MetaMath QA

Mathematical Questions for Large Language Models

By Huggingface Hub [source]

About this dataset

This dataset contains meta-mathematics questions and answers collected from the Mistral-7B question-answering system. The responses, types, and queries are all provided in order to help boost the performance of MetaMathQA while maintaining high accuracy. With its well-structured design, this dataset provides users with an efficient way to investigate various aspects of question answering models and further understand how they function. Whether you are a professional or beginner, this dataset is sure to offer invaluable insights into the development of more powerful QA systems!

More Datasets

For more datasets, click here.

Featured Notebooks

• 🚨 Your notebook can be here! 🚨!

How to use the dataset

Data Dictionary

The MetaMathQA dataset contains three columns: response, type, and query. - Response: the response to the query given by the question answering system. (String) - Type: the type of query provided as input to the system. (String) - Query:the question posed to the system for which a response is required. (String)

Preparing data for analysis

It’s important that before you dive into analysis, you first familiarize yourself with what kind data values are present in each column and also check if any preprocessing needs to be done on them such as removing unwanted characters or filling in missing values etc., so that it can be used without any issue while training or testing your model further down in your process flow.

##### Training Models using Mistral 7B

Mistral 7B is an open source framework designed for building machine learning models quickly and easily from tabular (csv) datasets such as those found in this dataset 'MetaMathQA ' . After collecting and preprocessing your dataset accordingly Mistral 7B provides with support for various Machine Learning algorithms like Support Vector Machines (SVM), Logistic Regression , Decision trees etc , allowing one to select from various popular libraries these offered algorithms with powerful overall hyperparameter optimization techniques so soon after selecting algorithm configuration its good practice that one use GridSearchCV & RandomSearchCV methods further tune both optimizations during model building stages . Post selection process one can then go ahead validate performances of selected models through metrics like accuracy score , F1 Metric , Precision Score & Recall Scores .

##### Testing phosphors :

After successful completion building phase right way would be robustly testing phosphors on different evaluation metrics mentioned above Model infusion stage helps here immediately make predictions based on earlier trained model OK auto back new test cases presented by domain experts could hey run quality assurance check again base score metrics mentioned above know asses confidence value post execution HHO updating baseline scores running experiments better preferred methodology AI workflows because Core advantage finally being have relevancy inexactness induced errors altogether impact low

Research Ideas

• Generating natural language processing (NLP) models to better identify patterns and connections between questions, answers, and types.
• Developing understandings on the efficiency of certain language features in producing successful question-answering results for different types of queries.
• Optimizing search algorithms that surface relevant answer results based on types of queries

Acknowledgements

If you use this dataset in your research, please credit the original authors. Data Source

License

License: CC0 1.0 Universal (CC0 1.0) - Public Domain Dedication No Copyright - You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. See Other Information.

Columns

File: train.csv | Column name | Description | |:--------------|:------------------------------------| | response | The response to the query. (String) | | type | The type of query. (String) |

Acknowledgements

If you use this dataset in your research, please credit the original authors. If you use this dataset in your research, please credit Huggingface Hub.

The IBEM dataset consists of 600 documents with a total number of 8272 pages, containing 29603 isolated and 137089 embedded Mathematical Expressions (MEs). The objective of the IBEM dataset is to facilitate the indexing and searching of MEs in massive collections of STEM documents. The dataset was built by parsing the LaTeX source files of documents from the KDD Cup Collection. Several experiments can be carried out with the IBEM dataset ground-truth (GT): ME detection and extraction, ME recognition, etc.

The dataset consists of the following files:

• “IBEM.json”: file containing the IBEM GT information. The data is firstly organized by pages, then by the type of expression (“embedded” or “displayed”), and lastly by the GT of each individual ME. For each ME we provide:
  • xy page-level coordinates, reported as relative (%) to the width/height of the page image.
  • “split” attribute indicating the number of fragments in which the ME has been split. MEs can be split over various lines, columns or pages. The LaTeX transcript of split MEs have been exactly replicated (entire LaTeX definition) for each fragment.
  • “latex” original transcript as extracted from the LaTeX source files of the documents. This definition can contain user-defined macros. In order to be able to compile these expressions, each page includes the preamble of the source files containing the defined macros and the packages used by the authors of the documents.
  • “latex_expand” transcript reconstructed from the output stream of the LuaLaTeX engine in which user-defined macros have been expanded. The transcript has the same visual representation as the original transcript, with the addition that the LaTeX definitions are tokenized, the order of sub/super script elements have been fixed, and matrices have been transformed to arrays.
  • “latex_norm” transcript resulting from applying an extra normalization process to the “latex_expand” expression. This normalization process includes removing font information such as slant, style, and weight.
• “partitions/*.lst”: files containing list of pages forming the partition sets.
• “pages/*.jpg”: individual pages extracted from the documents.

The dataset is partitioned into various sets as provided for the ICDAR 2021 Competition on Mathematical Formula Detection. The ground-truth related to this competition, which is included in this dataset version, can also be found here. More information about the competition can be found in the following paper:

D. Anitei, J.A. Sánchez, J.M. Fuentes, R. Paredes, and J.M. Benedí. ICDAR 2021 Competition on Mathematical Formula Detection. In ICDAR, pages 783–795, 2021.

For ME recognition tasks, we recommend rendering the “latex_expand” version of the formulae in order to create standalone expressions that have the same visual representation as MEs found in the original documents (see attached python script “extract_GT.py”). Extracting MEs from the documents based on coordinates is more complex, as special care is needed to concatenate the fragments of split expressions. Baseline results for ME recognition tasks will soon be made available.

This dataset is about book subjects. It has 1 row and is filtered where the books is 7-11 maths dictionary. It features 10 columns including number of authors, number of books, earliest publication date, and latest publication date.

Data from a comparative judgement survey consisting of 62 working mathematics educators (ME) at Norwegian universities or city colleges, and 57 working mathematicians at Norwegian universities. A total of 3607 comparisons of which 1780 comparisons by the ME and 1827 ME. The comparative judgement survey consisted of respondents comparing pairs of statements on mathematical definitions compiled from a literature review on mathematical definitions in the mathematics education literature. Each WM was asked to judge 40 pairs of statements with the following question: “As a researcher in mathematics, where your target group is other mathematicians, what is more important about mathematical definitions?” Each ME was asked to judge 41 pairs of statements with the following question: “For a mathematical definition in the context of teaching and learning, what is more important?” The comparative judgement was done with No More Marking software (nomoremarking.com) The data set consists of the following data: comparisons made by ME (ME.csv) comparisons made by WM (WM.csv) Look up table of codes of statements and statement formulations (key.csv) Each line in the comparison represents a comparison, where the "winner" column represents the winner and the "loser" column the loser of the comparison.

📌 Description - The SAT is a standardized test adminstered by the College Board and widely used for college admissions in the United States. - The source dataset gives the mean SAT math and verbal scores for males (M), for females (F), and for all students (A) for the years 1967 to 2001. - I have added the last three columns for verbal+math averages: for males, females, and for all students.

🎯 Objective: - To compare scores by year. - To compare scores by gender. - To compare students' performance in verbal and math.

📦 Source: The College Board

📥 Download TSV source file: SATbyYear.tsv

The dataset contains mean temperature of the city of Yaounde in Cameroon from 1976 to 2021.

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

*This indicator was discontinued in 2014 due to the national changes in GCSEs.

The release of the LCA Commons Unit Process Data: field crop production Version 1.1 includes the following updates:Added meta data to reflect USDA LCA Digital Commons data submission guidance including descriptions of the process (reference to which the size of the inputs and outputs in the process relate, description of the process and technical scope and any aggregation; definition of the technology being used, its operating conditions); temporal representatives; geographic representativeness; allocation methods; process type (U: unit process, S: system process); treatment of missing intermediate flow data; treatment of missing flow data to or from the environment; intermediate flow data sources; mass balance; data treatment (description of the methods and assumptions used to transform primary and secondary data into flow quantities through recalculating, reformatting, aggregation, or proxy data and a description of data quality according to LCADC convention); sampling procedures; and review details. Also, dataset documentation and related archival publications are cited in the APA format.Changed intermediate flow categories and subcategories to reflect the ISIC International Standard Industrial Classification (ISIC).Added “US-” to the US state abbreviations for intermediate flow locations.Corrected the ISIC code for “CUTOFF domestic barge transport; average fuel” (changed to ISIC 5022: Inland freight water transport).Corrected flow names as follows: "Propachlor" renamed "Atrazine". “Bromoxynil octanoate” renamed “Bromoxynil heptanoate”. “water; plant uptake; biogenic” renamed “water; from plant uptake; biogenic” half the instances of “Benzene, pentachloronitro-“ replaced with Etridiazole and half with “Quintozene”. “CUTOFF phosphatic fertilizer, superphos. grades 22% & under; at point-of-sale” replaced with “CUTOFF phosphatic fertilizer, superphos. grades 22% and under; at point-of-sale”.Corrected flow values for “water; from plant uptake; biogenic” and “dry matter except CNPK; from plant uptake; biogenic” in some datasets.Presented data in the International Reference Life Cycle Data System (ILCD)1 format, allowing the parameterization of raw data and mathematical relations to be presented within the datasets and the inclusion of parameter uncertainty data. Note that ILCD formatted data can be converted to the ecospold v1 format using the OpenLCA software.Data quality rankings have been updated to reflect the inclusion of uncertainty data in the ILCD formatted data.Changed all parameter names to “pxxxx” to accommodate mathematical relation character limitations in OpenLCA. Also adjusted select mathematical relations to recognize zero entries. The revised list of parameter names is provided in the documentation attached.Resources in this dataset:Resource Title: Cooper-crop-production-data-parameterization-version-1.1 .File Name: Cooper-crop-production-data-parameterization-version-1.1.xlsxResource Description: Description of parameters that define the Cooper Unit process data for field crop production version 1.1Resource Title: Cooper_Crop_Data_v1.1_ILCD.File Name: Cooper_Crop_Data_v1.1_ILCD.zipResource Description: .zip archive of ILCD xml files that comprise crop production unit process modelsResource Software Recommended: openLCA,url: http://www.openlca.org/Resource Title: Summary of Revisions of the LCA Digital Commons Unit Process Data: field crop production for version 1.1 (August 2013).File Name: Summary of Revisions of the LCA Digital Commons Unit Process Data- field crop production, Version 1.1 (August 2013).pdfResource Description: Documentation of revisions to version 1 data that constitute version 1.1

Reading, science and math mean scores from the Pan-Canadian Assessment Program (PCAP), by province.

Reading, science and math mean scores from the Pan-Canadian Assessment Program (PCAP), by province.

Fractional order algorithms demonstrate superior efficacy in signal processing while retaining the same level of implementation simplicity as traditional algorithms. The self-adjusting dual-stage fractional order least mean square algorithm, denoted as LFLMS, is developed to expedite convergence, improve precision, and incurring only a slight increase in computational complexity. The initial segment employs the least mean square (LMS), succeeded by the fractional LMS (FLMS) approach in the subsequent stage. The latter multiplies the LMS output, with a replica of the steering vector (Ŕ) of the intended signal. Mathematical convergence analysis and the mathematical derivation of the proposed approach are provided. Its weight adjustment integrates the conventional integer ordered gradient with a fractional-ordered. Its effectiveness is gauged through the minimization of mean square error (MSE), and thorough comparisons with alternative methods are conducted across various parameters in simulations. Simulation results underscore the superior performance of LFLMS. Notably, the convergence rate of LFLMS surpasses that of LMS by 59%, accompanied by a 49% improvement in MSE relative to LMS. So it is concluded that the LFLMS approach is a suitable choice for next generation wireless networks, including Internet of Things, 6G, radars and satellite communication.

####### # Data description #

This dataset have been constructed and used for scientific purpose, available in the paper "Detecting the effects of inter-annual and seasonal changes of environmental factors on the the striped red mullet population in the Bay of Biscay" authored by Kermorvant C., Caill-Milly N., Sous D., Paradinas I., Lissardy M. and Liquet B. and published in Journal of Sea Research. This file is an extraction from the SACROIS fisheries database created by Ifremer (for more information see https://sextant.ifremer.fr/record/3e177f76-96b0-42e2-8007-62210767dc07/) and from the Copernicus database. Biochemestry comes from the product GLOBAL_ANALYSIS_FORECAST_BIO_001_028 (https://resources.marine.copernicus.eu/?option=com_csw&view=details&product_id=GLOBAL_ANALYSIS_FORECAST_BIO_001_028). Temperature and salinity comes from GLOBAL_ANALYSIS_FORECAST_PHY_001_024 product (https://resources.marine.copernicus.eu/?option=com_csw&view=details&product_id=GLOBAL_ANALYSIS_FORECAST_PHY_001_024). As fisheries landing per unit of effort is only available per ICES rectangle and by month, environmental data have been aggregated accordingly.

######### # Colomns description # ############### rectangle - The 6 ICES statistical rectangles used in the study. time_m - Time in months, from the beginning to the end of the study. annee = year mois = month (from 1 to 12) Poids = Weight of red mullet landed valeur = Temps_peche = fishing time Nb_sequence = number of fishing sequences Moy / Med / Var / StD Quartil_1 / Quartil_3 / min / max / CV / IQR = statistical descriptors of landing by rectangle and by month log_cpue = log of Med colomn mean_surface_s = mean of surface salinity by month and by rectangle median_surface_s = median of surface salinity by month and by rectangle mean_surface_t = mean of surface temperature by month and by rectangle median_surface_t = median of surface temperature by month and by rectangle si / zeu /po4 / pyc / o2/ nppv / no3 and nh4 mean and median concentration by rectangle and by month pc3 / pc2 / pc1 - projections of previous biochemestry variables on the three first axes of a PCA

The dataset provides simulated insights into student engagement and performance within the THM platform. It outlines mathematical representations of student learning profiles, detailing behaviors ranging from high achievers to inconsistent performers. Additionally, the dataset includes key performance indicators, offering metrics like room completion, points earned, and time spent to gauge student progress and interaction within the platform's modules. Here are definitions of the learning profiles, along with mathematical representations of their behaviors:

High Achiever: These are students who consistently perform well across all modules. Their performance can be described as a normal distribution centered at a high mean value. Their performance P in a given module can be modelled as: P = N(90, 5) where N is the normal distribution function, 90 is the mean, and 5 is the standard deviation. Average Performer: These are students who typically perform at the average level across all modules. Their performance can be described as a normal distribution centered at a medium mean value: P = N(70, 10), where 70 is the mean, and 10 is the standard deviation. Late Bloomer: These are students whose performance improves as they progress through the modules. Their performance can be modelled as: P = N(50 + i*10, 10), where i is the module index and shows an increasing trend. Specialized Talent: These are students who have average performance in most modules but excel in a particular module (e.g., module5). Their performance can be described as: P = N(90, 5) if the module is module 5, else P = N(70, 10). Inconsistent Performer: These are students whose performance varies significantly across modules. Their performance can be described as a normal distribution with a high standard deviation: P = N(70, 30), where 70 is the mean, and 30 is the high standard deviation, reflecting inconsistency. Note that the actual performances are bounded between 0 and 100 using the function max(0, min(100, performance)) to ensure valid percentages. In these formulas, the np.random.normal function is used to simulate the variability in student performance around the mean values. The first argument to this function is the mean, and the second argument is the standard deviation, reflecting the level of variability around the mean. The function returns a number drawn from the normal distribution described by these parameters. Note that the proposed method is experimental and has not been validated.

List of Key Performance Indicators (KPIs) for Student Engagement and Progress within the Platform:

Room Name: This represents the unique identifier or name of a specific room (or module). Think of each room as a separate module or lesson within an educational platform. For example, Room1, Room2, etc. Total rooms completed: Indicates the cumulative number of rooms that a student has fully completed. Completion is typically determined by meeting certain criteria, like answering all questions or achieving a certain score. Rooms registered in: Represents the number of rooms a student has registered or enrolled in. This could be different from the total number of rooms they've completed. Ratio of Questions completed per room: This gives an insight into a student's progress in a particular room. For instance, a ratio of 7/10 suggests the student has completed 7 out of 10 available questions in that room. Room Completed (yes no): Indicates whether a student has fully completed a specific room or not. This could be determined by the percentage of material covered, questions answered, or a certain score achieved. Room Last deploy (count of days): Refers to the number of days since the last update or deployment was made to that room. It can give an idea about the effort of the student. Points in room used for the leaderboard (range 0-560): Each room assigns points based on student performance, and these points contribute to leaderboards. The range suggests that a student can earn anywhere from 0 to 560 points in a particular room. Last answered question in a room (27th Jan 2023): This indicates the date when a student last answered a question in a specific room. It can provide insights into a student's recent activity and engagement. Total points in all rooms (range 0-560): The cumulative score a student has achieved across all rooms. Path Percentage completed (range 0-100): Indicates the percentage of the overall learning path that the student has completed. A path could consist of multiple modules or rooms. Module Percentage completed (range 0-100): Represents how much of a specific module (which could have multiple lessons or topics) a student has completed. Room Percentage completed (range 0-100): Shows the percentage of a specific room that has been completed by a student. Time Spent on the platform (seconds): This provides an aggregate of the total time a student has spent on the entire educational platform. Time spent on each room (seconds): Represents the amount of time a student has dedicated to a specific room. This can give insights into which rooms or modules are the most time-consuming or engaging for students.

Analysis of ‘Breast Cancer Wisconsin (Diagnostic) Data Set’ provided by Analyst-2 (analyst-2.ai), based on source dataset retrieved from https://www.kaggle.com/uciml/breast-cancer-wisconsin-data on 28 January 2022.

--- Dataset description provided by original source is as follows ---

Features are computed from a digitized image of a fine needle aspirate (FNA) of a breast mass. They describe characteristics of the cell nuclei present in the image. n the 3-dimensional space is that described in: [K. P. Bennett and O. L. Mangasarian: "Robust Linear Programming Discrimination of Two Linearly Inseparable Sets", Optimization Methods and Software 1, 1992, 23-34].

This database is also available through the UW CS ftp server: ftp ftp.cs.wisc.edu cd math-prog/cpo-dataset/machine-learn/WDBC/

Also can be found on UCI Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29

Attribute Information:

1) ID number 2) Diagnosis (M = malignant, B = benign) 3-32)

Ten real-valued features are computed for each cell nucleus:

a) radius (mean of distances from center to points on the perimeter) b) texture (standard deviation of gray-scale values) c) perimeter d) area e) smoothness (local variation in radius lengths) f) compactness (perimeter^2 / area - 1.0) g) concavity (severity of concave portions of the contour) h) concave points (number of concave portions of the contour) i) symmetry j) fractal dimension ("coastline approximation" - 1)

The mean, standard error and "worst" or largest (mean of the three largest values) of these features were computed for each image, resulting in 30 features. For instance, field 3 is Mean Radius, field 13 is Radius SE, field 23 is Worst Radius.

All feature values are recoded with four significant digits.

Missing attribute values: none

Class distribution: 357 benign, 212 malignant

--- Original source retains full ownership of the source dataset ---

We study a fast local-global window-based attention method to accelerate Informer for long sequence time-series forecasting (LSTF) in a robust manner. While window attention being local is a considerable computational saving, it lacks the ability to capture global token information which is compensated by a subsequent Fourier transform block. Our method, named FWin, does not rely on query sparsity hypothesis and an empirical approximation underlying the ProbSparse attention of Informer. Experiments on univariate and multivariate datasets show that FWin transformers improve the overall prediction accuracies of Informer while accelerating its inference speeds by 1.6 to 2 times. On strongly non-stationary data (power grid and dengue disease data), FWin outperforms Informer and recent SOTAs thereby demonstrating its superior robustness. We give mathematical definition of FWin attention, and prove its equivalency to the canonical full attention under the block diagonal invertibility (BDI) condition of the attention matrix. The BDI is verified to hold with high probability on benchmark datasets experimentally.

Mean difference between the accuracy of classifier in row and the classifier in column . The last column shows the mean accuracy of the respective classifier for all datasets considered in our study.

This repository contains the key supporting data (in the netcdf format) for the following paper:

Zhang, R. and M. Thomas, 2021, Horizontal circulation across density surfaces contributes substantially to the long-term mean northern Atlantic Meridional Overturning Circulation.

In this study, Robust Diagnostic Calculations (RDC) are conducted using a high-resolution global fully coupled climate model, in which the ocean potential temperature and salinity are relaxed back to the observed long-term mean hydrographic data to provide a holistic picture of the long-term mean AMOC structure at northern high latitudes over the past several decades. For comparison, the high-resolution global coupled climate model used for the RDC experiments in this study is also employed to generate a present-day control simulation.

Descriptions of data files in this repository:

1. Mean sea surface height (SSH, in unit of m) from Robust Diagnostic Calculations (RDC) and the control simulation (MODEL), as shown in Fig. 2b,c in the paper. All are referenced to their own averages over the entire domain (80^oW-20^oE, 30^o-80^oN).

RDC_SSH_30N80N_80w20E.nc

MODEL_SSH_30N80N_80w20E.nc

2. Mean AMOC streamfunctions (Sv) across the OSNAP section, in density-space (potential density \(\sigma_0, kg/m^3\) ) and depth-space (z, m) from RDC and MODEL, as shown in Fig. 3 in the paper.

OSNAP West:

RDC_moc_sigma0_OSNAP_West.nc

RDC_moc_z_OSNAP_West.nc

MODEL_moc_sigma0_OSNAP_West.nc

MODEL_moc_z_OSNAP_East.nc

OSNAP East:

RDC_moc_sigma0_OSNAP_East.nc

RDC_moc_z_OSNAP_East.nc

MODEL_moc_sigma0_OSNAP_East.nc

MODEL_moc_z_OSNAP_West.nc

Entire OSNAP section:

RDC_moc_sigma0_OSNAP_Total.nc

RDC_moc_z_OSNAP_Total.nc

MODEL_moc_sigma0_OSNAP_Total.nc

MODEL_moc_z_OSNAP_Total.nc

3. Mean velocity (m/s) and potential density \((\sigma_0, kg/m^3)\) across the OSNAP section from RDC and MODEL, as shown in Fig. 4b,c in the paper.

RDC_velocity_OSNAP.nc

RDC_sigma0_OSNAP.nc

MODEL_velocity_OSNAP.nc

MODEL_sigma0_OSNAP.nc

4. Mean -z diagram of AMOC transport (Sv), i.e. integrated volume transport across OSNAP West and OSNAP East over each potential density \((\sigma_0, kg/m^3)\) bin and depth (z, m) bin, derived from OSNAP observations (OBS), RDC, and MODEL, as shown in Fig. 6 in the paper.

OBS_transport_sigma0-z_OSNAP_West.nc

OBS_transport_sigma0-z_OSNAP_East.nc

RDC_transport_sigma0-z_OSNAP_West.nc

RDC_transport_sigma0-z_OSNAP_East.nc

MODEL_transport_sigma0-z_OSNAP_West.nc

MODEL_transport_sigma0-z_OSNAP_East.nc

5. Mean AMOC streamfunctions (Sv) across Arctic-Atlantic gateways sections in density-space (potential density \(\sigma_0, kg/m^3\)) and depth-space (z, m) from RDC and MODEL, as shown in Fig. 7 in the paper.

Section across the Fram Strait and Barents Sea Opening:

RDC_moc_sigma0_FS_BSO.nc

RDC_moc_z_FS_BSO.nc

MODEL_moc_sigma0_FS_BSO.nc

MODEL_moc_z_FS_BSO.nc

Section across 68^oN in Nordic Seas:

RDC_moc_sigma0_NS_68N.nc

RDC_moc_z_NS_68N.nc

MODEL_moc_sigma0_NS_68N.nc

MODEL_moc_z_NS_68N.nc

Section across the Greenland-Scotland Ridge (GSR):

RDC_moc_sigma0_GSR.nc

RDC_moc_z_GSR.nc

MODEL_moc_sigma0_GSR.nc

MODEL_moc_z_GSR.nc

6. Mean velocity (m/s) and potential density \((\sigma_0, kg/m^3)\) across Arctic-Atlantic gateways sections from RDC and MODEL, as shown in Fig. 8 in the paper.

Section across the Fram Strait and Barents Sea Opening:

RDC_velocity_FS_BSO.nc

RDC_sigma0_FS_BSO.nc

MODEL_velocity_FS_BSO.nc

MODEL_sigma0_FS_BSO.nc

Section across 68^oN in Nordic Seas:

RDC_velocity_NS_68N.nc

RDC_sigma0_NS_68N.nc

MODEL_velocity_NS_68N.nc

MODEL_sigma0_NS_68N.nc

Section across the Greenland-Scotland Ridge (GSR), also called the Greenland-Iceland-Scotland (GIS) Ridge:

RDC_velocity_GSR.nc

RDC_sigma0_GSR.nc

MODEL_velocity_GSR.nc

MODEL_sigma0_GSR.nc

Acknowledgements We acknowledge the use of the following datasets and model code in this study: The World Ocean Atlas 2013 (WOA13) data were downloaded from the NOAA National Centers for Environmental Information (formerly the National Oceanographic Data) https://www.nodc.noaa.gov/cgi-bin/OC5/woa13/woa13.pl. The CSIRO ATLAS of REGIONAL SEAS 2009 version (CARS2009) data (http://www.marine.csiro.au/~dunn/cars2009/) were developed and provided by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Marine and Atmospheric Research, and downloaded from http://www.marine.csiro.au/atlas/. The climatological surface wind stress data are from the European Centre for Medium-range Weather Forecast (ECMWF): The ERA-Interim reanalysis data, Copernicus Climate Change Service (C3S) (accessed September 18, 2019), available from:

https://www.ecmwf.int/en/forecasts/datasets/archive-datasets/reanalysis-datasets/era-interim. The observed mean dynamic topography data were produced by CLS and distributed by Aviso+ with support from Cnes (https://www.aviso.altimetry.fr/), and downloaded from ftp://ftp-access.aviso.altimetry.fr/auxiliary/mdt/mdt_cnes_cls2013_global/. Data from the full OSNAP (Overturning in the Subpolar North Atlantic Program) array for the first 21 months (31-Jul-2014 to 20-Apr-2016) were downloaded from https://www.o-snap.org/. OSNAP data were collected and made freely available by the OSNAP project and all the national programs that contribute to it (www.o-snap.org). The code of the Geophysical Fluid Dynamics Laboratory (GFDL) coupled climate model version 2.5 (CM2.5) used in this study is publicly available at https://www.gfdl.noaa.gov/cm2-5-and-flor-quickstart/. The relevant citations for the above datasets and model code are listed in Zhang and Thomas, 2021.

Multivariate model prediction accuracy on the test dataset (RMSE mean and standard deviation for 30 experimental runs across 4 prediction horizons).

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.

ObjectiveEmergency department (ED) frequent attenders (FA) have been the subject of discussion in many countries. This group of patients have contributed to the high expenses of health services and strained capacity in the department. Studies related to ED FAs aim to describe the characteristics of patients such as demographic and socioeconomic factors. The analysis may explore the relationship between these factors and multiple patient visits. However, the definition used for classifying patients varies across studies. While most studies used frequency of attendance to define the FA, the derivation of the frequency is not clear.MethodsWe propose a mathematical methodology to define the time interval between ED returns for classifying FAs. K-means clustering and the Elbow method were used to identify suitable FA definitions. Recursive clustering on the smallest time interval cluster created a new, smaller cluster and formal FA definition.ResultsApplied to a case study dataset of approximately 336,000 ED attendances, this framework can consistently and effectively identify FAs across EDs. Based on our data, a FA is defined as a patient with three or more attendances within sequential 21-day periods.ConclusionThis study introduces a standardized framework for defining ED FAs, providing a consistent and effective means of identification across different EDs. Furthermore, the methodology can be used to identify patients who are at risk of becoming a FA. This allows for the implementation of targeted interventions aimed at reducing the number of future attendances.