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Twin primes visualized over an Ulam Spiral in HTML5

Click here for the HTML5 demo in Javacript.

Two numbers p and q are twin primes if they are primes and |p| = 2.

The Ulam spiral, discovered by the mathematician Stanislaw Ulam in 1963, is a simple method to visualize prim numbers. Put the natural numbers in a spiral and draw only the ones which are primes.

In the visualization below, I’m drawing the prime numbers in two shades of green. Twin primes in light green and regular primes in dark green.

twin primes ulam spiral

The “vortex effect” is created because every twin prime is followed by its twin two steps before in the spiral. Below the same image with the zoom in the center:

twin primes ulam spiralIn the HTML5 demo in Javacriptthe spiral is draw dynamically in a image (warning: it can be a little bit computationally intensive for your machine). You can play with the source-code on Github, and change the parameters. If you are looking for a plain ulam spiral, here it is one.

Update (May 30, 2013): This post was featured on the Blog of Math Blogs.

Update (November 25, 2013): I created a standalone Github project for this code.
https://github.com/silveira/ulam

Latex test

This:

i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>

Produce this:
$latex i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$

If you are seeing a complicated math formula in a image then it worked.

GWU Computer Science Graduate Classes Graph

In order to help me to take decisions about which class to take every semester I did a web scrapping from the graduate and undergraduate bulletin. For every class I could get classe name, prerequisites, credits, teacher, program, description, etc, in a formated tabular document.

Using Python CSV library I could read the tables and parse the data to other formats. One format very useful to handle graph structures is the DOT language script (included in the Graphviz project), in which you can describe both the graph structure and the elements of the graph layout.

Here is the Python source-code to convert the tables to graphs at Github.

The final result (click to view in full size):

Limitations and comments:

  • Prerequisites are only displayed using AND logic. It’s not showing other logics as OR (equivalent classes).
  • Errors may exists due to the scrapping process, conversions, or in the errors in the original source.
  • In the sources there is also a function to convert the graph in Dracula (a JavaScript interactive graph representation) but the current result is too tangled.

 

Bioperl Install and examples

Creative Commons ATT-SA http://www.flickr.com/photos/chigley/3003248261/

Perl is a widely used language in bioinformatics. As I already experimented Python and Biopython for handling a few simple bioinformatics tasks I will now try Perl and Bioperl.

Install on Ubuntu 11.10 (oneiric)

Perl already comes with Ubuntu. Bioperl can be installed (without CPAN):

$ sudo apt-get install bioperl

After the installation on have several tools in your PATH:

bp_aacomp, bp_biblio, bp_biofetch_genbank_proxy, bp_bioflat_index, bp_biogetseq, bp_blast2tree, bp_bulk_load_gff, bp_chaos_plot, bp_classify_hits_kingdom, bp_composite_LD, bp_das_server, bp_dbsplit, bp_download_query_genbank, bp_einfo, bp_extract_feature_seq, bp_fast_load_gff, bp_fastam9_to_table, bp_fetch, bp_filter_search, bp_flanks, bp_gccalc, bp_genbank2gff, bp_genbank2gff3, bp_generate_histogram, bp_heterogeneity_test, bp_hivq, bp_hmmer_to_table, bp_index, bp_load_gff, bp_local_taxonomydb_query, bp_make_mrna_protein, bp_mask_by_search, bp_meta_gff, bp_mrtrans, bp_mutate, bp_netinstall, bp_nexus2nh, bp_nrdb, bp_oligo_count, bp_pairwise_kaks, bp_parse_hmmsearch, bp_process_gadfly, bp_process_sgd, bp_process_wormbase, bp_query_entrez_taxa, bp_remote_blast, bp_revtrans-motif, bp_search2BSML, bp_search2alnblocks, bp_search2gff, bp_search2table, bp_search2tribe, bp_seq_length, bp_seqconvert, bp_seqfeature_delete, bp_seqfeature_gff3, bp_seqfeature_load, bp_seqret, bp_seqretsplit, bp_split_seq, bp_sreformat, bp_taxid4species, bp_taxonomy2tree, bp_translate_seq, bp_tree2pag, bp_unflatten_seq

You can try to import a Bioperl module to check if everything is working properly.

#!/bin/perl -w
 
use Bio::Seq; 

Writing a nucleotide sequence to a FASTA file

#!/usr/bin/perl -w
 
use Bio::Seq;
use Bio::SeqIO;
 
$seq_obj = Bio::Seq->new(-seq => "gattaca",                        
         -display_id => "#10191997",
         -desc => "Example",                        
         -alphabet => "dna" );
 
$seqio_obj = Bio::SeqIO->new(-file => '>sequence.fasta', -format => 'fasta' );
 
$seqio_obj->write_seq($seq_obj);

The output in the sequence.fasta created will be:

#10191997 Example
gattaca

Reading a Genbank file
Opening the same example I used last time (Hippopotamus amphibius mitochondrion, complete genome).

#!/usr/bin/perl -w

use Bio::Seq;
use Bio::SeqIO;

$seqio_obj = Bio::SeqIO->new(-file => "sequence.gb", -format => "genbank" );

while ($seq_obj = $seqio_obj->next_seq){ 
    print $seq_obj->seq,"\n";
}

Online Querying Genbank

With Bioperl is possible to programmatically query and retrieve data directly from GenBank. For example, to retrieve the same mitochondrial genome from the Hippopotamus I used in the example above.

#!/usr/bin/perl -w

use Bio::DB::GenBank;
use Bio::DB::Query::GenBank;
 
$query = "Hippopotamus amphibius[ORGN] AND NC_000889[LOCUS]";
$query_obj = Bio::DB::Query::GenBank->new(-db    => 'nucleotide',  -query => $query );
 
$gb_obj = Bio::DB::GenBank->new;
 
$stream_obj = $gb_obj->get_Stream_by_query($query_obj);

while ($seq_obj = $stream_obj->next_seq) {    
	print $seq_obj->display_id, "\t", $seq_obj->length, "\n";
}