Metaphysics, mathematics, and meaning is a book. It was written by Nathan U. Salmon and published by Clarendon Press in 2005.

This dataset is about books and is filtered where the book is Dictionary of mathematics. It has 7 columns such as author, BNB id, book, book publisher, and ISBN. The data is ordered by publication date (descending).

A new approach to the validation of surface texture form removal methods is introduced. A linear algebra technique is presented that obtains total least squares (TLS) model fits for a continuous mathematical surface definition. This model is applicable to both profile and areal form removal, and can be used for a range of form removal models including polynomial and spherical fits. The continuous TLS method enables the creation of mathematically traceable reference pairs suitable for the assessment of form removal algorithms in surface texture analysis software. Multiple example reference pairs are presented and used to assess the performance of four tested surface texture analysis software packages. The results of each software are compared against the mathematical reference, highlighting their strengths and weaknesses.

Harrap's book of mathematical tables and definitions is a book. It was written by Sydney Herbert Lamb and published by Harrap in 1970.

% of pupils achieving 5+ A*-Cs GCSE inc. English & Maths at Key Stage 4 (new First Entry definition) - (Snapshot)

*This indicator has been discontinued due to national changes in GCSEs in 2016.

Data Source: CA Department of Education

Data: Test Results for California's Assessments

English Language Arts Definition: Percentage of public school students in grades 3, 4, 5, 6, 7, 8, and 11 scoring in the standard met or standard exceeded achievement level on the CAASPP Smarter Balanced Summative Assessment for English language arts/literacy (ELA), by grade level (e.g., in 2021, 59.2% of 11th graders in California met or exceeded their grade-level standard in ELA).

Mathematics Definition: Percentage of public school students in grades 3, 4, 5, 6, 7, 8, and 11 scoring in the standard met or standard exceeded achievement level on the CAASPP Smarter Balanced Summative Assessment for mathematics, by grade level (e.g., in 2021, 34.4% of 11th graders in California met or exceeded their grade-level standard in mathematics).

Footnote: Years presented are the final year of a school year (e.g., 2020-21 is shown as 2021). Visit the California Assessment of Student Performance and Progress (CAASPP) website for detailed information about the CAASPP system and explanations of the achievement levels. Assessments were not administered in 2020. Due to changes in administration, and low and uneven participation in 2021, the Dept. of Education (2020-21 CAASPP and ELPAC Assessment Results) advises against comparing data for 2021—annotated here with an asterisk (*)—with earlier years. The notation S refers to data that have been suppressed because there were fewer than 20 students in that group. N/A means that data are not available.

A multidisciplinary repository of public data sets such as the Human Genome and US Census data that can be seamlessly integrated into AWS cloud-based applications. AWS is hosting the public data sets at no charge for the community. Anyone can access these data sets from their Amazon Elastic Compute Cloud (Amazon EC2) instances and start computing on the data within minutes. Users can also leverage the entire AWS ecosystem and easily collaborate with other AWS users. If you have a public domain or non-proprietary data set that you think is useful and interesting to the AWS community, please submit a request and the AWS team will review your submission and get back to you. Typically the data sets in the repository are between 1 GB to 1 TB in size (based on the Amazon EBS volume limit), but they can work with you to host larger data sets as well. You must have the right to make the data freely available.

This dataset is about book series and is filtered where the books is A dictionary of named effects and laws in chemistry, physics and mathematics, featuring 10 columns including authors, average publication date, book publishers, book series, and books. The preview is ordered by number of books (descending).

Reference data for the Perram and Wertheim (1985) contact function of ellipsoids

This dataset provides reference values of the contact function of two ellipsoids, as defined by Perram and Wertheim (Perram, J. W., & Wertheim, M. S. (1985). Statistical mechanics of hard ellipsoids. I. Overlap algorithm and the contact function. Journal of Computational Physics, 58(3), 409–416. DOI:10.1016/0021-9991(85)90171-8). This paper will be referred to as PW85 in what follows.

Reference values of the F function

The data is shared as a HDF5 file pw85_ref_data-YYYYMMDD.h5, which contains the following datasets (to be described below)

directions: a 12×3 array,

F: a 108×108×12×9 array,

lambdas: a length-9 array,

radii: a length-3 array,

spheroids: a 108×6 array.

The attached Python script pw85_gen_ref_data.py was used to generate the data; it uses the mpmath library.

Mathematical definition of the contact function

The contact function is defined in PW85 as the maximum over (0, 1) of the F function which is defined as follows [see Eq. (3.7) in PW85, with slightly different notations]

F(λ) = λ(1-λ)r₁₂ᵀ⋅Q⁻¹⋅r₁₂,

where 0 ≤ λ ≤ 1 is a scalar, r₁₂ is the center-to-center vector. Q is the matrix defined as follows

Q = (1-λ)Q₁ + λQ₂,

where Qᵢ is the symmetric, positive definite matrix that defines ellipsoid Ωᵢ through

m ∈ Ωᵢ iff (m-cᵢ)ᵀ⋅Qᵢ⁻¹⋅(m-cᵢ) ≤ 1,

where cᵢ is the center of Ωᵢ. Then, the contact function F₁₂ is defined as the maximum of F [see Eq. (3.8) in PW85]

F₁₂(r₁₂, Q₁, Q₂) = max{ F(λ), 0 ≤ λ ≤ 1 }.

Parametrization

The reference data is restricted to spheroids (equatorial radius: aᵢ; polar radius: cᵢ; direction of axis of revolution: nᵢ)

Qᵢ = aᵢ²I + (cᵢ²-aᵢ²)nᵢᵀ⋅nᵢ,

(I: identity matrix). The radii take the following values

aᵢ, cᵢ ∈ {0.01999, 1.999, 9.999}.

These values of the radii are stored in the radii dataset of the HDF5 file. The orientations nᵢ coincide with the vertices of an icosahedron

nᵢ = [0, ±u, ±v]ᵀ or nᵢ = [±v, 0, ±u]ᵀ or nᵢ = [±u, ±v, 0]ᵀ,

where

  1        φ         1+√5

u = ───────, v = ─────── and φ = ────. √(1+φ²) √(1+φ²) 2

The orientations are stored in the directions dataset as a 12×3 array. The matrices Qᵢ are precomputed and stored in the spheroids dataset as a 108×6 array (note: 108 = 12 orientations × 3 equatorial radii × 3 polar radii). spheroids[i, :] stores the upper triangular part of the corresponding matrix in row-major order

⎡ spheroids[i, 0] spheroids[i, 1] spheroids[i, 2] ⎤ ⎢ spheroids[i, 3] spheroids[i, 4] ⎥. ⎣ sym. spheroids[i, 5] ⎦

The scalar λ takes tabulated values (see the lambdas dataset)

λ ∈ {0.1, 0.2, …, 0.9}.

Note that λ = 0.0 and λ = 1.0 are excluded, since F is uniformly 0 in that case.

Reference values of the F function

The reference values of the function F are stored in the F dataset, which is a 108×108×12×9, such that F[i, j, h, k] is the value of F for

Q₁ = spheroids[i], Q₂ = spheroids[j], r₁₂ = directions[h] and λ = lambdas[k].

Note that the r₁₂ vector takes values in the directions dataset. In other words, only unit-length center-to-center vectors are considered here. Indeed, F trivially depends on the norm of r₁₂, which is therefore not considered here in order to reduce the size of the dataset.

Reference values of the contact function

Note: the following is not implemented yet, as reference values of the contact function were not deemed useful. Indeed, once F is validated, it is straightforward to check that the implementation of F₁₂ to be tested indeed maximizes F.

The reference values of the contact function F₁₂ are stored in the contact_function dataset, which is a 108×108×12×3 array, such that contact_function[i, j, h, k] is the value of F₁₂ for

Q₁ = spheroids[i], Q₂ = spheroids[j] and r₁₂ = radii[h] * directions[k].

Note that the r₁₂ vector is not normed, here.

Protein-Protein, Genetic, and Chemical Interactions for BATH-31 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: BTB and MATH domain containing

Contains the full text, images/drawings, and complex work units (tables, mathematical expressions, genetic sequence data, and chemical structures) of each patent application publication (non-provisional utility and plant) published weekly (Thursdays) from March 15, 2001 to Present. The file formats are eXtensible Markup Language (XML) in accordance with the U.S. Patent Application Version 1.5; 1.6; 4.0 International Common Element (ICE); 4.1 ICE; 4.2 ICE; 4.3 ICE and 4.4 ICE Document Type Definitions (DTDs). Tables and sequence data are included using CALS markup. Mathematical expressions are included using MATHML markup and external Mathematica Notebook (NB) files. Chemical structures are represented by external CambridgeSoft Corp. ChemDraw (CDX) files and MDL Information Systems (MOL) files. Drawings, mathematical expressions, and chemical structures are also included as external Tagged Image File Format (TIFF) Revision 6.0 with CCITT Group 4 Compression image files. Each weekly file contains approximately 5,000 published patent applications. There can be an optional weekly Supplemental zipfile that contains lengthy genetic sequence listings (anything over 300 pages) or a lengthy tables (anything over 200 pages). Approximately 1.5 GB per week. http://patents.reedtech.com/parbfti.php

Problem Statement

Topic Modeling for Research Articles Researchers have access to large online archives of scientific articles. As a consequence, finding relevant articles has become more difficult. Tagging or topic modelling provides a way to give token of identification to research articles which facilitates recommendation and search process.

Given the abstract and title for a set of research articles, predict the topics for each article included in the test set.

Note that a research article can possibly have more than 1 topic. The research article abstracts and titles are sourced from the following 6 topics:

1. Computer Science

2. Physics

3. Mathematics

4. Statistics

5. Quantitative Biology

6. Quantitative Finance

Data Dictionary

train.csv

Evaluation Metric

• Submissions are evaluated on micro F1 Score between the predicted and observed topics for each article in the test set.

Inspiration

Your data will be in front of the world's largest data science community. What questions do you want to see answered?

MMLU (Massive Multitask Language Understanding) is a new benchmark designed to measure knowledge acquired during pretraining by evaluating models exclusively in zero-shot and few-shot settings. This makes the benchmark more challenging and more similar to how we evaluate humans. The benchmark covers 57 subjects across STEM, the humanities, the social sciences, and more. It ranges in difficulty from an elementary level to an advanced professional level, and it tests both world knowledge and problem solving ability. Subjects range from traditional areas, such as mathematics and history, to more specialized areas like law and ethics. The granularity and breadth of the subjects makes the benchmark ideal for identifying a model’s blind spots.

Protein-Protein, Genetic, and Chemical Interactions for BPM5 (Arabidopsis thaliana (Columbia)) curated by BioGRID (https://thebiogrid.org); DEFINITION: BTB-POZ and math domain 5

Abstract

In 1991 the International Institute for Educational Planning (IIEP) and a number of Ministries of Education in Southern and Eastern Africa began to work together in order to address training and research needs in Education. The focus for this work was on establishing long-term strategies for building the capacity of educational planners to monitor and evaluate the quality of their basic education systems. The first two educational policy research projects undertaken by SACMEQ (widely known as "SACMEQ I" and "SACMEQ II") were designed to provide detailed information that could be used to guide planning decisions aimed at improving the quality of education in primary school systems.

During 1995-1998 seven Ministries of Education participated in the SACMEQ I Project. The SACMEQ II Project commenced in 1998 and the surveys of schools, involving 14 Ministries of Education, took place between 2000 and 2004. The survey was undertaken in schools in Botswana, Kenya, Lesotho, Malawi, Mauritius, Mozambique, Namibia, Seychelles, South Africa, Swaziland, Tanzania, Uganda, Zambia and Zanzibar.

Moving from the SACMEQ I Project (covering around 1100 schools and 20,000 pupils) to the SACMEQ II Project (covering around 2500 schools and 45,000 pupils) resulted in a major increase in the scale and complexity of SACMEQ's research and training programmes.

SACMEQ's mission is to: a) Expand opportunities for educational planners to gain the technical skills required to monitor and evaluate the quality of their education systems; and b) Generate information that can be used by decision-makers to plan and improve the quality of education.

Geographic coverage

National coverage

Analysis unit

• Pupils
• Teachers
• Schools

Universe

The target population for SACMEQ's Initial Project was defined as "all pupils at the Grade 6 level in 1995 who were attending registered government or non-government schools". Grade 6 was chosen because it was the grade level where the basics of reading literacy were expected to have been acquired.

Kind of data

Sample survey data [ssd]

Sampling procedure

Sampling The "best" sample design for a particular project is one that provides levels of sampling accuracy that are acceptable in terms of the main aims of the project, while simultaneously limiting cost, logistic, and procedural demands to manageable levels. The major constraints that were established prior to the preparation of the sample designs for the SACMEQ II Project have been listed below.

Target Population: The target population definitions should focus on Grade 6 pupils attending registered mainstream government or non-government schools. In addition, the defined target population should be constructed by excluding no more than 5 percent of pupils from the desired target population.

Bias Control: The sampling should conform to the accepted rules of scientific probability sampling. That is, the members of the defined target population should have a known and non-zero probability of selection into the sample so that any potential for bias in sample estimates due to variations from "epsem sampling" (equal probability of selection method) could be addressed through the use of appropriate sampling weights.

Sampling Errors: The sample estimates for the main criterion variables should conform to the sampling accuracy requirements that the standard error of sampling for the pupil tests should be of a magnitude that is equal to, or smaller than, what would be achieved by The Specification of the Target Population employing a simple random sample of 400 pupils.

Response Rates: Each SACMEQ country should aim to achieve an overall response rate for pupils of 80 percent. This figure was based on the wish to achieve or exceed a response rate of 90 percent for schools and a response rate of 90 percent for pupils within schools.

Administrative and Financial Costs: The number of schools selected in each country should recognise limitations in the administrative and financial resources available for data collection.

Other Constraints: The number of learners selected to participate in the data collection in each selected school should be set at a level that will maximise validity of the within-school data collection for the learner reading and mathematics tests.

For Namibia, the desired target population was all learners enrolled in Grade 6 in the ninth month of the school year (i.e. in September 2000). The net enrolment ratio for the age group 7-13 years old who were enrolled in Grades 1 to 7 in Namibia in 2000 was 91.3 percent. However, in Namibia it was decided to exclude certain learners. These were learners in schools having fewer than 15 Grade 6 learners in them, learners in 'inaccessible schools, and learners in special schools. In all 884 learners from 82 schools were excluded but this only amounted to 1.8 percent of all learners. In Namibia there were 849 primary schools having 48,567 learners. After excluding the 1.8 percent of learners the defined population from which a sample had to be drawn consisted of 47,683 learners from 767 schools.

The number of schools required in the sample is in part a function of the intra-class correlation (rho) which is an indicator of the proportion of variation (in achievement in this case) among schools of total variation. The following is the formula often used for estimating the value of rho in situations where two-stage cluster sampling is employed using (approximately) equal sized clusters.

estimated rho = (b. s(a)square - (s)square) / (b - 1)(s)square

where s(a)square is the variance of cluster means, (s)square is the variance of the element values, and b is the cluster size. In SACMEQ I the rho had been 0.60 in Namibia. That is 60 percent of the variation was among schools and only 40 percent within schools. Therefore, in the case of Namibia a rho of 0.60 was used. This meant drawing a sample of 248 schools.

The major aim of the sampling was to have the equivalent of a simple random sample of 400 learners. In Namibia, this was 767 for reading achievement and 810 for mathematics. Hence the sample was a very good one for Namibia. For SACMEQ I it had been 335 which was below the required 400. This was because SACMEQ I was the first sample survey in Namibia and at that time it was assumed that the rho was 0.30. It was not. In SACMEQ II the rhos were 0.60 for reading and 0.53 for mathematics. Thus, in 2000 the variation among schools was slightly lower than in 1995.

Mode of data collection

Face-to-face [f2f]

Research instrument

The data collection for SACMEQ’s Initial Project took place in October 1995 and involved the administration of questionnaires to pupils, teachers, and school heads. The pupil questionnaire contained questions about the pupils’ home backgrounds and their school life; the teacher questionnaire asked about classrooms, teaching practices, working conditions, and teacher housing; and the school head questionnaire collected information about teachers, enrolments, buildings, facilities, and management. A reading literacy test was also given to the pupils. The test was based on items that were selected after a trial-testing programme had been completed.

Cleaning operations

Data entry and data cleaning A team of five persons from the University of Namibia Multi-Disciplinary Research Centre computer lab was appointed and trained in the use of WINDEM, a special data entry package to be used in SACMEQ. The numbers of keystrokes required to enter one copy of each data collection instrument were as follows: learner questionnaire: 150; learner reading test: 85; learner mathematics test: 65; teacher questionnaire: 587; teacher reading test: 51; teacher mathematics test: 43; school head questionnaire: 319; school form: 58; and learner name form: 51.

In the case of Namibia the total number of keystrokes was as follows: learner questionnaire: 762,600; learner reading test: 429,080; learner mathematics test: 328,250; teacher questionnaire: 358,657; teacher reading test: 15,504; teacher mathematics test: 14,061; school head questionnaire: 86,130; school form: 39,150; and learner name form: 259,284. That is, a total of 2,292,716 keystrokes were required to enter all of the data for Namibia.

An experienced keyboard operator can work at a rate of 25 keystrokes per minute (working from multi-paged questionnaires and stopping occasionally to clarify individual questionnaire entries with the supervisor). Assuming that this kind of work rate could be sustained for, say, around a maximum of six hours per day, then the whole data entry operation for Namibia was estimated to amount to around 255 person days of data entry work. This implied an estimated 10 weeks of work for the 5-person data entry team that operated in Namibia. However, the work was completed in 7 weeks because the data enterers worked extra hours.

At the end of this procedure the data files were sent by email to the unit 'Monitoring Educational Quality' at the IIEP in Paris. Many consistency checks were made for many variables as well as for the identification codes used. The IIEP team had many queries. The first data files were sent to Paris in May 2001 and after nine to-ings and fro-ings the files were finally declared to be clean on 25 January 2002.

Response rate

Response rates for pupils and schools respectively were 91.8 percent and 100 percent. The reason for the shortfall in learner numbers was absenteeism by some learners in some of the schools on the day of data collection. However, sampling weights were used to correct for disproportionality among strata in the calculation

Computational modelling of biological processes poses multiple challenges in each stage of the modelling exercise. Some significant challenges include identifiability, precisely estimating parameters from limited data, informative experiments and anisotropic sensitivity in the parameter space. One of these challenges’ crucial but inconspicuous sources is the possible presence of large regions in the parameter space over which model predictions are nearly identical. This property, known as sloppiness, has been reasonably well-addressed in the past decade, studying its possible impacts and remedies. However, certain critical unanswered questions concerning sloppiness, particularly related to its quantification and practical implications in various stages of system identification, still prevail. In this work, we systematically examine sloppiness at a fundamental level and formalise two new theoretical definitions of sloppiness. Using the proposed definitions, we establish a mathematical relationship between the parameter estimates’ precision and sloppiness in linear predictors. Further, we develop a novel computational method and a visual tool to assess the goodness of a model around a point in parameter space by identifying local structural identifiability and sloppiness and finding the most sensitive and least sensitive parameters for non-infinitesimal perturbations. We demonstrate the working of our method in benchmark systems biology models of various complexities. The pharmacokinetic HIV infection model analysis identified a new set of biologically relevant parameters that can be used to control the free virus in an active HIV infection.

1The range is shown in brackets if there are two or more data points. The definition of each category of healthcare is stated in the methods. The values do not add up to 100% because of the varying categorisation of healthcare providers in the included studies and because some studies recorded more than one care seeking event.2Appropriate health facilities included all government and trained private health practitioners, but not traditional healers, pharmacies and unqualified medical practitioners.3Abbreviations: Gov  =  Governmental; CHW  =  Community Health Worker; Trad. Healer = Traditional Healer; ORT  =  Oral Rehydration Therapy; -  =  no data available.

AIC values (ΔAIC) are quoted relative to the minimum AIC value across all models. The model with ΔAIC = 0 is the model with lowest AIC and thus has most statistical support. See Table 1 for parameter definitions.