Author: meditationatae

Hello World!

ICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIDIwMjQgICAgICAgICAgICAgICAgICAgICAg ICAgICAgICAgCgogICAgICAgSmFudWFyeSAgICAgICAgICAgICAgIEZlYnJ1YXJ5ICAgICAgICAg ICAgICAgICBNYXJjaCAgICAgICAKU3UgTW8gVHUgV2UgVGggRnIgU2EgICBTdSBNbyBUdSBXZSBU aCBGciBTYSAgIFN1IE1vIFR1IFdlIFRoIEZyIFNhCiAgICAxICAyICAzICA0ICA1ICA2ICAgICAg ICAgICAgICAgIDEgIDIgIDMgICAgICAgICAgICAgICAgICAgMSAgMgogNyAgOCAgOSAxMCAxMSAx MiAxMyAgICA0ICA1ICA2ICA3ICA4ICA5IDEwICAgIDMgIDQgIDUgIDYgIDcgIDggIDkKMTQgMTUg MTYgMTcgMTggMTkgMjAgICAxMSAxMiAxMyAxNCAxNSAxNiAxNyAgIDEwIDExIDEyIDEzIDE0IDE1 IDE2CjIxIDIyIDIzIDI0IDI1IDI2IDI3ICAgMTggMTkgMjAgMjEgMjIgMjMgMjQgICAxNyAxOCAx OSAyMCAyMSAyMiAyMwoyOCAyOSAzMCAzMSAgICAgICAgICAgIDI1IDI2IDI3IDI4IDI5ICAgICAg ICAgMjQgMjUgMjYgMjcgMjggMjkgMzAKICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg ICAgICAgICAgICAgIDMxCiAgICAgICAgQXByaWwgICAgICAgICAgICAgICAgICAgTWF5ICAgICAg ICAgICAgICAgICAgIEp1bmUgICAgICAgIApTdSBNbyBUdSBXZSBUaCBGciBTYSAgIFN1IE1vIFR1 IFdlIFRoIEZyIFNhICAgU3UgTW8gVHUgV2UgVGggRnIgU2EKICAgIDEgIDIgIDMgIDQgIDUgIDYg ICAgICAgICAgICAgMSAgMiAgMyAgNCAgICAgICAgICAgICAgICAgICAgICAxCiA3ICA4ICA5IDEw IDExIDEyIDEzICAgIDUgIDYgIDcgIDggIDkgMTAgMTEgICAgMiAgMyAgNCAgNSAgNiAgNyAgOAox NCAxNSAxNiAxNyAxOCAxOSAyMCAgIDEyIDEzIDE0IDE1IDE2IDE3IDE4ICAgIDkgMTAgMTEgMTIg MTMgMTQgMTUKMjEgMjIgMjMgMjQgMjUgMjYgMjcgICAxOSAyMCAyMSAyMiAyMyAyNCAyNSAgIDE2 IDE3IDE4IDE5IDIwIDIxIDIyCjI4IDI5IDMwICAgICAgICAgICAgICAgMjYgMjcgMjggMjkgMzAg MzEgICAgICAyMyAyNCAyNSAyNiAyNyAyOCAyOQogICAgICAgICAgICAgICAgICAgICAgICAgICAg ICAgICAgICAgICAgICAgICAgMzAKICAgICAgICBKdWx5ICAgICAgICAgICAgICAgICAgQXVndXN0 ICAgICAgICAgICAgICAgIFNlcHRlbWJlciAgICAgClN1IE1vIFR1IFdlIFRoIEZyIFNhICAgU3Ug TW8gVHUgV2UgVGggRnIgU2EgICBTdSBNbyBUdSBXZSBUaCBGciBTYQogICAgMSAgMiAgMyAgNCAg NSAgNiAgICAgICAgICAgICAgICAxICAyICAzICAgIDEgIDIgIDMgIDQgIDUgIDYgIDcKIDcgIDgg IDkgMTAgMTEgMTIgMTMgICAgNCAgNSAgNiAgNyAgOCAgOSAxMCAgICA4ICA5IDEwIDExIDEyIDEz IDE0CjE0IDE1IDE2IDE3IDE4IDE5IDIwICAgMTEgMTIgMTMgMTQgMTUgMTYgMTcgICAxNSAxNiAx NyAxOCAxOSAyMCAyMQoyMSAyMiAyMyAyNCAyNSAyNiAyNyAgIDE4IDE5IDIwIDIxIDIyIDIzIDI0 ICAgMjIgMjMgMjQgMjUgMjYgMjcgMjgKMjggMjkgMzAgMzEgICAgICAgICAgICAyNSAyNiAyNyAy OCAyOSAzMCAzMSAgIDI5IDMwCgogICAgICAgT2N0b2JlciAgICAgICAgICAgICAgIE5vdmVtYmVy ICAgICAgICAgICAgICAgRGVjZW1iZXIgICAgICAKU3UgTW8gVHUgV2UgVGggRnIgU2EgICBTdSBN byBUdSBXZSBUaCBGciBTYSAgIFN1IE1vIFR1IFdlIFRoIEZyIFNhCiAgICAgICAxICAyICAzICA0 ICA1ICAgICAgICAgICAgICAgICAgIDEgIDIgICAgMSAgMiAgMyAgNCAgNSAgNiAgNwogNiAgNyAg OCAgOSAxMCAxMSAxMiAgICAzICA0ICA1ICA2ICA3ICA4ICA5ICAgIDggIDkgMTAgMTEgMTIgMTMg MTQKMTMgMTQgMTUgMTYgMTcgMTggMTkgICAxMCAxMSAxMiAxMyAxNCAxNSAxNiAgIDE1IDE2IDE3 IDE4IDE5IDIwIDIxCjIwIDIxIDIyIDIzIDI0IDI1IDI2ICAgMTcgMTggMTkgMjAgMjEgMjIgMjMg ICAyMiAyMyAyNCAyNSAyNiAyNyAyOAoyNyAyOCAyOSAzMCAzMSAgICAgICAgIDI0IDI1IDI2IDI3 IDI4IDI5IDMwICAgMjkgMzAgMzEKCgo=

This is a continuation of the previous post on b-numbers. === For a b-number ‘x’ in the range 4096 to 8191 (13 bit length), it appears at first glance that, modulo 4096, x == y (mod 4096), where y is a b-number in the range 1-4095; Details:   k up to 4095:   5 //… Continue reading More on b-numbers, part B

If we write the (hypothetical, from now on understood) sequence from TM #4 (chaotic), 5-state, 2-symbol tape of Marxen and Buntrock in rows of 8, the 3rd column has a complex structure. Suppose we use “index 1”-notation, which just means that the first term of the sequence, 3, is written s(1) instead of s(0) as… Continue reading The b-numbers again

The code compiles and executes without problems using the GCC compiler on architecture x86_64 on Linux. It only needs the standard C library. It’s an accelerated simulator that combines many repated operations into one big operation. It was checked against a conventional un-accelerated TM simulator, and the outputs matched. (no name program, or sim12g84.c locally):… Continue reading C source code to current TM #4 (chaotic) simulator

Patterns in the b’-numbers related to TM #4 (chaotic) presumptive sequence   b’ numbers = ((( {1, 2, 3, 4, 5, 6, 7} Union the following disjoint sets, one per number of bits in the base 2 representations of these numbers, 4 bits for v8, 5 bits for v16, 6 bits for v32, 7 bits… Continue reading Patterns in the b’-numbers related to TM #4 (chaotic) presumptive sequence

? for(X=1,158, print(binary(yyy[X]) )) [1] [1, 0] [1, 1] [1, 0, 0] [1, 0, 1] [1, 1, 0] [1, 1, 1] [1, 0, 0, 1] [1, 0, 1, 0] [1, 0, 1, 1] [1, 1, 1, 0] [1, 0, 0, 0, 1] [1, 0, 0, 1, 0] [1, 0, 0, 1, 1] [1, 0, 1,… Continue reading b'(n) sequence in binary, n = 1 to 158:

If the n’th b-number is b(n), then b(n) == 3 (mod 8). Therefore, b(n)+5 is divisible by 8, and we can form: b'(n) := ( b(n) + 5)/8. For n = 1, 2, 3, … we have b'(n) as copied below, an irregular sequence: 1 2 3 4 5 6 7 9 10 11 14… Continue reading Irregular sequence derived from the b-numbers

For a b-number ‘b’ , empirically, s(2^m – b – 2) = 2^m – b, as long as b > 0 (always true) AND b < 2^(m-1). Being connected to Column 3 of 8, a “b-number” b is such that b == 3 (mod 8). A b-number ‘b’ predicts relationships of the type: s(y) =… Continue reading The sequence of “b-numbers” determines some values in Column 3 of the TM #4 presumptive sequence

For the TM #4 , hypothetically, an infinite sequence is generated a bit at a time. By arranging this sequence into rows of eight, some simplication occurs: (a) The first column is all 3s (b) The second column is all 1s. (c) And so on. Suppose we denote the sequence by s(1), s(2), s(3), s(4),… Continue reading Observations on column 3 of TM #4 sequence, and mystery remains

Below, the first 350 values of j for which 8j +5 is an allowable number:   0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 18 21 22 23 25 26 27 28 29 30 31 38 42 45 46 47 50 53 54 55 57 58 59 60… Continue reading Allowable numbers: when is 8j + 5 allowable?

1000000110110101 l16 1000011111101101 l16 1000101101110101 l16 1000101111110101 l16 1000110011101101 l16 1000110110110101 l16 1000111011010101 l16 1001000110110101 l16 1001001011010101 l16 1001010111010101 l16 1001011011101101 l16 1001011110110101 l16 1001011111101101 l16 1001100111101101 l16 1001101011111101 l16 1001101101110101 l16 1001101111110101 l16 1001110011101101 l16 1001110110110101 l16 1001110111101101 l16 1001111011010101 l16 1001111011111101 l16 1001111101110101 l16 1001111111110101 l16 1010000110110101 l16 1010001011010101 l16 1010010111010101 l16 1010011011101101… Continue reading The 234 allowable numbers of bit-length 16 for TM #4 (chaotic)

100000000000000101 l18 100000000000001101 l18 100000000000010101 l18 100000000000011101 l18 100000000000100101 l18 100000000000101101 l18 100000000000110101 l18 100000000000111101 l18 100000000001001101 l18 100000000001010101 l18 100000000001011101 l18 100000000001100101 l18 100000000001101101 l18 100000000001110101 l18 100000000001111101 l18 100000000010010101 l18 100000000010101101 l18 100000000010110101 l18 100000000010111101 l18 100000000011001101 l18 100000000011010101 l18 100000000011011101 l18 100000000011100101 l18 100000000011101101 l18 100000000011110101 l18 100000000011111101 l18 100000000100110101 l18 100000000101010101… Continue reading List of the 543 atomic forbidden numbers of bit-length 18

1000101 10000101 10001101 10011101 10100101 100000101 100001101 100010101 100011101 100100101 100101101 100111101 101001101 101011101 101100101 1000000101 1000001101 1000010101 1000011101 1000100101 1000101101 1000110101 1000111101 1001001101 1001010101 1001011101 1001100101 1001101101 1001111101 1010010101 1010101101 1010111101 1011001101 1011011101 1011100101 10000000101 10000001101 10000010101 10000011101 10000100101 10000101101 10000110101 10000111101 10001001101 10001010101 10001011101 10001100101 10001101101 10001110101 10001111101 10010010101 10010101101 10010111101 10011001101 10011011101… Continue reading List of the first 200 atomic forbidden numbers for TM #4 (chaotic)

Please refer to the earlier post about the subsequence expressed in base 8 (octal).   Here,  I changed base 8 to base 2, and secondly, I’ve had the program print the difference between the first and second number in third position: 101 101 000 1101 1101 0000 10101 10101 00000 11101 11101 00000 100101 100101… Continue reading Terms from subsequence of TM #4 chaotic in base 2

A pattern shows up if we put the output (the runs of 1s and runs of 0s) of TM #4 in rows of 8 numbers. So far, columns 1 and 2 appear to be “all 3” and “all 1”. We turn to column 3, the terms with index 8*J + 3, J = 0, 1,… Continue reading Terms from subsequence of TM #4 chaotic in octal

3 1 5 3 7 1 9 3 3 1 13 3 15 1 17 11 3 1 21 3 7 1 25 3 3 1 29 3 31 1 33 27 3 1 37 3 7 1 9 3 3 1 45 3 15 1 49 11 3 1 53 3 7 1 57… Continue reading Content of Tape of TM #4 (chaos machine) in rows of 8

These are exceptions to the general rule that n1 >= n0 , that the count of 1 bits is equal to or greater than the count of 0 bits in the base 2 representation of numbers in the hypothetical sequence computed by TM #4 chaotic, 5-state, Marxen and Buntrock, 1990. Please refer to previous post… Continue reading List of exceptions

The numbers of the hypothetical sequence are represented in base 2, for a fixed width of 18 bits. It’s observed that, with few exceptions, if n1 is the number of 1 bits in standard base 2 notation, and n0 is the number of 0 bits in standard base 2 notation, which always begins with a… Continue reading Content of Tape of TM #4 or “chaotic” in binary

The variation begins with: 23. Ra8 Rxb7 24. Rda1 , which sets up connected white rooks on the A-file on A1 and A8. ================================================================= [Event “World Cup 2017”] [Site “Tbilisi”] [Date “2017.09.06”] [Round “9.10”] [White “Anand Viswanathan (IND)”] [Black “Kovalyov Anton (CAN)”] [Result “0-1”] [ECO “B90”] [WhiteElo “2794”] [BlackElo “2649”] [Annotator “,david250DavidBernier”] [PlyCount “86”] [EventDate… Continue reading Variation on 23. Nc5 in Anand-Kovalyov round 2 game

3 1 5 3 7 1 9 3 3 1 13 3 15 1 17 11 3 1 21 3 7 1 25 3 3 1 29 3 31 1 33 27 3 1 37 3 7 1 9 3 3 1 45 3 15 1 49 11 3 1 53 3 7 1 57… Continue reading Content of Tape of TM #4 (chaos machine)

From the series of 200 lines beginning alternately with “3” then “1” from the previous post, I removed all lines that began with a “1”. That left 100 lines beginning with a “3” followed by one or more “4”s. I removed from each line the initial “3”. What remains is a series of 100 lines… Continue reading On TM #4 of Marxen & Buntrock, Part 2

Turing Machine number 4 (5 states, 2 symbols) of Heiner Marxen and Buntrock ( “chaotic”): Transition table = on A read 0: B1L on A read 1: B1R on B read 0: C1R on B read 1: E0L on C read 0: D0R on C read 1: A0L on D read 0: A1L on D… Continue reading Observations on TM #4 of Marxen & Buntrock (chaotic 5-state TM)

The quantity y being graphed is related to prime numbers, and the separation of the odd primes into those of the form 4k+1 and those of the form 4k+3. The non-principal Dirichlet character of period 4 can be defined by: chi(1) = 1, chi(2) = 0, chi(3) = -1, chi(4) = 0 plus the periodicity… Continue reading Graph of y = psi(x, chi), chi a non-principal Dirichlet character

On asymptotics of some large character sums. ================================================= Added Monday January 1, 2018: FOREWORD: I now consider what follows this foreword as numerical data on some large character sums. The implied asymptotic constant , 2*(exp(Euler)/Pi)^2 , is not backed by any theoretical work. I had a few email exchanges with Andrew Granville about asymptotics of… Continue reading On asymptotics of some large character sums

Today, I’m posting a variant of the PARI/gp script to solve the Lorenz system of differential equations. The use of factorials and binomial coefficients has been eliminated, so I’d expect it to run somewhat faster than the script from an earlier post.   The lorenzy4.gp PARI/gp script:   Lorenz(X0, Y0, Z0) = { order =… Continue reading An improved PARI/gp script for solving the Lorenz ODE system

At the GECCO 2017 conference in Berlin, Moalic and Gondran gave a presentation of a novel algorithm for graph coloring. The title of their presentation is: “Heuristic rope team : a parallel algorithm for graph coloring”. I made a best effort attempt to implement this in the C programming language. I was able to find… Continue reading Update on Parallel Rope Team Coloring

That’s my intention, you can ask questions, answer questions, etc. once I have this figured out. David Bernier  

The Lorenz system of differential equations is challenging to solve over extended periods of of time ‘t’, the independent variable. In “Long-Time Computability of the Lorenz System”, the authors Kehlet and Logg from Norway give a numerical solution for x(t), y(t), z(t) for t in [0, 1000] and with initial values x(0) = 1, y(0)… Continue reading PARI/gp script for Lorenz system

Previously, I thought there could be zero conflicts, two or more conflicts, but not exactly one vertex conflict; I’m not sure what’s going on. For 500-vertex graph DSJC500.5.col , program reports 1 vertex conflict (??):   Added July 31: It’s one edge conflict, or two vertices connected by an edge, and who share the same… Continue reading Graph coloring program report 1 vertex conflict

I’ve got C code that seems to work quite well for their new algorithm, comparatively speaking, meaning compared to what I had before. I’m regularly getting improper 47-colorings of DSJC500.5 with just two conflicting vertices, which means precisely one edge with a conflict. It’s as close as it gets without having no conflicts, unless I’m… Continue reading Moalic and Gondran Heuristic rope team : a parallel algorithm for graph coloring (for DSJC500.5 graph)

At the GECCO 2017 Conference in Berlin in July, Moalic and Gondran gave a presentation with a conference paper entitled: “Heuristic rope team : a parallel algorithm for graph coloring”. It can be searched for along with ACM on Google, and it’s in PDF format. It uses Tabu local search, the Greedy Partitioning Crossover operator… Continue reading New evolutionary algorithm, implementation in C

As explained in the previous post, the C language program that implements the HEAD’ graph coloring algorithm of Moalic and Gondran needs as input the graph DSJC500.5.col (DIMACS challenge) in a format detailed previously, as well as a file of 14 “improper 48-colorings” of DSJC500.5, meaning 48-colorings of the 500 vertices of DSJC500.5, where about… Continue reading Data of July 14 to test HEA in Duet, version HEAD’

The source code file, pnewtbuza75a.c , can be compiled using the GCC compiler as follows: gcc -lm -O2 -o pnewtbuza75a.out pnewtbuza75a.c To run the program, at the Unix shell prompt, I type: ./pnewtbuza75a.out DSJC500.5.mt 500 DSJC500.5.mt is a file containing a description of the 500-vertex DSJC500.5 graph created by David Johnson. In substance, it can… Continue reading Source code of July 14 to test HEA in Duet, version HEAD’

There were some mistakes and some inefficiencies in my C implementation of the HEAD’ variation of HEA in Duet of Moalic and Gondran (please see previous post). In their arxiv preprint, they propose a hybrid evolutionary algorithm for graph coloring which is really quite sophisticated, and building on earlier work of Galinier and Hao, among… Continue reading HEA in Duet and graph coloring (continuation)

generation 600 done … 14 conflicts at 18 iterations 13 conflicts at 19 iterations 12 conflicts at 20 iterations 11 conflicts at 22 iterations 10 conflicts at 28 iterations 9 conflicts at 29 iterations 8 conflicts at 33 iterations 7 conflicts at 42 iterations 6 conflicts at 84 iterations 5 conflicts at 248 iterations 4… Continue reading HEA in Duet update (49 colors, DSJC500.5.col )

I intend to write code to implement the HEAD or HEAD’ algorithm for graph coloring of Moalic and Gondran: “Variations on Memetic Algorithms for Graph Coloring Problems”, https://arxiv.org/abs/1401.2184 . There, they use the Greedy Partition Crossover or GPX crossover , and their hybrid Tabu Search + evolutionary method is inspired by Galinier and Hao’s HEA… Continue reading Preparation for writing the evolutionary algorithm code

In the last few posts, I described my attempts at using Tabu Search only to find a 49-coloring for the standard DIMACS challenge graph: DSJC500.5 or DSJC500.5.col with 500 vertices and a density of 0.5 .  For a graph with V vertices, the density is (d^bar)/(V-1) , where d^bar is the average degree of a… Continue reading Plan to implement crossover operator GPX (graph coloring)

The program uses the improved tabu search from: Galinier and Hao (1999): “Hybrid evolutionary algorithms for graph coloring” . For maximum variability in the colorings, it starts each time with a random 500-coloring of the 500-vertex graph. Starting from a valid k-coloring, a (k-1)-coloring, not necessarily valid, is obtained by distributing the elements of one… Continue reading newtabuzz99a.c for DIMACS graph DSJC500.5.col

This is my best effort at implementing Galinier and Hao’s Tabu Search algoritm from their 1999 paper: “Hybrid Evolutionary Algorithms for Graph Coloring”. It produces 50-colorings of DSJC500.5.col after a few hours. Filename:   newtabuzf99a.c   #include <stdio.h> #include <stdlib.h> #include <math.h> #define MAX_VERTEX 1000 #define MAX_COLORS 500 int adj_mat[MAX_VERTEX][MAX_VERTEX]; int Gamma[MAX_VERTEX][MAX_COLORS]; int Fast_Gamma[MAX_VERTEX][MAX_COLORS]; int tabu_list[MAX_VERTEX][MAX_COLORS];… Continue reading newtabuzf99a.c for DIMACS DSJC500.5.col

[root@localhost ~]# cd /usr/local/lib I had built and installed a non-system readline library as root in /usr/local/lib . As far as I can tell, the system readline library is in the file: /lib64/libreadline.so.6.0 Running # ldd -d -r /lib64/libreadline.so.6.0 linux-vdso.so.1 =>  (0x00007ffd0139b000) libtinfo.so.5 => /lib64/libtinfo.so.5 (0x0000003e73200000) libc.so.6 => /lib64/libc.so.6 (0x0000003752000000) /lib64/ld-linux-x86-64.so.2 (0x0000003751c00000) gives no unresolved… Continue reading This guy has my vote: libreadline cleanup

Note: copied from the output of a computer program. === adjacency matrix: 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0… Continue reading Data on possible/probable 15-vertex, 37-edge unit distance graph

With respect to the readline library, some versions have various symbols (UP, etc.) defined, and some do not. For PARI/gp on my system, it only works when these various symbols are defined.   PARI/gp question: how does one get a history of the commands input at the terminal ?     We are in the… Continue reading Using the ldd command with the verbose option

The post from a few weeks ago shows a 14-vertex 33-edge probable unit distance graph with 324 4-colorings. The URL of that blog post = “Best candidate” graph, 14 vertices, udg

It’s a probable unit distance graph. It has 356 4-colorings, and is not 3-colorable. Its adjacency matrix is: 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1… Continue reading Figure of a 13-vertex 28-edge graph

I had read that EXIF metadata in files that are images, whether .jpg or other file formats, have embbedded data, sometimes inluding geotags (coordinates). Below is the copy/paste of my first test running exiftool.exe on Windows 10: C:\Users\abcde\Downloads> C:\Users\abcde\Downloads\exiftool -All Louvre_Museum_Wikimedia_Commons.jpg ExifTool Version Number : 10.45 File Name : Louvre_Museum_Wikimedia_Commons.jpg Directory : . File Size… Continue reading My first test-drive using exiftool on Windows

The 12-vertex, 26-edge graph shown above is not 3-colorable, and is 4-colorable in 178 ways, up to permutation of the four colors. Numerical evidence suggests that it is a unit distance graph, i.e. embeddable in the plane with all edges of unit length. My unit distance graph solver found no 12-vertex, non 3-colorable, 4-colorable udg… Continue reading A 12-vertex, 26-edge, probable unit distance graph

This program is a variation on the solver for 14 vertices. The solver for 15 vertices has the added ingredient that it forces the first seven vertices and the edges that join some of these 7 vertices to each other to form as a subgraph a Moser spindle: a particular 7-vertex, 11-edge graph decribed at… Continue reading Unit distance graph solver for 15 vertices