# Fractals Miner

**08**
*Tuesday*
May 2018

**08**
*Tuesday*
May 2018

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**24**
*Tuesday*
Apr 2018

in

**Tags**

Ancient Mathematicians, Famous Mathematicians, Math History, Mathematician Biographies, Mathematics, minerazzi, Modern Mathematicians

Math Bios is a new miner available at

http://www.minerazzi.com/mathbios

Find biographies of famous mathematicians from ancient to modern times.

Interested in the life of Euler, Fermat, Poincare, Blackwell, and other great mathematicians? Want to build a curated collection about math people from the ancient and modern times? This is the place to start.

A great tool for math history researchers and students in general.

**22**
*Sunday*
Apr 2018

**Tags**

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.

**09**
*Monday*
Apr 2018

Some developers build form-based graphical user interfaces (GUIs) that give users the illusion of mapping the value of an input field to all other fields. Typical examples are conversion unit tools and other types of converters used in science and business oriented sites. This is frequently done by coding in the background M number of fields M number of times, with most fields hidden or dynamically coded. These M x M fields are then conditionally processed.

As M increases said strategy becomes very inefficient from both the coding and processing standpoint. Modifying these types of GUIs can be messy. For instance, to display a simple unit conversion tool with five conversion units requires the coding of 25 fields. To add an additional conversion unit requires the coding of 6 x 6 = 36 fields. Insane!

To overcome all those drawbacks, we have developed what we call a one-to-many fields mapping algorithm or O2M. The algorithm is quite simple and works as follows. Given a form with M unique text fields, randomly using one as an input field instructs the algorithm to treat the remaining ones as output fields. It does not matter which field is initially used or from where the data comes from (i.e., a user or database). Its value will be mapped to the remaining M – 1 fields. As a whole, an O2M GUI behaves as a many-to-many (M2M) solution. To grasp the concept, try one of our O2M tools at

**03**
*Tuesday*
Apr 2018

**Tags**

Algorithms, Chaos, evolutionary patterns, fractals, manglar, Mathematics, Nonlinear Dynamics, plants evolution, tools

Do you see the algorithm behind this image? Hint: It corresponds to Manglar, an upcoming tool I’m building for simulating the growth of patterns. I’m still testing it.

Manglar. Coming Soon.

**30**
*Friday*
Mar 2018

The Chaos Game Explorer is our most recent tool. It was developed to help users replicate many of the patterns found in the fractal geometry literature. The tool is available at

**12**
*Monday*
Mar 2018

Posted Chaos, Data Mining, Dynamics, IR Tools, Mathematics, Programming, social mining, Software

inWe have recently launched the Bifurcation Diagrams Explorer. This is a tool for examining the behavior of low dimensional nonlinear dynamical systems.

http://www.minerazzi.com/tools/bifurcation/diagrams.php

Well, what does that have anything to do with information retrieval (IR)?

A lot!

If you are an IR guy at the intersection of nonlinear dynamics, you already probably know that bifurcation diagrams are relevant to:

- Google search inefficiencies and that popular sites are like attractors on the Web.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.036213

https://www.ncbi.nlm.nih.gov/pubmed/20365838

https://www.researchgate.net/publication/43020903_Google_matrix_dynamical_attractors_and_Ulam_networks - The growth and evolution of spatial networks can be modeled with bifurcation diagrams.

http://www.maths.nuigalway.ie/~eoghan/MSc_Eoghan.pdf

So the implications to social media, search, and data mining are there, if you can grasp the relevant research out there.

I wonder how long it will take for pseudo-scientific marketers/seos to prey on that, as they tried in the past with LSI/LSA, LDA, Vector Theory, and few other IR topics.

**15**
*Tuesday*
Aug 2017

**Tags**

Puerto Rico Statistics Institute (Instituto de Estadísticas de Puerto Rico) has a nice introductory manual on R, written by Dr. Orville M. Disdier. Check it out at

http://estadisticas.pr/iepr/LinkClick.aspx?fileticket=p71ePCZXuYM%3d&tabid=100

or get access by visiting

http://estadisticas.pr/iepr/Academias.aspx

BTW, there is a new version of the site which at the time of writing is still in beta at

**17**
*Monday*
Jul 2017

**Tags**

Correlation Coefficients, Data Mining, Mathematics, Pearson Correlation, Spearman Correlation, statistics, tutorials

This is Part 2 of a tutorial series on the nonadditivity of correlation coefficients. This time we discuss Fisher *r*-to-*Z* and *Z*-to-*r* transformations and the risks of arbitrarily implementing these.

Misusing the transformations can have a detrimental impact on significance testing, confidence intervals, reported standard errors of correlations, and meta-analysis.

The tutorial is available at

http://www.minerazzi.com/tutorials/nonadditivity-correlations-part-2.pdf

**11**
*Tuesday*
Jul 2017

This is a new Minerazzi tool available now at

http://www.minerazzi.com/tools/regression-correlation/calculator.php

The tool does simple linear regression and correlation analyses, computing Spearman and Pearson correlation coefficients and other relevant statistics.

The companion default example was intentionally selected to illustrate that for rank data free from ties, Spearman and Pearson correlation coefficients are the same thing.