range.

This paper addresses the computational methods and challenges associated with prime number generation, a critical component in encryption algorithms for ensuring data security. The generation of prime numbers efficiently is a critical challenge in various domains, including cryptography, number theory, and computer science. The quest to find more effective algorithms for prime number generation is driven by the increasing demand for secure communication and data storage and the need for efficient algorithms to solve complex mathematical problems. Our goal is to address this challenge by presenting two novel algorithms for generating prime numbers: one that generates primes up to a given limit and another that generates primes within a specified range. These innovative algorithms are founded on the formulas of odd-composed numbers, allowing them to achieve remarkable performance improvements compared to existing prime number generation algorithms. Our comprehensive experimental results reveal that our proposed algorithms outperform well-established prime number generation algorithms such as Miller-Rabin, Sieve of Atkin, Sieve of Eratosthenes, and Sieve of Sundaram regarding mean execution time. More notably, our algorithms exhibit the unique ability to provide prime numbers from range to range with a commendable performance. This substantial enhancement in performance and adaptability can significantly impact the effectiveness of various applications that depend on prime numbers, from cryptographic systems to distributed computing. By providing an efficient and flexible method for generating prime numbers, our proposed algorithms can develop more secure and reliable communication systems, enable faster computations in number theory, and support advanced computer science and mathematics research.

Home-range estimation is an important application of animal tracking data that is frequently complicated by autocorrelation, sampling irregularity, and small effective sample sizes. We introduce a novel, optimal weighting method that accounts for temporal sampling bias in autocorrelated tracking data. This method corrects for irregular and missing data, such that oversampled times are downweighted and undersampled times are upweighted to minimize error in the home-range estimate. We also introduce computationally efficient algorithms that make this method feasible with large datasets. Generally speaking, there are three situations where weight optimization improves the accuracy of home-range estimates: with marine data, where the sampling schedule is highly irregular, with duty cycled data, where the sampling schedule changes during the observation period, and when a small number of home-range crossings are observed, making the beginning and end times more independent and informative than the intermediate times. Using both simulated data and empirical examples including reef manta ray, Mongolian gazelle, and African buffalo, optimal weighting is shown to reduce the error and increase the spatial resolution of home-range estimates. With a conveniently packaged and computationally efficient software implementation, this method broadens the array of datasets with which accurate space-use assessments can be made.

📜 About this Dataset

This dataset contains the full Collatz sequences and associated statistical metrics for all integers from 1 to 20,000,000. It has been carefully generated and structured to support mathematical research, data analysis, and machine learning experimentation on this famous unsolved problem.

The dataset is split into multiple .parquet files, each covering 1 million numbers, to allow efficient loading and processing. It is ideal for use in time series modeling, integer sequence analysis, or algorithmic exploration of iterative processes.

Key Features:

• Complete Collatz Sequences for 20 million integers
• Statistical summaries for each number:
  • Length of the sequence
  • Maximum value reached
  • Time to reach 1 (stop time)
  • Even/Odd ratio
  • Total sum of the sequence
• Optimized storage format (parquet with snappy compression)
• Clean naming convention for easy integration

Why this matters:

The Collatz Conjecture remains one of the simplest unsolved problems in mathematics, and this dataset enables scalable, empirical investigation over a large numerical range. It is particularly useful for: - Researchers exploring patterns or heuristics in sequence dynamics - Data scientists interested in feature extraction or predictive modeling - Educators looking for clean datasets to teach recursive algorithms and data pipelines

🔍 What we did:

In addition to providing raw sequences and metrics, we conducted a large-scale coverage analysis of the Collatz dynamics.
For each integer range [1, x], we computed:

• The number of integers within [1, x] never generated by any Collatz sequence starting from 1 to x (excluding the seeds themselves).
• The number of integers strictly greater than x that were generated as a byproduct of these same sequences.

This analysis revealed two striking patterns: - A significant and steadily growing number of integers in [1, x] are never reached, even when all x seeds are considered. - Conversely, the number of integers generated beyond x increases rapidly, often exceeding the initial range.

These results suggest that Collatz sequences, while converging to 1, expand far beyond their starting interval and do not uniformly explore the space [1, x] — hinting at an underlying structure worth investigating.

🚀 Next research directions:

This dataset and its coverage extension open up many avenues for exploration: - Analyze the proportion of missing values over larger intervals: does it stabilize, grow linearly, or oscillate? - Study the structure of unreachable integers: are there arithmetic patterns, density clusters, or forbidden residue classes? - Model the overshoot effect: how far do sequences typically escape beyond their seeds, and what governs that behavior? - Compare empirical patterns with theoretical predictions from probabilistic Collatz models. - Use machine learning to predict missing values or to classify sequence behaviors based on their metrics. - Visualize the growth trees or inverse paths of generated numbers to uncover propagation patterns.

Motivation

The goal of introducing the Rescaled Fashion-MNIST dataset is to provide a dataset that contains scale variations (up to a factor of 4), to evaluate the ability of networks to generalise to scales not present in the training data.

The Rescaled Fashion-MNIST dataset was introduced in the paper:

[1] A. Perzanowski and T. Lindeberg (2025) "Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations”, Journal of Mathematical Imaging and Vision, 67(29), https://doi.org/10.1007/s10851-025-01245-x.

with a pre-print available at arXiv:

[2] Perzanowski and Lindeberg (2024) "Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations”, arXiv preprint arXiv:2409.11140.

Importantly, the Rescaled Fashion-MNIST dataset is more challenging than the MNIST Large Scale dataset, introduced in:

[3] Y. Jansson and T. Lindeberg (2022) "Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales", Journal of Mathematical Imaging and Vision, 64(5): 506-536, https://doi.org/10.1007/s10851-022-01082-2.

Access and rights

The Rescaled Fashion-MNIST dataset is provided on the condition that you provide proper citation for the original Fashion-MNIST dataset:

[4] Xiao, H., Rasul, K., and Vollgraf, R. (2017) “Fashion-MNIST: A novel image dataset for benchmarking machine learning algorithms”, arXiv preprint arXiv:1708.07747

and also for this new rescaled version, using the reference [1] above.

The data set is made available on request. If you would be interested in trying out this data set, please make a request in the system below, and we will grant you access as soon as possible.

The dataset

The Rescaled FashionMNIST dataset is generated by rescaling 28×28 gray-scale images of clothes from the original FashionMNIST dataset [4]. The scale variations are up to a factor of 4, and the images are embedded within black images of size 72x72, with the object in the frame always centred. The imresize() function in Matlab was used for the rescaling, with default anti-aliasing turned on, and bicubic interpolation overshoot removed by clipping to the [0, 255] range. The details of how the dataset was created can be found in [1].

There are 10 different classes in the dataset: “T-shirt/top”, “trouser”, “pullover”, “dress”, “coat”, “sandal”, “shirt”, “sneaker”, “bag” and “ankle boot”. In the dataset, these are represented by integer labels in the range [0, 9].

The dataset is split into 50 000 training samples, 10 000 validation samples and 10 000 testing samples. The training dataset is generated using the initial 50 000 samples from the original Fashion-MNIST training set. The validation dataset, on the other hand, is formed from the final 10 000 images of that same training set. For testing, all test datasets are built from the 10 000 images contained in the original Fashion-MNIST test set.

The h5 files containing the dataset

The training dataset file (~2.9 GB) for scale 1, which also contains the corresponding validation and test data for the same scale, is:

fashionmnist_with_scale_variations_tr50000_vl10000_te10000_outsize72-72_scte1p000_scte1p000.h5

Additionally, for the Rescaled FashionMNIST dataset, there are 9 datasets (~415 MB each) for testing scale generalisation at scales not present in the training set. Each of these datasets is rescaled using a different image scaling factor, 2^k/4, with k being integers in the range [-4, 4]:

fashionmnist_with_scale_variations_te10000_outsize72-72_scte0p500.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte0p595.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte0p707.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte0p841.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte1p000.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte1p189.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte1p414.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte1p682.h5
fashionmnist_with_scale_variations_te10000_outsize72-72_scte2p000.h5

These dataset files were used for the experiments presented in Figures 6, 7, 14, 16, 19 and 23 in [1].

Instructions for loading the data set

The datasets are saved in HDF5 format, with the partitions in the respective h5 files named as
('/x_train', '/x_val', '/x_test', '/y_train', '/y_test', '/y_val'); which ones exist depends on which data split is used.

The training dataset can be loaded in Python as:

with h5py.File(`

x_train = np.array( f["/x_train"], dtype=np.float32)
x_val = np.array( f["/x_val"], dtype=np.float32)
x_test = np.array( f["/x_test"], dtype=np.float32)
y_train = np.array( f["/y_train"], dtype=np.int32)
y_val = np.array( f["/y_val"], dtype=np.int32)
y_test = np.array( f["/y_test"], dtype=np.int32)

We also need to permute the data, since Pytorch uses the format [num_samples, channels, width, height], while the data is saved as [num_samples, width, height, channels]:

x_train = np.transpose(x_train, (0, 3, 1, 2))
x_val = np.transpose(x_val, (0, 3, 1, 2))
x_test = np.transpose(x_test, (0, 3, 1, 2))

The test datasets can be loaded in Python as:

with h5py.File(`

x_test = np.array( f["/x_test"], dtype=np.float32)
y_test = np.array( f["/y_test"], dtype=np.int32)

The test datasets can be loaded in Matlab as:

x_test = h5read(`

The images are stored as [num_samples, x_dim, y_dim, channels] in HDF5 files. The pixel intensity values are not normalised, and are in a [0, 255] range.

There is also a closely related Fashion-MNIST with translations dataset, which in addition to scaling variations also comprises spatial translations of the objects.

These are simulated data without any identifying information or informative birth-level covariates. We also standardize the pollution exposures on each week by subtracting off the median exposure amount on a given week and dividing by the interquartile range (IQR) (as in the actual application to the true NC birth records data). The dataset that we provide includes weekly average pregnancy exposures that have already been standardized in this way while the medians and IQRs are not given. This further protects identifiability of the spatial locations used in the analysis. This dataset is not publicly accessible because: EPA cannot release personally identifiable information regarding living individuals, according to the Privacy Act and the Freedom of Information Act (FOIA). This dataset contains information about human research subjects. Because there is potential to identify individual participants and disclose personal information, either alone or in combination with other datasets, individual level data are not appropriate to post for public access. Restricted access may be granted to authorized persons by contacting the party listed. It can be accessed through the following means: File format: R workspace file; “Simulated_Dataset.RData”. Metadata (including data dictionary) • y: Vector of binary responses (1: adverse outcome, 0: control) • x: Matrix of covariates; one row for each simulated individual • z: Matrix of standardized pollution exposures • n: Number of simulated individuals • m: Number of exposure time periods (e.g., weeks of pregnancy) • p: Number of columns in the covariate design matrix • alpha_true: Vector of “true” critical window locations/magnitudes (i.e., the ground truth that we want to estimate) Code Abstract We provide R statistical software code (“CWVS_LMC.txt”) to fit the linear model of coregionalization (LMC) version of the Critical Window Variable Selection (CWVS) method developed in the manuscript. We also provide R code (“Results_Summary.txt”) to summarize/plot the estimated critical windows and posterior marginal inclusion probabilities. Description “CWVS_LMC.txt”: This code is delivered to the user in the form of a .txt file that contains R statistical software code. Once the “Simulated_Dataset.RData” workspace has been loaded into R, the text in the file can be used to identify/estimate critical windows of susceptibility and posterior marginal inclusion probabilities. “Results_Summary.txt”: This code is also delivered to the user in the form of a .txt file that contains R statistical software code. Once the “CWVS_LMC.txt” code is applied to the simulated dataset and the program has completed, this code can be used to summarize and plot the identified/estimated critical windows and posterior marginal inclusion probabilities (similar to the plots shown in the manuscript). Optional Information (complete as necessary) Required R packages: • For running “CWVS_LMC.txt”: • msm: Sampling from the truncated normal distribution • mnormt: Sampling from the multivariate normal distribution • BayesLogit: Sampling from the Polya-Gamma distribution • For running “Results_Summary.txt”: • plotrix: Plotting the posterior means and credible intervals Instructions for Use Reproducibility (Mandatory) What can be reproduced: The data and code can be used to identify/estimate critical windows from one of the actual simulated datasets generated under setting E4 from the presented simulation study. How to use the information: • Load the “Simulated_Dataset.RData” workspace • Run the code contained in “CWVS_LMC.txt” • Once the “CWVS_LMC.txt” code is complete, run “Results_Summary.txt”. Format: Below is the replication procedure for the attached data set for the portion of the analyses using a simulated data set: Data The data used in the application section of the manuscript consist of geocoded birth records from the North Carolina State Center for Health Statistics, 2005-2008. In the simulation study section of the manuscript, we simulate synthetic data that closely match some of the key features of the birth certificate data while maintaining confidentiality of any actual pregnant women. Availability Due to the highly sensitive and identifying information contained in the birth certificate data (including latitude/longitude and address of residence at delivery), we are unable to make the data from the application section publically available. However, we will make one of the simulated datasets available for any reader interested in applying the method to realistic simulated birth records data. This will also allow the user to become familiar with the required inputs of the model, how the data should be structured, and what type of output is obtained. While we cannot provide the application data here, access to the North Carolina birth records can be requested through the North Carolina State Center for Health Statistics, and requires an appropriate data use agreement. Description Permissions: These are simulated data without any identifying information or informative birth-level covariates. We also standardize the pollution exposures on each week by subtracting off the median exposure amount on a given week and dividing by the interquartile range (IQR) (as in the actual application to the true NC birth records data). The dataset that we provide includes weekly average pregnancy exposures that have already been standardized in this way while the medians and IQRs are not given. This further protects identifiability of the spatial locations used in the analysis. This dataset is associated with the following publication: Warren, J., W. Kong, T. Luben, and H. Chang. Critical Window Variable Selection: Estimating the Impact of Air Pollution on Very Preterm Birth. Biostatistics. Oxford University Press, OXFORD, UK, 1-30, (2019).

Please cite the following paper when using this dataset: N. Thakur, “Twitter Big Data as a Resource for Exoskeleton Research: A Large-Scale Dataset of about 140,000 Tweets and 100 Research Questions,” Preprints, 2022, DOI: 10.20944/preprints202206.0383.v1 Abstract The exoskeleton technology has been rapidly advancing in the recent past due to its multitude of applications and use cases in assisted living, military, healthcare, firefighting, and industries. With the projected increase in the diverse uses of exoskeletons in the next few years in these application domains and beyond, it is crucial to study, interpret, and analyze user perspectives, public opinion, reviews, and feedback related to exoskeletons, for which a dataset is necessary. The Internet of Everything era of today's living, characterized by people spending more time on the Internet than ever before, holds the potential for developing such a dataset by mining relevant web behavior data from social media communications, which have increased exponentially in the last few years. Twitter, one such social media platform, is highly popular amongst all age groups, who communicate on diverse topics including but not limited to news, current events, politics, emerging technologies, family, relationships, and career opportunities, via tweets, while sharing their views, opinions, perspectives, and feedback towards the same. Therefore, this work presents a dataset of about 140,000 Tweets related to exoskeletons. that were mined for a period of 5-years from May 21, 2017, to May 21, 2022. The tweets contain diverse forms of communications and conversations which communicate user interests, user perspectives, public opinion, reviews, feedback, suggestions, etc., related to exoskeletons. Instructions: This dataset contains about 140,000 Tweets related to exoskeletons. that were mined for a period of 5-years from May 21, 2017, to May 21, 2022. The tweets contain diverse forms of communications and conversations which communicate user interests, user perspectives, public opinion, reviews, feedback, suggestions, etc., related to exoskeletons. The dataset contains only tweet identifiers (Tweet IDs) due to the terms and conditions of Twitter to re-distribute Twitter data only for research purposes. They need to be hydrated to be used. The process of retrieving a tweet's complete information (such as the text of the tweet, username, user ID, date and time, etc.) using its ID is known as the hydration of a tweet ID. The Hydrator application (link to download the application: https://github.com/DocNow/hydrator/releases and link to a step-by-step tutorial: https://towardsdatascience.com/learn-how-to-easily-hydrate-tweets-a0f393ed340e#:~:text=Hydrating%20Tweets) or any similar application may be used for hydrating this dataset. Data Description This dataset consists of 7 .txt files. The following shows the number of Tweet IDs and the date range (of the associated tweets) in each of these files. Filename: Exoskeleton_TweetIDs_Set1.txt (Number of Tweet IDs – 22945, Date Range of Tweets - July 20, 2021 – May 21, 2022) Filename: Exoskeleton_TweetIDs_Set2.txt (Number of Tweet IDs – 19416, Date Range of Tweets - Dec 1, 2020 – July 19, 2021) Filename: Exoskeleton_TweetIDs_Set3.txt (Number of Tweet IDs – 16673, Date Range of Tweets - April 29, 2020 - Nov 30, 2020) Filename: Exoskeleton_TweetIDs_Set4.txt (Number of Tweet IDs – 16208, Date Range of Tweets - Oct 5, 2019 - Apr 28, 2020) Filename: Exoskeleton_TweetIDs_Set5.txt (Number of Tweet IDs – 17983, Date Range of Tweets - Feb 13, 2019 - Oct 4, 2019) Filename: Exoskeleton_TweetIDs_Set6.txt (Number of Tweet IDs – 34009, Date Range of Tweets - Nov 9, 2017 - Feb 12, 2019) Filename: Exoskeleton_TweetIDs_Set7.txt (Number of Tweet IDs – 11351, Date Range of Tweets - May 21, 2017 - Nov 8, 2017) Here, the last date for May is May 21 as it was the most recent date at the time of data collection. The dataset would be updated soon to incorporate more recent tweets.

Abstract copyright UK Data Service and data collection copyright owner.

In recent years there has been considerable interest in reassessing the role of mathematical proof, influenced by developments in computer technology and an increasing awareness of the role of proof in conveying and illuminating as well as verifying mathematical ideas. Research in mathematics education has shown proof to be an elusive concept for many students. This has been one influence underlying the shift away from formal methods in schools to the more process-orientated approaches now enshrined in the UK National Curriculum Using and Applying Mathematics.
In this project a nationwide survey was conducted to ascertain the current profile of conceptions amongst 15-year-old high-attaining students of the validity of a range of modes of justification in geometry and algebra. Analysis of the survey data informed the design of two teaching experiments in these mathematical domains incorporating computer use and aiming specifically to encourage links between empirical and deductive reasoning. Case studies were constructed to evaluate the influence of these innovations on students' understanding of proving the role of formal mathematical proof.
Both strands of the research contributed to the formulation of recommendations concerning the emphasis on and positioning of mathematical proof in the school curriculum.
Main Topics:

The study consists of two datasets:
the larger dataset contains the responses of the sample of Year 10 students (14 or 15 years old) to a proof questionnaire, which comprised a question to ascertain students' views on the role of proof, followed by items in two domains of mathematics - arithmetic/algebra and geometry - presented in open and multiple-choice formats. In the open format, students were asked to construct one familiar and one unfamiliar proof in each domain. In the multiple-choice format, students were required to choose from a range of arguments in support of or refuting a conjecture in accordance with two criteria: which argument would be nearest to their own approach if asked to prove the given statement, and which they believed would receive the best mark.
The smaller dataset contains responses of the respondent students' teachers to the school questionnaire. This questionnaire was designed to obtain data about the school and the mathematics teacher of the class selected to complete the proof questionnaire. These teachers also completed all the multiple-choice questions in the proof questionnaire, in order to obtain their choices of argument and to identify the proof they thought their students believed would receive the best mark. The responses are included in this dataset.

This report includes species only if they have a Spatial Current Range in ECOS. The state lists in this report will not include species without a Spatial Current Range, and the report totals will not reflect such species. It is therefore possible that some state totals in this report are lower than the true number of species listed.