So, consider a dynamic wireless sensor network. We wish to minimize the average wait time for each of the nodes in the network to be serviced by new information. We however do not want to increase the By using the bounty hunting algorithm we can do this. I might want to look into routing… Continue reading Spatial Queuing Theory with Holes
Category: Math
Ethics and Incompleteness
So, I was talking to my wife 🙂 about ethics and the types of ethics. She told me that there is this form called consequential ethics and deontological ethics. And there are I’m sure a bunch more. But, what I have discovered is that they each have a set of axioms and from these they… Continue reading Ethics and Incompleteness
Math problem of the day
Since I’m taking my last semester of classes I realized that I might never take a math class again :(. So, I was thinking to keep my math skills sharp I might start a problem of the day (or in some other increment). I really don’t want to loose my mathematics skills. Also, I can’t… Continue reading Math problem of the day
Adaptive Data Analysis
Google Research recently wrote a piece The reusable holdout: Preserving validity in adaptive data analysis (so I’m not go to write much). It details the problem with statistics generated when the machine learning methods are adapted to the data through data analysis and repeated trials on the same hold out data. This is a problem that is… Continue reading Adaptive Data Analysis
Comparison Continued
I took a look at the R source code for the tukey test (HSD test) from the agricolae library http://cran.r-project.org/web/packages/agricolae/index.html. The interesting thing is that they purposefully call round: round(1-ptukey(abs(dif[k])*sqrt(2)/sdtdif,ntr,DFerror),6) Also, they assume lm or aov. So, we know that they don’t like big numbers. However, the nice thing is that the R file shows how… Continue reading Comparison Continued
Handcoded Tukey
So, it seems that if I want a fast tukey test I need a fast ANOVA. Which seems to be where the bottle neck is. If I had time I would code ANOVA and borrow a Tukey implementation in C. I think that all of these programming languages are doing it wrong for what I… Continue reading Handcoded Tukey
large numbers
Well I’ve been looking into using R to calculate the tukey test. I’m doing this because I have a 10 files of 200,000 integers (all around 5000 and above). That is about 200MB per file. So, right now the ANOVA with a post hoc tukey test takes about 1hr to run in Mathematica. THIS IS… Continue reading large numbers
N-Queens
n-queens problem is a very interesting problem. Especially when you start imagining more than 2 dimensions and start thinking d-dimensions it becomes an even more interesting and challenging combinatorics problem. The link also points to some applications including traffic control, which makes sense.
Roots of Branching Processes
In branching processes you can find the probability of the system going extinct by finding the roots of the polynomial where the coefficients are the probabilities and the exponents are the number generated. The smallest root between 0 and 1 will be the answer. What do the other roots mean? Basically the root corresponds to… Continue reading Roots of Branching Processes
Ryacas
must run in a terminal yacas –server 9734 then can use Ryacas in R. yacas – yet another computer algebra system. http://yacas.sourceforge.net/homepage.html