A Tutorial on Polynomial Regression through Linear Algebra


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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


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.




One-to-Many (O2M) Tools

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


Manglar: Evolutionary Patterns


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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.


The Chaos Game Explorer Tool


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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


On Chaos, Fractals, and the Google Matrix


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Again, for those at the intersection of IR/Data Mining/Chaos/Fractals, check this out

Google matrix analysis of directed networks, by Leonardo Ermann, Klaus M. Frahm, and Dima L. Shepelyansky

A great article.

My research career is now in its first full circle.

On PageRank, Spatial Networks, and Bifurcation Diagrams

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

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:

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.

Bifurcation Diagrams Explorer


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Quadratic Map

Bifurcation diagrams are used in the study of dynamical systems and are applicable to a wide range of fields: from the modeling of biological populations and financial systems to the modeling of chemical reactions and nonlinear circuits, to mention a few.

We have developed a new tool for students and researchers interested in Nonlinear Dynamical Systems, called the Bifurcation Diagrams Explorer. It is available at


This tool lets you explore many of the bifurcation diagrams found in the literature, providing a visualization of the underlying behavior of a dynamical system as a parameter c is changed. We assume that you have a basic knowledge of bifurcation diagrams and dynamical systems.

The tool is powered by our Minerazzi Grapher, a lightweight PHP class that generates all kind of graphs through a web browser. No additional libraries or software needed. A great resource for introducing users to Chaos Theory.

Tired of Newspaper Paywalls?


Paywalls are intrusive code designed for the sole purpose of inducing readers to sign or pay for access to content, effectively acting as reader roadblocks. Some newspaper sites are still insisting in using them.

To try to avoid them, give a chance to this: Refresh the page you want to access and press few times and as soon as you can the Esc key from you keyboard. Another option is to append this to the end of the page url:


then resubmit url using a javascript enabled browser. It stops many paywalls, though might not work 100% of the time (e.g., if the target uses countermeasures).

If you know of other solutions, let me know.