A Tutorial on Polynomial Regression through Linear Algebra

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Algorithms, Linear Algebra, Mathematics, Matrices, Polynomial Regression, Regression, tools, tutorials

If you are a chemist, biodesigner, or a researcher working in other fields, eventually you may need to fit a paired data set to a polynomial regression model. You could use software to do that, or build your own solution. This tutorial is aimed at those interested in the latter. Access it now at

http://www.minerazzi.com/tutorials/polynomial-regression-tutorial.pdf

Three different methods for implementing polynomial regression are described. Teachers and students might benefit from the tutorial since the calculations can be done with a spreadsheet software like Excel, by writing a computer program, or with a programmable calculator.

 

 

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Acid-Base Systems Tool

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chemical mining, chemistry, chemistry mining, chemistry tools

This is a new tool, available now at

http://www.minerazzi.com/tools/acid-base-systems/calculator.php

The tool replaces a previous one (removed from the web) where only simple acid-base solutions were considered.

The current one is not limited to the analysis of one solution or to acid-base titrations. Actually the tool also supports pH calculations of systems not undergoing titrations.

This is a great tool for real world applications like pH calculations from natural acid-base systems where a sample might consist of multiple acids mixed with several bases and/or their salts.

Examples of such systems are bio-samples (blood, saliva…) as well as geo-samples (sea and river water) and urban samples (sewage, wastewater,..).

This new tool is based on a general equation for acid-base systems that is solved using a residual analysis algorithm, avoiding the need for using inversion techniques, successive approximations, Newton-Raphson method, or the evaluation of derivatives or high-degree polynomials.

Activity Coefficient Models Calculator

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activity coefficient models, activity coefficients, chemical mining, chemistry, chemistry calculators, chemistry tools, computational chemists, electrochemistry

This is a new tool available at

http://www.minerazzi.com/tools/activity-coefficients/calculator.php

If you are into chemical data mining, this post might interest you.

This new Minerazzi tool easily solves activity coefficient models for a missing term.

Thus the tool allows you to cross-map activity coefficients to ionic strengths and vice versa using the following models:

Debye-Hückel Limiting Law

Debye-Hückel Extended Limiting Law

Güntelberg

Davis

Truesdell-Jones

The tool , written in PHP, was inspired in the WATEQF program originally written in FORTRAN (https://www.nrc.gov/docs/ML0331/ML033170395.pdf).

Recent versions of that program are available for download from the U.S. Geological Survey site at https://wwwbrr.cr.usgs.gov/projects/GWC_chemtherm/software.htm

Chemistry researchers, teachers and students can benefit from this tool, which is part of an ongoing effort of making available online scientific research tools across different disciplines.

04-05-2017 Update: Additional content and literature references added.

Physiology and Chemistry Tools

Tags

chemistry, chemistry tools, Physiology, physiology tools, tools

Recent available tools relevant to physiology and chemistry, with some interesting exercises.

Body Mass Index (BMI)
http://www.minerazzi.com/tools/body-mass-index/calculator.php

Corpulence Index (CI)
http://www.minerazzi.com/tools/corpulence-index/calculator.php

Membrane Potentials
http://www.minerazzi.com/tools/membrane-potentials/calculator.php

Cell Electrode Potentials
http://www.minerazzi.com/tools/cell-electrode-potentials/calculator.php

Standard Electrode Potentials
http://www.minerazzi.com/tools/standard-electrode-potentials/calculator.php

Membrane Potentials Calculator for Cross-Mapping Goldman-Hodgkin-Katz (GHK) Equation

Tags

chemistry, cross-mapping, Data Mining, Mathematics, variables

In a recent post,

https://irthoughts.wordpress.com/2017/02/28/a-cross-mapping-tool-for-standard-electrode-potential-calculations/

we mentioned a design pattern for easily cross-mapping all experimental variables from a given model. By applying the pattern to the Nernst Equation, we were able to develop the Standard Electrode Potentials Calculator which cross-maps all 4 experimental terms from said equation. This tool is available at

http://www.minerazzi.com/tools/standard-electrode-potentials/calculator.php

In this post we just want to mention that by applying the same design pattern to the Goldman-Hodgkin-Katz (GHK) Equation we were able to develop the Membrane Potentials Calculator, which cross-maps 12 experimental terms. This new tool is available now at

http://www.minerazzi.com/tools/membrane-potentials/calculator.php

Examples on how to do the mapping of variables are given in the Suggested Exercises section of the tool.

Overall, we are confident that the patterns used in the design of these tools can be applied, across disciplines, to mathematical models consisting of more experimental variables.

 

A Cross-Mapping Tool for Standard Electrode Potential Calculations

Tags

chemistry, chemistry tools, chemistry tutorials, electrochemistry

This is a cross-mapping tool for the analysis and manipulation of scientific data in an interactive fashion. Its design pattern will be used to build new upcoming tools across several and dissimilar disciplines.

The tool is available at

http://www.minerazzi.com/tools/standard-electrode-potentials/calculator.php

The tool easily solves the Standard Electrode Potential equation for a missing term. That is, given all but one of the experimental terms, the tool solves for the missing one.

There is no doubt that cross-mapping variables from a single tool set up is more engaging than single-mapping them: A great instructive tool for students and teachers alike.

Enjoy it.

Reagent Solutions Maker

Tags

chemistry, chemistry calculators, chemistry tools

The Reagent Solutions Maker is a new tool available now in the Tools section of Minerazzi at

http://www.minerazzi.com/tools/reagent-solutions/maker.php

The tool is not really relevant to information retrieval, but the algorithm that runs behind it describes a useful pattern applicable to many fields and disciplines, including IR.

Anyway, the tool is aimed at solving the following problem.

An undiluted reagent solution is typically prepared by dissolving an amount of solid reagent in a solvent, usually water. Additional solvent is then added to bring the solution up to a specific volume.

With the reagent formula weight the solution concentration can be expressed in moles per liter, after proper unit conversions. A set of undiluted solutions at specific concentration intervals can be prepared in this way, but the calculations can be tedious. This tool was developed to simplify all these calculations.

The tool computes the amount of solid reagent needed to prepare n number of undiluted solutions at specific concentration intervals, ∆C, and up to a maximum concentration level, C, and volume, V, where C > ∆C > 0.

Notice that the set of solutions to be prepared, n, is not known in advance.

Chemistry Exams Miner

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chemistry, Chemistry Exams, Chemistry Exams Miner, chemistry miner, chemistry tools

This is a new miner, available at

http://www.minerazzi.com/chemexams

Find chemistry exams, practice tests, assessment studies, & more.

Great for chemistry teachers and their students.

Use it to find practice tests with(out) answers, standardized tests, and course-specific exams, or build chemistry exams curated collections. Whether you are taking analytical, organic, physical, or general chemistry, this miner is for you.

Litmus test yourself!

Nobel Prize Laureates Miner

Tags

Algorithms, chemistry, Data Mining, Mathematics, Physics, statistics, tools

This is a new Minerazzi.com miner, available now at

http://www.minerazzi.com/nobel-prize/

Use it to find resources relevant to laureates of the Nobel Prize. Search by laureates, country, discipline, or field. Find Nobel Prize Laureates in Chemistry, Physics, and other fields.

 

 

72 Binary Similarity Measures

Tags

Algorithms, bioinformatics, chemical mining, chemistry, Data Conversion, data miners, Data Mining, information retrieval, ir, minerazzi, miners, mining, news, social mining, statistics, tools, tutorials, Vector Space Models

We have expanded the number of similarity measures that our Binary Similarity Calculator computes from 30 to 72 (and counting…)

Same measures with different names have been consolidated into a single record, and different measures with same name have been enumerated as necessary.

These similarity coefficients have many applications across disciplines: from bioinformatics to chemistry, chemometrics, statistics, data mining, information retrieval, marketing research, etc.

The tool is available at

http://www.minerazzi.com/tools/similarity/binary-similarity-calculator.php

We have also included the new similarity measures proposed by Consonni & Todeschini (2012), and Todeschini, et al (2012).

Our Tutorial on Distance and Similarity was also updated, accordingly. Check it out at

http://www.minerazzi.com/tutorials/distance-similarity-tutorial.pdf

 

References

Consonni, V. and Todeschini, R. (2012). New Similarity Coefficients for Binary Data. MATCH Commun. Math. Comput. Chem. 68, 581-592.

Todeschini, R., Consonni, V., Xiang, H., Holliday, J., Buscema, M., and Willet, P. (2012). Similarity Coefficients for Binary Chemoinformatics Data: Overview and Extended Comparison Using Simulated and Real Data Sets. J. Chem. Inf. Model. 52 (11).