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Complex coloring and contour levels

January 5, 2020
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Complex coloring and contour levels

I was recently fascinated by the illustration taken from the leaflet https://www.maa.org/sites/default/files/pdf/Mathhorizons/pdfs/ColoringPage_MH_Nov17.pdfI knew that complex functions could be colored in mesmerizing ways but the little book by Julie Barnes, William Kreahling, and Beth Schaubroeck, “Coloring book of complex function repesentation”, MAA Press, 2017, explores new avenues and, say, I never realized that contour lines could be used to obtain...

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Chaos, bifurcation diagrams and Lyapunov exponents with R (2)

December 12, 2016
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Chaos, bifurcation diagrams and Lyapunov exponents with R (2)

(The first part of this article can be read here)Iteration of one-dimensional maps can generate stunning complexity and famed examples of chaotic behavior.  R can be used to get the flavor of this richness and reproduce some of the most famous pictures in the history of science, such as the bifurcation diagram of the logistic map or the representation...

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Non-linear dynamics and chaos using R (1)

December 3, 2016
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Non-linear dynamics and chaos using R (1)

I have been teaching the course "Mathematics" for the PhD students at Ca' Foscari University for a few years. In the lectures I cover some "scattered" material that may prove useful, sooner or later, to develop quantitative models in Economics. One of the weeks of the course is devoted to non-linear dynamics, one-dimensional maps and chaos.R can be extremely...

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MOOC "Take lineaR decisions" (Ca’ Foscari University)

August 22, 2016
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MOOC "Take lineaR decisions" (Ca’ Foscari University)

The MOOC "Take lineaR decisions" will begin on September 19th 2016, covering some models of decision making mainly based on computational linear algebra (linear systems and eigenvalues/vectors). The course, delivered by prof. Paolo Pellizzari, can be used to acquire practical skills in the use of the open software R in dealing with matrices, vectors and related optimization problems. In...

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Nonlinear constraints with a modified constrOptim

September 7, 2015
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Nonlinear constraints with a modified constrOptim

I often use constrOptim to quickly solve nonlinear optimization problems. constrOptim works well as a general tool to tackle constrained problems like\  There are many other options and packages for specific problems but constrOptim is likely to be the first choice when little is known on the problem at hand or for exploratory/quick-and-dirty analysis.The main problem...

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