Universidad Nacional Abierta Matemáticas El Tigre

martes, 27 de diciembre de 2016

Interacción

Mi nombre es José Loreto Romero Palma y soy asesor del Área Matemática del Centro Local Anzoátegui, ubicado en la Unidad de Apoyo El Tigre. Actualmente, soy nivel corrector de las siguientes asignaturas:

Asignatura	Estudiantes de las sedes
Matemática I (códigos 175-177)	Barcelona y El Tigre
Matemática II (códigos 178 y 179)	Barcelona y El Tigre
Matemática III (código 733)	El Tigre
Introducción a la Probabilidad (códigos 737 y 747)	Barcelona, El Tigre y Anaco
Inferencia Estadística (códigos 738, 748)	El Tigre y Anaco
Estadística General (745)	Barcelona, El Tigre y Anaco
Estadística Aplicada (746)	Barcelona, El Tigre y Anaco

¿Cuál forma de interacción prefieres, presencial o virtual?

Modo Presencial

Horario de Atención	Teléfono
Miercoles, Jueves y Viernes: 4:00 pm a 6:00 pm Sábado: 8:00 am a 12:00 m.	0283- 9893503
Ubicación

Nota

Los talleres (presenciales) serán en la sede de la UNA o en la EB Trujillo (ver mapa).
Las asesorías individuales (presenciales) serán en la sede de la UNA en el horario indicado arriba. Si vienes de Anaco o de Barcelona, por favor avísame por algún medio (correo electrónico o por los comentarios de Google+ abajo) con anticipación para asegurarte que te atienda y no hagas el viaje en vano.
Queda terminantemente prohibido llamarme por celular, a menos que estes cansado de vivir o quieras que te recuerde a tu progenitora. Hablando en serio- sencillamente no atiendo llamadas de números desconocidos y mucho menos fuera de mi horario de trabajo.

Modo Virtual

Es mi modo de contacto favorito y seguramente, en la medida en que te vayas adaptando al sistema de estudios a distancia, con el tiempo será tu modo de contacto favorito también. La ventaja principal de este modo de interacción con el asesor es que es asíncrono y a distancia- te comunicas conmigo cuando quieras y desde donde estés. Constantemente estoy monitoreando los canales de comunicación de comunicación en línea que he dispuesto para ti- en cuestión de minutos u horas o en todo caso a la brevedad posible, te responderé.

Empecemos por el correo electrónico- un medio de comunicación más personal y más uno-a-uno. El mío es jlaurentum@gmail.com. Si para plantear tus dudas debes escribir formulismos matemáticos, te sugiero que utilices el método indicado en mi entrada sobre LaTeX. Para este método requieres tener una cuenta de correos Gmail. Por cierto, si no dispones de una cuenta de correos Gmail, te sugiero que crees una.

Lo que antes era el buzón de mensajes (o Chat Box) ubicado en la parte superior derecha del blog lo he cambiado por dos mecanismos de interacción: el Twitter y el sistema de comentarios propio de Google+. El Twitter lo utilizo más que todo para hacer anuncios sobre la publicación de objetivos logrados en exámenes, aclarar dudas muy generales o cosas así. Es un canal de comunicación de una sola vía (asesor ⇒ estudiante) tipo noticioso. Puedes ver mis tweets donde antes estaba el buzón de mensajes al abrir el blog. Por cierto, si me sigues (haciendo clic sobre el botón debajo del feed de Twitter), podrás recibir mis actualizaciones via el app de tu smartphone o en la página de Twitter también.

Los marcos para comentarios de Google+ sustituyen y amplian las funcionalidades del viejo buzón de mensajes en esta página, pero debes disponer de una cuenta Gmail para comentar. Las ventajas de este sistema de interacción son varias. Por una parte, como todos los servicios de google son integrados, cuando alguién responde a tu comentario o hace referencia a tí en un comentario, recibes una notificación de Google si te encuentras navegando en alguna página de Google (como por ejemplo en tu correo Gmail). Por otra parte, los marcos de comentarios, la comunicación es multidireccional (asesor ⇔ estudiante ⇔ estudiante) y multi-hilo.

Los invito a hacer uso de los marcos de comentarios en este sitio. El de esta página de "Interacción" en particular reservémoslo para temas y preguntas generales sobre la asesoría académica. En este caso, recuerden indicar su nombre, la asignatura y la pregunta específica. En las entradas del blog también hay marcos de comentarios. Los invito a comentar allí si quieren discutir sobre el tema presentado en la entrada. En todo caso, aplican las normas de cortesía para hacer que las conversaciones por los marcos de comentarios fluyan de la forma más natural y provechosa para todos. No toleraré conductas de troleo o insultos hacia mi persona u otros estudiantes, ni comentarios discriminatorios hacia un grupo de personas (cero racismo, misoginia, comentarios homofóbicos, etc.)- tales comentarios serán eliminados. Evita escribir todo en mayúsculas porque al hacerlo das a entender que estas gritando. Por último, si quieres dirigirte hacia una persona, puedes escribir el símbolo + (signo de más) seguido del nombre de esa persona tal como aparece en Google+ (por ejemplo, yo sería +José Romero. ¡Les deseo un feliz y provechoso aprendizaje virtual!

viernes, 23 de diciembre de 2016

Feliz Navidad 2016 (en R)

Quisiera desearle a mis lectores una feliz Navidad 2016 ... al estilo R. Vacílense mi arbolito navideño 3d creado usando el paquete plot3D de R:

Árbol de navidad en perspectiva y animado

Aunque esto sería aún otra decoración navideña hecha en R, lo original de esta es que el árbol se muestra en perspectiva tridimensional. Hace un tiempo, yo mismo elaboré un código en R para visualizar un árbol navideño en dos dimensiones (ver esta entrada), el cual a su vez era basado en el código que apareció en el blog Wiekvoet. Sin embargo, esta vez el reto era crear un modelo tridimensional del árbol visualizado en perspectiva con una animación mostrando el árbol en rotación.

Leer más / Read on ...»

jueves, 22 de diciembre de 2016

Merry Christmas 2016 (with R)

I'd like to wish all my readers a Merry Christmas 2016- R style! Behold my 3d Christmas tree created using the plot3D R package:

While this might seem like yet another Christmas decoration done in R, it is unique in that the tree is rendered in 3d perspective. I myself wrote some code for a 2d Christmas tree a while ago (see this entry in Spanish), in turn based on the code in the Wiekvoet blog. This time around though, I took it a bit further- the challenge now being to create a 3d model of a Christmas tree that I could rotate and animate in perspective. Heck, if others ~~with enough leisure/boredom time to spare~~ were to join in and showcase their own Christmas R creations for this time of the year, we might be witnessing the start of a new Christmas tradition for all R geekdom across the planet.

Mathematical model of a Christmas tree

Long before the birth of Jesus, most pagan cultures in Europe were sun worshipers and in December they celebrated the rebirth of the sun and the rich harvests. This is the significance of the Christmas tree in these festivities of fire and light, abounding in evergreens and holly branches. In Spanish America, instead of Christmas trees, people would place Nativity scenes (Nacimientos) in their homes, but with globalization and the prevalence of the Anglo-Saxon culture, the Christmas tree eventually found its way into our homes. At any rate, I for one have always found the lights and the bright decorations of the Christmas tree captivating and reminiscent of happier moments when friends are remembered and grudges are forgotten. So in a sort of weird tribute to the spirit of these festivities, I decided I would make a mathematical model of the Christmas tree. How geeky is that?

Mathematically, a Christmas tree is nothing but a fractal. A fractal consisting of a stub or segment of a tree trunk with two or three branches that separate outward from the trunk, and an extension, or outward projection of the trunk in the same direction as the trunk. The branches can in turn be considered as trunk segments, each comprising more branches and an extension outward in the same direction. The extension or outward projection of a trunk is in turn another stub with more branching off points and so on. Consequently, the tree construction process is recursive. Being a descendant of LISP, base R supports the list as the data structure of choice for implementing this recursive definition of a tree.

There are, to be sure, some considerations to be made so that this recursively-built tree ends up looking like a pine tree and not a palm tree, a cherry blossom tree, a mango tree or a bonzai tree. For one thing, pine trees are characteristically conical. This means that the angle of separation of the branches from the trunk is initially larger but "closes up" as the pine tree extends out or up. To control the degree of "outwardness" or "upness" associated to a particular tree-trunk stub there will be a depth parameter. Initially, the pine tree starts as one little green trunk stub of depth 1. As this stub branches off and extends upward, each of the children stubs has a lower depth than the parent stub. The most outward branches and leafs of the tree have a depth of almost 0. This will be useful for the dressing the tree with lights and decorations, as these lights are usually found on the more superficial or outward parts of the tree.

Another aspect of our tree growth model worth mentioning is how the tree trunk becomes thicker as the tree grows out an up. This is done via a width parameter that will eventually determine how thick the lines representing the trunk and the branches should be drawn. This width parameter also determines when the tree stem changes color from dark green to brown. In each growth cycle, the growth algorithm increases the width of each stub by a factor of 1.4, it then goes through the branches and the extension looking for the ending stubs (those whose branches and extensions are NULL or nonexistent). It then adds the branches and the extension and backtracks down to find the remaining end stubs. The width of the new branches and extensions is initialized to 1, but as can be seen, the width of the older stubs has been increased more.

The Christmas tree data structure is a list whose components are:

The starting point of the trunk segment, given as a vector with coordinates in $\mathbb{R}^3$ as $(x_0,y_0,z_0)$.
The ending point of the trunk segment, as given by the vector with coordinates $(x_1,y_1,z_1)$. Together, the start and end points determine the direction vector of the tree stem as $\vec{u}=(x_1-x_0,y_1-y_0,z_1-z_0)$. This direction vector will be useful for creating the extension stub, since the extension stub grows in the same direction as the parent stub. It is also used for determining where along the stub the branches start off and in what direction those branches are created.
The width parameter lwd which is also the thickness with which the tree stem is drawn as a segment when plotted.
The depth, which indicates how outward a branch or tree stem is, as already explained above.
Slots for three branches and one extension (branch1, branch2, branch3 and extension), which are nothing but lists recursively defined like this one. When a branch or extension is created, these slots are initialized to NULL.

Creating the extension of a tree stem poses no major problem. One simply takes as starting point of the extension the ending point of the parent tree stem. The ending point of the extension is determined by adding to its starting point a multiple of the direction vector $\vec{u}=(x_1-x_0,y_1-y_0,z_1-z_0)$. This scalar multiple is such that the resulting length of the extension stem is slightly shorter than that of the parent stem. The most difficult issue in creating the Christmas tree lies with the creation of the branches. How can we create the branches so that they branch out from the stem in apparently uniform angles around the stem and not have all the branches branch out from the same side of the stem? How can we obtain the direction vectors for those branches so that they extend outwards from the stem? A little trigonometry and vector geometry is of use to us here.

If the $\vec{u}$ vector is the direction of the tree stem being considered, then what we need is a vector perpendicular to $\vec{u}$ - let's call it $\vec{v}$ - so that we can obtain the direction vector of the branch $\vec{b}$ by adding $\vec{u}+\vec{v}$ and then multiplying $\vec{b}$ by a scalar to set its length to the desired magnitude (see Fig. 1). However, considering we're dealing with the $\mathbb{R}^3$ metric space, there are infinitely many such vectors. In fact, there is an entire two-dimensional space - a plane $\mathcal{V}$ comprised of vectors that are all perpendicular to $\vec{u}$ (see Fig. 2). So what we need to obtain $\vec{v}$ is a orthonormal base of two vectors $\{\vec{v_1},\vec{v_2}\}$ that will permit us to express $\vec{v}$ as a linear combination of the two base vectors of $\mathcal{V}$.

Geometrical relationship between a tree stem and one of its branches

Fig. 1 Geometrical relationship between the main tree stem ($\vec{u}$) and one of its branches ($\vec{b}$). $\theta$ is the angle at which $\vec{b}$ branches outward from the main stem.

This is easy enough. Two vectors are said to be orthogonal if their dot-product is zero. So if we have a vector, say $(x,y,z)$ all we need to do is pick any non-zero coordinate and switch it with one of the remaining coordinates, changing one of the signs to negative and setting the remaining third coordinate to zero. So for example $(-z,0,x)$, $(0,z,-y)$, and $(-y,x,0)$ are all perpendicular to $(x,y,z)$, provided they are all non-null vectors. In short, to find an orthonormal base for the plane perpendicular to a vector $\vec{u}$, pick any non-zero component of this vector, pick a second component to interchange it with while changing the sign of any of the two and set the third component to zero. This will give you a perpendicular vector to $\vec{u}$. To find the other perpendicular vector, just repeat the above process, but interchanging the chosen non-zero component of $\vec{u}$ with the component you had set to zero for the first vector. Finally, once you have your two vectors $\vec{v_1}$ and $\vec{v_2}$, you must multiply them by the inverse of their norms to set their norms to one. The procedure is better illustrated in the R code on this post.

Vector v as a linear combination of v1 and v2

Fig. 2 Finding vector $\vec{v}$ as a linear combination of an orthonormal base of perpendicular plane $\mathcal{V}$ and then using it to find the direction vector $\vec{b}$ of the branch.

So once you have the base of the perpendicular plane to a given tree stem $\vec{u}$, all you need is two scalar components $c_1$ and $c_2$ to define the perpendicular vector $v$ used for constructing the branch, as a linear combination of the base. How are we to go about this? Well, let's think about what we really need. For some parts of the tree - the deeper parts - we need three branches to a stem. For the more outward parts, two branches to a stem will suffice. We want these branches to be evenly distributed about the stem: in the case of 3 branches, we would like the angle of separation between the branches to be $120^\circ$ (like the Mercedes-Benz star symbol), in the case of 2 branches, an angle of separation between them of about $180^\circ\pm 20^\circ$ should be adequate.

What this means is that we want to choose the $\vec{v}$ vectors in $\mathcal{V}$ to have the sort of layout shown in Fig. 3. This is to ensure the pine tree will have a nice conical shape and not have its branches all projecting to the same side.


Fig. 3a 3 branch defining vectors	Fig. 3b 2 branch defining vectors
Fig. 3 Distribution of two and three branch generating vectors on $\mathcal{V}$

Our problem now is to generate 2 or 3 vectors on a plane with such angles of separations. The good news is that we can define the vectors on the regular 2d plane with the canonical base $\{\hat{i},\hat{j}\}$, and, because linear algebra is so cool, we can use the components of those vectors as $c_1$ and $c_2$ - the scalar coeficients used to define the $\vec{v}$ vectors as linear combinations of $\vec{v_1}$ and $\vec{v_2}$. This is so because $\{\vec{v_1},\vec{v_2}\}$ is an orthonormal base of a plane in the 3d space. So for example if the angle between $(0,1)$ and $(-\tfrac{1}{2},\tfrac{\sqrt{3}}{2})$ is $120^\circ$, then the angle between $\vec{v_2}$ and $-\tfrac{1}{2}\vec{v_1} + \tfrac{\sqrt{3}}{2}\vec{v_2}$ will also be $120^\circ$. Not only that, but the two vectors will lie on the $\mathcal{V}$ plane in three dimensional space. Thus, we can translate the 2 dimensional vectors into vectors located on the $\mathcal{V}$ plane perpendicular to the tree stem $\vec{u}$.

Choosing the 2 or 3 vectors on the regular 2d plane later translating them as vectors on the $\mathcal{V}$ plane is a question of doing the following:

2 branches: We first consider $(1,0)$ as the first vector and we determine the second unit-length vector by choosing a random angle between $160^\circ$ and $200^\circ$. We choose another random angle between $0^\circ$ and $360^\circ$ to rotate the entire set of two vectors.
3 branches: Our three vectors will initially be $(1,0)$, $(\tfrac{\sqrt{3}}{2},-\tfrac{1}{2})$, and $(-\tfrac{\sqrt{3}}{2},-\tfrac{1}{2})$. We then choose a random angle between $0^\circ$ and $360^\circ$ to rotate the entire set of three vectors.

The reason we subsequently rotate the two or three vector set is to randomize the orientation of the branches so that our trees branches will project in all sorts of different directions. In either case, to rotate a 2d vector by an angle of $\theta$ about the origin, we use the following linear transformation:

\[ (x,y)\quad\mapsto (x\,cos(\theta)-y\,sin(\theta),x\,sin(\theta)+y\,cos(\theta)) \]

There are a few remaining details to explain before we go into the R code. As we have already mentioned, the more superficial stems of the three have two branches whereas the deeper parts of the tree (those closest to the original thick stub from which the entire Christmas tree branches out) have three branches. This is controlled by the depth parameter. Whenever $depth>0.8$, the tree stem will branch out into three branches, otherwise it will have only two. The depth parameter also controls where along the stem the branches are chosen. Stems of greater depth tend to branch off closer to its ending point $(x_1,y_1,z_1)$ whereas the more superficial stems branch off at points closer to its starting point $(x_0,y_0,z_0)$. Needless to say, the branching off points are chosen randomly. Finally, the placement of the lights and the tree decorations is also controlled by the depth parameter. The more superficial parts of the tree have a higher likelihood of containing lights and decorations. Again, the placement of these decorations is done stochastically.

R script for the 3d Christmas tree

library(plot3D)

trunk <- list(
  x0=0, y0=0, z0=0,
  x1=0, y1=0, z1=6,
  extension=NULL,
  branch1=NULL, branch2=NULL,
  branch3=NULL, branch4=NULL,
  depth=1,
  lwd=1,
  stub_color="brown"
)

draw_tree <- function(tree) {
  #function to draw the tree recursively
  if (is.null(tree)) return()
  with(tree,{
    segments3D(x0,y0,z0,x1,y1,z1,col=stub_color,
      lwd=lwd,add=TRUE)
    draw_tree(branch1)
    draw_tree(branch2)
    draw_tree(branch3)
    draw_tree(extension)
  })
}

extend <- function(tree) {
  #creates an extension of the main branch
  #in the same direction vector u=p1-p0
  with(tree,{
    growth_factor <- runif(1,min=0.9,max=1)
    return(list(x0=x1,y0=y1,z0=z1,
         x1=x1+growth_factor*(x1-x0),
         y1=y1+growth_factor*(y1-y0),
         z1=z1+growth_factor*(z1-z0),
         extension=NULL,
         branch1=NULL, branch2= NULL,
         branch3=NULL, branch4= NULL,
         depth=depth*0.9,
         lwd=1,
         stub_color="darkgreen"))
  })
}

create_branch <- function(tree,c1,c2) {
  #this function returns a branch for tree
  #c1 and c2 are the components for the vector
  #base {v1,v2}. v1 and v2 are two orthonrmal
  #vectors, both perpedicular to the direction
  #vector u=p1-p0 (p1 and p0 are the endpoints
  #of the tree trunk).
  #where_at is a scalar value in (0,1), indicating
  #where along p0=(x0,y0,z0) and p1=(x1,y1,z1)
  #the branch will grow.
  with(tree,{
    #vector u=(x1-x0,y1-y0,z1-z0) gives the 
    #direction of the tree trunk.
    #stub_length is the length of that trunk.
    u <- c(x1-x0,y1-y0,z1-z0)
    stub_length <- sqrt(sum(u*u))
    #growth_factor is how long the branch
    #will be with respect to stub_length
    growth_factor <- runif(1,min=0.7,max=0.8)
    where_at <- runif(1,min=0.4,max=0.8)
    #create two perpendicular vectors to u
    #and set their norms to 1
    i <- which(u!=0)[1]
    oi <- setdiff(1:3,i)
    v1 <- rep(0,3); v1[i] <- -u[oi[1]]; v1[oi[1]] <- u[i]
    v2 <- rep(0,3); v2[i] <- -u[oi[2]]; v2[oi[2]] <- u[i]
    v1 <- v1/sqrt(sum(v1*v1)); v2 <- v2/sqrt(sum(v2*v2))
    #vector v is a linear combination of v1 and v2,
    #hence it lies on the plane perpendicular to u
    v <- v1*c1+v2*c2
    #beta is the angle of separation between the
    #branch and the trunk. The angle is larger
    #for the "deeper" parts of the tree.
    beta <- runif(1,min=0.7*depth,max=0.9*depth)    
    #calculate the scalar k for multiplying with v
    #so that u+kv, the branch, will form a beta
    #angle with the trunk.
    k <- tan(beta)*sqrt(sum(u*u))/sqrt(sum(v*v))
    #new_u is the direction vector of the branch,
    #whose length will be the length of the branch 
    new_u <- u+k*v
    new_u <- new_u / sqrt(sum(new_u*new_u))*
             stub_length*growth_factor
    #the new (x0,y0,z0) point of the branch
    #is where along the main trunk the branch begins.
    new_x0 <- x0+(x1-x0)*where_at
    new_y0 <- y0+(y1-y0)*where_at
    new_z0 <- z0+(z1-z0)*where_at
    #the new (x1,y1,z1) point of the branch is
    #its ending point.
    new_x1 <- new_x0+new_u[1]
    new_y1 <- new_y0+new_u[2]
    new_z1 <- new_z0+new_u[3]
    list(
      x0=new_x0,y0=new_y0,z0=new_z0,
      x1=new_x1,y1=new_y1,z1=new_z1,
      extension=NULL,
      branch1=NULL, branch2= NULL,
      branch3=NULL, branch4= NULL,
      depth=depth*0.8,
      lwd=1,
      stub_color="darkgreen")    
  })
}

grow_tree <- function(tree) {
  if (is.null(tree) ) return(NULL)
  tree$lwd <- tree$lwd*1.4
  if (tree$lwd>2.0) tree$stub_color <- 'brown4'
  if (is.null(tree$extension)) {
    tree$extension <- extend(tree)
    if (tree$depth<0.5) {
      #make two branches at an angle of more than 160 degrees
      rot1 <- runif(1,min=0,max=2*pi)
      rot2 <- (runif(1,min=8*pi/9,max=10*pi/9)+rot1)%%(2*pi)
      tree$branch1 <- create_branch(tree,cos(rot1),sin(rot1))
      tree$branch2 <- create_branch(tree,cos(rot2),sin(rot2))
    } else { 
      #make 3 branches with 120 degree angles between them and
      #rotate the entire branch set.
      rot <- runif(1,min=0,max=2*pi)
      tree$branch1 <- create_branch(tree,-sin(rot),cos(rot))
      tree$branch2 <- create_branch(tree,
                        sqrt(3)/2*cos(rot)+sin(rot)/2,
                        sqrt(3)/2*sin(rot)-cos(rot)/2)
      tree$branch3 <- create_branch(tree,
                        -sqrt(3)/2*cos(rot)+sin(rot)/2,
                        -sqrt(3)/2*sin(rot)-cos(rot)/2)
    }
  } else {
    tree$extension <- grow_tree(tree$extension)
    tree$branch1 <- grow_tree(tree$branch1)
    tree$branch2 <- grow_tree(tree$branch2)
    if (tree$depth>=0.5) 
      tree$branch3 <- grow_tree(tree$branch3)
  }
  return(tree)
}

create_ornaments <- function(tree) {
  if (is.null(tree)) return()
  po <- (1-tree$depth)^6
  ornament <- sample(c(T,F),size=1,prob=c(po,1-po))
  co <- sample(c("red","darkgoldenrod4"),size=1,
               prob=c(0.6,0.4))
  if (ornament)
    ornaments <<- rbind(ornaments,
      data.frame(x=tree$x1,y=tree$y1,z=tree$z1,color=co))
  create_ornaments(tree$branch1)
  create_ornaments(tree$branch2)
  create_ornaments(tree$branch3)
  create_ornaments(tree$extension)
}

create_lights1 <- function(tree) {
  if (is.null(tree)) return()
  po <- (1-tree$depth)^4
  light <- sample(c(T,F),size=1,prob=c(po,1-po))
  if (light)
    lights1 <<- rbind(lights1,
      data.frame(x=tree$x1,y=tree$y1,z=tree$z1))
  create_lights1(tree$branch1)
  create_lights1(tree$branch2)
  create_lights1(tree$branch3)
  create_lights1(tree$extension)
}

create_lights2 <- function(tree) {
  if (is.null(tree)) return()
  po <- (1-tree$depth)^4
  light <- sample(c(T,F),size=1,prob=c(po,1-po))
  if (light)
    lights2 <<- rbind(lights2,
      data.frame(x=(tree$x1+tree$x0)/2,
                 y=(tree$y1+tree$y0)/2,
                 z=(tree$z1+tree$z0)/2))
  create_lights2(tree$branch1)
  create_lights2(tree$branch2)
  create_lights2(tree$branch3)
  create_lights2(tree$extension)
}

draw_ornaments <- function() {
  with(ornaments,
    {points3D(x=x,y=y,z=z,
              pch=19,cex=1.2,col=as.character(color),
              colkey=FALSE,add=TRUE)})
}

draw_lights1 <- function() {
  with(lights1,
    {points3D(x=x,y=y,z=z,pch="+",cex=0.8,col="white",
              colkey=FALSE,add=TRUE)})
}

draw_lights2 <- function() {
  with(lights2,
    {points3D(x=x,y=y,z=z,pch="+",cex=0.8,col="yellow",
              colkey=FALSE,add=TRUE)})
}

set.seed(20161224)
pine_tree <- trunk
for (i in 1:5) pine_tree <- grow_tree(pine_tree)
ornaments <- NULL;
lights1 <- NULL;
lights2 <- NULL;
create_ornaments(pine_tree)
create_lights1(pine_tree)
create_lights2(pine_tree)

png("tree%02d.png")
for (i in 0:35) {
    perspbox(x=c(-25,25),y=c(-25,25),z=c(0,40),bty="n",
             phi=8,theta=i*10,col="white",alpha=0)
    draw_tree(pine_tree)
    draw_ornaments()
    switch((i%%4)+1,{},
     {draw_lights1()},
     {draw_lights2()},
     {draw_lights1(); draw_lights2()})
}
graphics.off()

Bibliography

Apostol, T. (1985). Calculus, Vol. II (2nd ed). (F. Veléz trans.). Caracas: Editorial Reverté.
carlop. (April 26, 2012). Answer to "How to find vector perpendicular to another vector?" on math.stackexchange. [Retrieved 12/20/2016 from http://math.stackexchange.com/questions/137362/how-to-find-perpendicular-vector-to-another-vector].
Cooney, B. (1967). Christmas. New York: Thomas Y. Crowell Company.
Duineveld, K. (2013, December). "Merry Christmas". Blog post. [Retrieved 12/20/2016 from http://wiekvoet.blogspot.com/2013/12/merry-christmas.html].
R DEVELOPMENT CORE TEAM (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org.
Soetaert, K. (2016). plot3D: Plotting multi-dimensional data. R package version 1.1. https://cran.r-project.org/web/packages/plot3D/index.html.

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domingo, 11 de diciembre de 2016

La Era de la Información: ¿Ilustración o Ignorancia?

Este es un ensayo en el cual intento precisar el significado de la frase "Era de la Información" con la cual comúnmente nos referimos a nuestra época. Es ya lugar común decir que las Tecnologías de Información y Comunicación han masificado el acceso a la información en una escala planetaria sin precedentes, pero ¿quiere decir esto que ahora somos más sabios que nuestros antepasados? ¿Estamos ante las puertas de una revolución educativa? Estas son algunas de las cuestiones que abordo en este ensayo que, aunque escrito en el 2011, sigue plenamente vigente.

Leer más / Read on ...»

jueves, 1 de diciembre de 2016

How to send bulk email to your students using R

In this post I write about a technique I use to send personalized bulk emails to my students at the open and distance education university where I teach (the Universidad Nacional Abierta in Venezuela, or UNA, for short). Being able to mass-email students with personalized messages is should be an important issue in any distance education setup. However, as the UNA does not provide teachers with institutional tools to perform such an outreach, we teachers are left to our own devices. I use R for all sorts of teaching and research tasks, and this was not going to be the exception. That's how I came across an R package for sending emails called mailR, which proved to be the right tool for this task.

In what follows I will give some information of context to explain why mass-emailing would be a necessary strategy for us course facilitators to implement at the UNA. If you are only interested in how to implement this using R, you can skip directly to the R implementation section.

A brief outline of the educational process at the UNA

Perhaps many of you are not aware that the UNA was one of the first open and distance education institutions of higher learning in the world when it was founded in 1977, following Great Britain's Open University, created in 1970¹. Being very much based on the Open University's instructional and organizational model at the time, it is still pretty much a product of the principles and the approach to distance education prevailing back then. It was designed to bring education to the masses in remote or rural areas of the country and to target working adults who could not comply with the time and place constraints imposed by traditional, presential universities. The mass-produced paper book was the principal medium of instruction delivery. Although other media such as vcr tapes, radio/tv broadcasts were at some point produced or contemplated, their use never really caught on.

The production of these books, and indeed the entire educational process of the UNA, is a typical industrial-age process entailing a division of labor among the academic personel of the institution. On the one hand, you have the content specialists, evaluators and validators at the central level of the institution who are directly involved in the book and course production processes. This personnel is also responsible for creating the exams and oher instruments of assessment each semester. Additionally, they are responsible for scheduling the exam dates of all courses each semester. Content specialists, evaluators and validators do not have contact with students; that is the role of course facilitators, such as myself, who operate at the periphery of the institution in the various regional locations across the length and breadth of Venezuela.

The primary task of the course facilitators is to serve as a bridge between students and the contents of the course embodied in the course textbooks. This means that if, in the process of self-study, the student has issues understanding some contents of the course, he or she contacts the facilitator for individual assistance. Ocassionally, facilitators also hold workshops where groups of students attend. However, attendance to these workshops, ressembling a more traditional learning environment in which a teacher addresses the class to expound some subject, is optional. Grading exams is another task facilitators do, although actually administering the exams is something done by another type of personel - the proctors - who are not necessarily academics.

As can be seen, the distance learning model of the UNA involves a separation of teaching tasks and it is centered around the concept of self-learning. Facilitator-student interaction is predominantly presential. I don't have any statistics to back this up, but I do believe that for the majority of the UNA facilitators, phone interaction with students occurs very rarely and internet interaction (email, forum or video-conferencing) is virtually (no pun intended) inexistent. In this, regard, my presonal case is an outlier. For example, for the july-september trimester, of the total 1643 facilitator-student interaction events, 1605 of those were online, in the form of grade consultations in my online system, messages in my blog's chatbox, email consultations and of course, the bulk emailing system I'll be presenting in this entry.

On the necessity of creating a better communicational platform

As it was made evident in the previous section, the UNA's model of distance education is outdated and needs to be urgently revamped. Unfortunately, I don't see this happening soon from within the institution itself, which maintains a very conservative structure and hierarchy. I've assumed this blog to be my own personal experiment as to how a facilitator like me could create an alternative platform for teacher-student interaction using free or easily available technology. This new structure has to take into account the "natural" communication channels.

By far, Facebook is the most frequently used social network by the student population in Venezuela (and the general population of this country, for that matter). However, as an educational tool, Facebook has its disadvantages: it is a very noisy and distracting communication channel more oriented towards aimless chatter and gossip². Furthermore, although Facebook is immensely popular, there is a more universal communication channel in the digital era: email.

In 2013, there were approximately 1.19 billion Facebook users and 0.2 billion Twitter users in the world versus 2.5 billion email users³. In spite of seeming less "fashionable" than the popular social media today, email is, and will certainly continue to be, the most widely used digital communication tool, if only because to register for any of these social media, you need to provide an email address! Truisms aside, email does present some important advantages over social media in the educational context: one can be more certain that a student will read a message if we send it by email than if we post it on Facebook, Twitter, Google+, etc. And besides being a less noisy communication medium, email is more personal. Therefore, in the distance education context, email is arguably the most natural communication channel between facilitator and students.

In distance education, distance is both a strength and a weakness of this instructional modality. Distance is an essential attribute of open and flexible education in which the learner's autonomy, time and obligations to family and work are respected. However, too much distance alienates the student from the learning community, which in my opinion accounts for a large portion of dropouts in MOOCs and other distance learning contexts. This is where email comes in. Addressing each student by name and making the student feel that the conversation is about him or her personally works wonders in these contexts, where communication is usually more generical and inclined towards anonymity. Email enables the instructor to create a more personal rapport with the students and making them feel that they are being taken into account personally.

This is the reason why email is the tool of choice for telemarketing and this is why media experts like Michael Hyatt, Anna Hoffman, Neil Patel or Jon Morrow insist that the most important asset of a blog is its list of email subscribers. Surely, telemarketing brings to mind ideas about sales, profits and customers, whereas education is seen as an entirely different phenomenon. At the end of the day, however, we educators are trying to exert influence over our students and if we consider education to be a service to others, then it wouldn't be a bad idea to consider our students as customers. Exerting influence, leadership and using digital communication platforms- these are some of the topics Michael Hyatt discusses in his blog⁴.

Why do I employ R with the mailR package for bulk emailing instead of other tools?

There are, to be sure, services like MailChimp which allow you to run bulk emailing campaigns. Although MailChimp has a free service that allows you to send up to 12000 emails a month to over 2000 subscribers⁵ and it seems very easy to set up and get running, for me, it has one major disadvantage: due to DMARC policies, MailChimp cannot send bulk emails from adresses associated to free-service provider domains, like Gmail, Yahoo and Outlook. Surely, academic faculty members of the UNA have our UNA-domain email address (mine is jromero@una.edu.ve). However, I rarely use it and for me, it's more convenient to use my gmail address (it's my natural communication channel). Furthermore, I'm not sure about the bulk-emailing restrictions on my una-domain email address, although in truth, I haven't explored the matter throughly. As for purchasing a hosting/domain+email addresses package adequate enough in terms of server response times and maximum concurrent users online, while I'm sure this is very inexpensive in the rest of the world, it is almost prohibitive for most Venezuelans, whose socialist government has imposed an extremely restricted currency exchange mechanism⁶.

There is another disadvantage to using ready-made tools like MailChimp, in my case. While addressing recipients by their name is something easily done with MailChimp, I'm not sure if you can easily configure for using male or female gender adjectives (in Spanish, adjectives change in form based on the gender of the thing or person described). Or for example, as a teacher I might be interested in saying something or other on my message based on certain conditions of each individual student (eg. I might advise failing or at risk of failing students to take such and such remedial action). These sort of things require a tool for programmatically tailoring the message to each student. They require using a general programming language like R. At least to me, it seems much easier this way, since I already use R for a whole bunch of other tasks, as this blog testifies to.

Now that I have (I hope) justified my use of R for bulk emailing tasks, I must point out that there are several packages for that. There is sendmailR, mailR and gmailr. The latter package looks interesting and on the author's GitHub site⁷, there is a tutorial of sorts on how to set it up for sending bulk emails from a Gmail account, coincidentally with an online course application example such as the one I'm discussing in this post. However, I had tried this package before and for some reason, could not get it to work. In deciding between sendmailR and mailR, I considered that mailR's send.mail function has an option for sending pure text or HTML mails, whereare the equivalent sendmailR function had text mail only hardcoded within (this is a bug that they apparently fixed now⁸). Being able to end HTML was important to me, as I wanted to be able to send nicely formatted emails like this one:

UNIVERSIDAD NACIONAL ABIERTA
CENTRO LOCAL ANZOATEGUI
UA EL TIGRE

Hola PEDRO:

Ante todo quiero desearte éxito en este semestre 2016-1 y particularmente en la primera prueba parcial de la asignatura XXX (código xxx) que presentarás este sábado. El propósito de este mensaje es presentarme: mi nombre es José Romero, soy egresado en la Licenciatura de Matemáticas de la UNA y actualmente, soy el asesor del área de matemáticas en la unidad de apoyo de El Tigre.

Estoy contactando por correo a todos los estudiantes de la asignatura XXX (xxx) de la UNA a nivel nacional para invitarlos a que visiten mi blog.

Huelga decir que en caso de cualquier duda, no dudes en consultarme por el buzón de mensajes del blog o a través de mi correo: jlaurentum@gmail.com. (NOTA: No respondas a este correo ya que es una cuenta para envios automatizados solamente). Estoy a tus ordenes,

Atentamente,

José Romero

Materials needed for this experiment

Besides an R installation with the mailR package, you will need a file with the data of your students: their email addresses, their names, and any other relevant information you wish to convey to them, such as grades, personal feedback for each student, etc. The file needs to be a csv file, which is essentially a text file in which each line is a row of the data table and the fields or columns in each line are separated by a special character such as a comma, a semicolon, or a tab⁹. If you have your data in a spreadsheet, you can easily convert this to a csv file by using "Save As" and then choosing the "Text/CSV" file type. Indicate the separation character- that will be the same character you indicate when you read in the csv file from R. Your csv file could contain something like this:

id       lastname  firstname   gender  c_code una_location  email_address
12345678 PEREZ      PEDRO        M       126    02-01       pedroperezm@dontcare.com
87654321 PEREZ      JOSEFINA     F       126    02-01       jperez@noneofyourbizwaks.com
    :      :          :          :        :        :           :              
    :      :          :          :        :        :           :

It is worth noting that with this R/mailR method, you can send up to 100 email messages a day from any of the free email domains such as Gmail, Yahoo or Outlook. If you go beyond this limit, your email account will be temporarily suspended for a day (24 hours), after which you can continue to send messages as usual (never exceeding the 100 emails a day maximum quota). In experimenting with this method, I discovered I had to use a time delay between each email. In the script below, you will see that I uniformly distributed random delays between 3 and 6 seconds. Maybe, by using bigger max/min values and a greater range (spread) for the random delays, you can ensure that the message sending process will proceed 100% smoothly, without having the script interrupted by this error:

Error in ls(envir = envir, all.names = private) : 
  invalid 'envir' parameter

Should you get the above error, you simply have to modify the first and last indexes in the for-loop so that the message sending script will resume the batch sending process from the last student where you left off. The script is the following:

R script for batch emailing

#Batch email sending script
#The following function crafts the message for each student,
#represented by the x parameter
message_text <- function(x) {
  tmp <- paste(c(
    '<!DOCTYPE html>',
    '<html xml:lang="es" lang="es">',
    '<head>',
    '<meta http-equiv="content-type" content="text/html;charset=utf-8" />',
    '<meta name="author" content="José Loreto Romero Palma" />',
    '<STYLE type="text/css">',
    'h1 { text-align: center; font-family: Helvetica, FreeSans; font-size: 40px;',
    'font-variant: small-caps }',
    'h2 { text-align: center; font-family: Helvetica, FreeSans; font-size: 32px;}',
    'h3 { text-align: center; font-family: Helvetica, FreeSans; font-size: 28px;}',
    'p { text-align: justify; font-family: Helvetica, FreeSans; font-size: 16px;',
    'width: 640px}',
    'ul { text-align: justify; font-family: Helvetica, FreeSans; font-size: 16px}',
    'td { font-family : Helvetica, FreeSans; font-size: 12px}',
    '</STYLE>','</head>','<body>',
    paste(c(
    paste0("<table><tbody><tr><td width='60px'>",
    "<IMG SRC='https://lh3.googleusercontent.com/hgDApmnzAf2TrP9lzTUc3U9ZG9",
    "EBaUn9s9OM4DWD4BXtO6j51GCfgLyfyjTdHJ5G8CfXD6_XeipYaQ=w1366-h768-no' ",
    "NAME='logo_UNA' ALIGN='LEFT' WIDTH='51' HEIGHT='51' BORDER='0'>",
    "</td><td width='580px'>UNIVERSIDAD NACIONAL ABIERTA<br/>",
    "CENTRO LOCAL ANZOATEGUI<br/>UA EL TIGRE</td></tr></tbody></table>"),
    paste0("<br/>"),
    paste0("<p>Hola ",x$firstname," ",x$lastname,":</p>"),
    paste0("<p>",
    "Ante todo quiero desearte éxito en este semestre 2016-1 y ",
    "particularmente en la primera prueba parcial de la asignatura ",
    "XXX (código xxx) que presentarás ",
    "este sábado.  El propósito de este mensaje es ",
    "presentarme: mi nombre es <b>José Romero</b>, soy egresado en la ",
    "Licenciatura de Matemáticas de la UNA y actualmente, soy el ",
    "asesor del área de matemáticas en la unidad de apoyo de El Tigre.</p>"),
    paste0("<p>",
    "Estoy contactando por correo a todos los estudiantes de la asignatura ",
    "XXX (xxx) de la UNA a nivel nacional para invitarlos a que ",
    "visiten mi <a href='http://unamatematicaseltigre.blogspot.com'",
    " target='_blank'>blog</a>.</p>",
    "<p>Huelga decir que en caso de cualquier duda, no dudes en ",
    "consultarme por el buzón de mensajes del blog o a través de mi ",
    "correo: <a href=\"mailto:jlaurentum@gmail.com\">jlaurentum@gmail.com</a>.",
    " (NOTA: No respondas a este correo ya que es una cuenta para envios ",
    "automatizados solamente). Estoy a tus ordenes,</p>"),"","",
    "<p>Atentamente,</p>","<br />","<p>José Romero</p>")),
    '</body>','</html>'),
    collapse="")
    return(tmp)
}

library(mailR)
#note: turn on/off less secure apps access for gmail (?)
#note: the daily quota is 100 emails 
#read in the mailing list in the csv
mail_list <- read.csv2("roster.csv",as.is=TRUE)
file_h <- file('test.html',open="w")
writeLines(message_text(mail_list[1,]),file_h)
close(file_h)
ext_f <- file("mail.out",open="w")
close(ext_f)
for (recipient in 1:nrow(mail_list)) {
  email <- message_text(mail_list[recipient,])
  send.mail(from="mygmail@gmail.com",
    to=as.character(lista_correos[recipient,]$email_address),
    subject="Invitation to the unamatematicaseltigre blog",
    body=email,
    html=TRUE,
    authenticate=TRUE,
    smtp = list(host.name = "smtp.gmail.com",
    user.name = "mygmail", passwd = "mypasswd", ssl = TRUE),
    encoding = "utf-8",send=TRUE)
  print(mail_list[recipient,])
  Sys.sleep(runif(n=1,min=3,max=6))
  #write each recipient to a file
  ext_f <- file("mail.out",open="a")
  writeLines(text=paste0("[",recipient,"] ",
    paste0(as.character(mail_list[recipient,]),collapse="\t")),
    sep="\n",con=ext_f)
  close(ext_f)  
}

Lines 4-52 define a function - message_text that builds the HTML message body for a given recipient. This script produces a message body such as the one shown in the example above. Notice the meta tags in the header defining the CSS to give format to your message and the ability to include images like the UNA logo in line 23-25.

Line 58 reads in the roster.csv file as a data frame placed in the mail_list variable. The read.csv2 function assumes your separation character is a semicolon (;) and the decimal point is the , (this is so in spanish speaking countries). However, you can configure other settings by using the read.table or read.csv functions. Lines 59-61 simply write a test message to an HTML file. I usually run the script up to these lines first to ensure that the message text comes out like I want it before starting the batch sending processs. The for loop in lines 64-83 is responsible for batch emailing to all the students in the roster data frame.

The index variable recipient of the for loop (line 64) is an integer going from 1 to the number of rows in the roster data frame. Bear in mind that the daily quota is 100 emails a day if you are emailing from a free email account like gmail or yahoo. Therefore, if your roster file consists of more than 100 students, you will want to split this up into groups of 100 students, batch sending for each group on different days. Besides, there may be problems while emailing to a particular address that cause the script to stop with an error (the Error in ls(envir = ... mentioned earlier). Therefore, you need some way of keeping track of the emails that you send.

This is the reason I create a file (lines 62-63) where I will be writing the information of each individual row in the roster as I send each message (lines 78-82). If the script execution stops for some reason (besides the error mentioned above, power blackouts are quite common in Venezuela), I can use this file to see from what row of the roster I should resume the batch sending. Besides, it's always a good idea to keep a record of all emails sent. While running this code, If you open the email client from a browser, you will see how the Sent email box starts to populate with messages as the script sends them. If for some reason the postmaster cannot send to a certain email address, you will get a notification email in your Inbox.

The actual email sending is done via the send.mail function of the mailR package in lines 66-74. In this example, I'm sending from a fake gmail account: mygmail@gmail.com. The user name before the ad sign of your gmail address is the one you will pass to the user.name parameter in line 73. In the same line of code, you also have to indicate the password you use to login to your email account as parameter to passwd. The host name for gmail addresses is smtp.gmail.com, but if you use yahoo or some other free email provider, you have to find what the smtp host name is for that provider and indicate it in the host.name parameter at line 72. A Google lookup should suffice.

As already mentioned, I introduce a random delay between each call to the send.mail function. This is so my gmail client won't suspect I'm sending emails in "automatic pilot mode" and my account won't be temporarily suspended. For me, random delays between 3 and 6 seconds worked fairly well, but you may want to experiment with higher delay values to be safe.

Finally, if you have any questions or comments, feel free to let me know in the comment section of this post. I'd be happy to answer them.

Notes

See McIsaac and Gunawardena (2002) for an account on the history and theoretical constructs behind distance education.
See What Is Google+? (An African Perspective), an interesting post by Rotimi Orimoloye for his blog Digital Africa. In it, he argues that Nigerians, who also use Facebook more often than any other social network, should transition into Google+, the latter being more suitable for getting to know who the experts in a particular field are and to engage in learning about these fields.
See the statistics in the FAQ section of Specific Feeds: https://www.specificfeeds.com/page/faq-email-publishers.
Michael Hyatt, author of a book titled "Platform: Get Noticed in a Noisy World", is a expert in this subject. I strongly reccomend visiting his blog https://michaelhyatt.com.
See http://kb.mailchimp.com/getting-started/mailchimp-fundamentals.
While there are experts on the subject of platforms like Michael Hyatt and the others I have mentioned, I think that out of necessity, I'm on my way to becoming an expert myself on the subject of building a platform with free or freely available tools. I believe that while technology is in some cases widening the gap between the rich and the poor, free and open source technology holds enormous potential as empowering tools for people who, like myself, live in countries with failed economies.
See https://github.com/jennybc/send-email-with-r.
See Premraj, 2014.
Hence the acronym CSV: Comma Separated Values. The separation character can be any character you choose. For this example, we will assume the semicolon (;) is the separation character.

Bibliography

McIsaac, M. S. and Gunawardena, C. N. (2002). Distance Education. [Retrieved November 26 , 2016 from http://www.aect.org/edtech/ed1/pdf/13.pdf.
WTFPL. (10/18/2016). In Wikipedia, The Free Encyclopedia. [Retrieved 11/15/2016 from: https://en.wikipedia.org/wiki/WTFPL].
R DEVELOPMENT CORE TEAM (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org.
Premraj, R. (2014). How to send HTML email using R. [Question on Stackoverlow available at: http://stackoverflow.com/questions/19844762/how-to-send-html-email-using-r].
.
YETESOFT.COM. (2015). Email Sending Limit and Send Rate - Gmail, Hotmail, Yahoo! Mail, AOL. [Available at: http://www.yetesoft.com/free-email-marketing-resources/email-sending-limit/].