What Are the Four Spatial Dimensions?

A spacial dimension refers to the number of coordinates required to
locate a point in space. For example, a point on a Cartesian plane, a
two-dimensional construct, requires only two coordinates to describe
its location -- x and y values. A point in three-dimensional space
requires x, y and z coordinates because space has the added dimension
of height. Scientists have proposed additional dimensions, such as the
fourth dimension, which requires four coordinates to describe the
location of a point. First DimensionThe first dimension is length.
One-dimensional objects have neither width nor height and are called
lines. Mathematical lines are not the same as the lines you may be
familiar with

I'm trying to write a program in C to solve a PDE in 2 spatial
dimentions numerically: W(x,p,t). The acctual equasion involves too
many signs that I don't know how to write here, so forgive me for not
providing it, but it is fairly irrelevant anyways.

solve the equation, from what I know - I need three loops:

/>For (t=0;t<t_max;t+=1)
For (x=0;x<x_max;x+=1) /> For (p=0;p<p_max;p+=1)
( The numerical form of the
equation, using a 2D array - W[x_max][p_max] )

This works fine for one dimension. - but problem is : in the
above case the program simply runs in a million years! - I am serio

Network & Servers

I'm trying to design an implementation of Vector Quantization as a
c++ template class that can handle different types and dimensions of
vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles,

I've been reading up on the algorithms, and I
understand most of it:

here and here

I want to
implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having
difficulty figuring out the general algorithm for partitioning the
clusters. I think I need to define a plane (hyperplane?) that splits
the vectors in a cluster so there is an equal number on each side of
the plane.

[edit to add more info]

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I have a case requirement where I need to find the nearest N
suppliers who supply specific product types. The types in an int range
of 0..1048575, which represents an hierarchy. Any supplier could have
multiple points since they could supply multiple product types.


I could store the long & lat in PostGIS and the types in an
indexed int array column, and query against both with a limit of N.
However, I don't believe this will be efficient as I am not sure that
PostgreSQL will use both indexes.

Another idea I have is
to store the types in a third "vertical" dimension. This would create
stacked "vertical" shape segments at the long & lat shape


Let's say I have a container div that is 765px wide by 530px

I want to dynamically fill as much of that div with
30 smaller divs. Since the container div is a rectangle, the filling
divs should be a rectangle as well. Basically, I don't want squares, I
want to fill the space.

What is the formula?



I am trying to use R to model grids of agents that change their
decisions based on the decisions of other agents in their direct
proximity. Basically - each agent looks to the other agents around him
on the grid, and might change its behaviour based on the the actions
around him. I have included some sample dinky-toy code per below to
show (one iteration) of such dynamic.I am wondering whether a) there
is an elegant manner to address the boundaries of the grid (currently
the t+1, i+1 code does
Programming Languages
Hi All,
I have the following query which was based on a working
query in MySQL:
(dont be afraid of the size of the query you see
below, later on I will concentrate on part of this query)
count(*) FROM ((SELECT * FROM tileinfo where julianDay BETWEEN
DATE2JDAY((2003-03-01 00:00:00),0) AND DATE2JDAY((2003-03-01 23:59:59
),0) AND intersects(tile, geomFromText(POLYGON((-10.84 35.8,18.14
35.8,18.14 59.41,-10.84 59.41,-10.84 35.8)),4326))) tic0 LEFT JOIN
(tileinfo_meta__2p left join meta__2p on tileinfo_meta__2p.fk_name =
meta__2p.pk_name) on tic0.pk_tileinfo = tileinfo_meta__2p.fk_tileinfo
((SELECT * FROM tileinfo where julianDay BETWEEN

I'm trying to produce a nice bubble plot overlaid on top of a
basemap of the US (i could import a shapefile if that is preferred but
i've been using the R basemaps.

myData =

Using this code below, that i adapted from another stack overflow
post ( href="http://stackoverflow.com/questions/23427479/create-bubble-plot-in-r-using-satellite-map">Create
bubble plot in R using satellite map), i am able to overlay a
bubble plot on a map of the US. However this renders very slowly, the
extent is too tight, it is bounded in a box, i'm not able to add other
layers to the plot from what i can tell, and the base map is thick and
not visually clean.

xy <- myData[,c("long", "lat")]
nl <- getData('GADM', country="USA", level=1) #raster data, format
nl <- gSimiplify(nl, tol=0.01, topologyPreserve=TRUE)
# coercing the polygon outlines to a SpatialLines object
spl <- list("sp.lines", as(nl, "SpatialLines"))
SPDF <- SpatialPointsDataFrame(coords=xy, data=myData)
coordinates(myData) <- c("lat", "long")
projection(SPDF)<- "+proj=longlat +ellps=WGS84 +datum=WGS84
+no_defs +towgs84=0,0,0"
coordinates(SPDF)[1:5,] #retrieves spatial coordinates form the
bubble(SPDF, "pop", sp.layout=spl, main="This is It!")

I can draw a nice basemap using this code. I add points to the map
but they are not sized by the pop column in my data. And i can add
additional layers to this map. But can i control the size of the
points and the symbol itself like i can using a bubble plot?

map(database= "world", ylim=c(45,90), 
xlim=c(-160,-50), col="grey80",
fill=TRUE, projection="gilbert",
orientation= c(90,0,225))

coord <- mapproject(myData$lon, myData$lat,
proj="gilbert",orientation=c(90, 0, 225))
points(coord, pch=20, cex=1.2, col="red")

Can anyone please guide me towards the best way to plot a bubble
map in R where i can adjust the fill and outline of the symbols in the
bubble map, And i can add a clean basemap, that i can a) control the
colors of (fill and lines) and b) add additional layers to (for
instance another shapefile layer).

Thank you in advance for any advice.

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