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Daniel Shawul

Joined: 14 Mar 2006
Posts: 2187
Location: Ethiopia

Post subject: Re: Defect of a node?    Posted: Sun Jul 31, 2011 8:34 pm

Here is a simplistic formula for variance reduction.
 Code: X = (child_nodes / parent_nodes) - (child_visits / parent_visits)

So this will try to match exactly the proportion of visits (probability p) with the ratio of nodes, which is what we think will reduce the variance significantly. I can also take the log if that makes more sense.. Anyway, I think you should modify your formula like that. The default UCB formula gives exponentially more visits to the selected node so it might not be optimum..

I did a test without splitting that is only at the root for perft(12). First for uniform allocation every x million simulations upto 20 million. The exact perft value is 6.2854e16 for comparison.
 Code: ------------ 8 -------------- 0 h2h3   1.813302e+015  400000 0 h2h4   2.616134e+015  400000 0 g2g3   2.495857e+015  400000 0 g2g4   2.216429e+015  400000 0 f2f3   1.554160e+015  400000 0 f2f4   2.048562e+015  400000 0 e2e3   7.166771e+015  400000 0 e2e4   7.249186e+015  400000 0 d2d3   4.583958e+015  400000 0 d2d4   6.333048e+015  400000 0 c2c3   2.753783e+015  400000 0 c2c4   3.127248e+015  400000 0 b2b3   2.408044e+015  400000 0 b2b4   2.411038e+015  400000 0 a2a3   1.822216e+015  400000 0 a2a4   2.576983e+015  400000 0 g1h3   2.131080e+015  400000 0 g1f3   2.699393e+015  400000 0 b1c3   2.728673e+015  400000 0 b1a3   2.098231e+015  400000 Perft 6.283410e+016 ------------ 9 -------------- 0 h2h3   1.814723e+015  450000 0 h2h4   2.617783e+015  450000 0 g2g3   2.495254e+015  450000 0 g2g4   2.215698e+015  450000 0 f2f3   1.553956e+015  450000 0 f2f4   2.048454e+015  450000 0 e2e3   7.163548e+015  450000 0 e2e4   7.256218e+015  450000 0 d2d3   4.587213e+015  450000 0 d2d4   6.331049e+015  450000 0 c2c3   2.752864e+015  450000 0 c2c4   3.126464e+015  450000 0 b2b3   2.408961e+015  450000 0 b2b4   2.410975e+015  450000 0 a2a3   1.822817e+015  450000 0 a2a4   2.573954e+015  450000 0 g1h3   2.132079e+015  450000 0 g1f3   2.701815e+015  450000 0 b1c3   2.731700e+015  450000 0 b1a3   2.100345e+015  450000 Perft 6.284587e+016 ------------ 10 -------------- 0 h2h3   1.815171e+015  500000 0 h2h4   2.617650e+015  500000 0 g2g3   2.494990e+015  500000 0 g2g4   2.215388e+015  500000 0 f2f3   1.553766e+015  500000 0 f2f4   2.049380e+015  500000 0 e2e3   7.160351e+015  500000 0 e2e4   7.259996e+015  500000 0 d2d3   4.589976e+015  500000 0 d2d4   6.336715e+015  500000 0 c2c3   2.754723e+015  500000 0 c2c4   3.124217e+015  500000 0 b2b3   2.410776e+015  500000 0 b2b4   2.410020e+015  500000 0 a2a3   1.822980e+015  500000 0 a2a4   2.573983e+015  500000 0 g1h3   2.131692e+015  500000 0 g1f3   2.702720e+015  500000 0 b1c3   2.731418e+015  500000 0 b1a3   2.098746e+015  500000 Perft 6.285466e+016 ------------ 11 -------------- 0 h2h3   1.813940e+015  550000 0 h2h4   2.617958e+015  550000 0 g2g3   2.496539e+015  550000 0 g2g4   2.215605e+015  550000 0 f2f3   1.553451e+015  550000 0 f2f4   2.051968e+015  550000 0 e2e3   7.159425e+015  550000 0 e2e4   7.259527e+015  550000 0 d2d3   4.590969e+015  550000 0 d2d4   6.330726e+015  550000 0 c2c3   2.758148e+015  550000 0 c2c4   3.123013e+015  550000 0 b2b3   2.410686e+015  550000 0 b2b4   2.411235e+015  550000 0 a2a3   1.822786e+015  550000 0 a2a4   2.575811e+015  550000 0 g1h3   2.130972e+015  550000 0 g1f3   2.704258e+015  550000 0 b1c3   2.732802e+015  550000 0 b1a3   2.098855e+015  550000 Perft 6.285867e+016 ------------ 12 -------------- 0 h2h3   1.813440e+015  600000 0 h2h4   2.619919e+015  600000 0 g2g3   2.494971e+015  600000 0 g2g4   2.214365e+015  600000 0 f2f3   1.553487e+015  600000 0 f2f4   2.052206e+015  600000 0 e2e3   7.162753e+015  600000 0 e2e4   7.254358e+015  600000 0 d2d3   4.592824e+015  600000 0 d2d4   6.327676e+015  600000 0 c2c3   2.757145e+015  600000 0 c2c4   3.122555e+015  600000 0 b2b3   2.411423e+015  600000 0 b2b4   2.409885e+015  600000 0 a2a3   1.822653e+015  600000 0 a2a4   2.575090e+015  600000 0 g1h3   2.130967e+015  600000 0 g1f3   2.702950e+015  600000 0 b1c3   2.732230e+015  600000 0 b1a3   2.099691e+015  600000 Perft 6.285059e+016 ------------ 13 -------------- 0 h2h3   1.814229e+015  650000 0 h2h4   2.620978e+015  650000 0 g2g3   2.495462e+015  650000 0 g2g4   2.215475e+015  650000 0 f2f3   1.553379e+015  650000 0 f2f4   2.051682e+015  650000 0 e2e3   7.160288e+015  650000 0 e2e4   7.250356e+015  650000 0 d2d3   4.590598e+015  650000 0 d2d4   6.330433e+015  650000 0 c2c3   2.754787e+015  650000 0 c2c4   3.121723e+015  650000 0 b2b3   2.409998e+015  650000 0 b2b4   2.408850e+015  650000 0 a2a3   1.823009e+015  650000 0 a2a4   2.574284e+015  650000 0 g1h3   2.131403e+015  650000 0 g1f3   2.703566e+015  650000 0 b1c3   2.731481e+015  650000 0 b1a3   2.099698e+015  650000 Perft 6.284168e+016 ------------ 14 -------------- 0 h2h3   1.815404e+015  700000 0 h2h4   2.621107e+015  700000 0 g2g3   2.497124e+015  700000 0 g2g4   2.215094e+015  700000 0 f2f3   1.552745e+015  700000 0 f2f4   2.051714e+015  700000 0 e2e3   7.157191e+015  700000 0 e2e4   7.256448e+015  700000 0 d2d3   4.589509e+015  700000 0 d2d4   6.329140e+015  700000 0 c2c3   2.754336e+015  700000 0 c2c4   3.121496e+015  700000 0 b2b3   2.408253e+015  700000 0 b2b4   2.409516e+015  700000 0 a2a3   1.823545e+015  700000 0 a2a4   2.574178e+015  700000 0 g1h3   2.132176e+015  700000 0 g1f3   2.703329e+015  700000 0 b1c3   2.734887e+015  700000 0 b1a3   2.101075e+015  700000 Perft 6.284827e+016 ------------ 15 -------------- 0 h2h3   1.816503e+015  750000 0 h2h4   2.620579e+015  750000 0 g2g3   2.497220e+015  750000 0 g2g4   2.214367e+015  750000 0 f2f3   1.552321e+015  750000 0 f2f4   2.052038e+015  750000 0 e2e3   7.152168e+015  750000 0 e2e4   7.257143e+015  750000 0 d2d3   4.592314e+015  750000 0 d2d4   6.324743e+015  750000 0 c2c3   2.753150e+015  750000 0 c2c4   3.121696e+015  750000 0 b2b3   2.407816e+015  750000 0 b2b4   2.409532e+015  750000 0 a2a3   1.823040e+015  750000 0 a2a4   2.574209e+015  750000 0 g1h3   2.132449e+015  750000 0 g1f3   2.702751e+015  750000 0 b1c3   2.733749e+015  750000 0 b1a3   2.101213e+015  750000 Perft 6.283900e+016 ------------ 16 -------------- 0 h2h3   1.815944e+015  800000 0 h2h4   2.620315e+015  800000 0 g2g3   2.499890e+015  800000 0 g2g4   2.215288e+015  800000 0 f2f3   1.551713e+015  800000 0 f2f4   2.051139e+015  800000 0 e2e3   7.151355e+015  800000 0 e2e4   7.262185e+015  800000 0 d2d3   4.591226e+015  800000 0 d2d4   6.325666e+015  800000 0 c2c3   2.753631e+015  800000 0 c2c4   3.121308e+015  800000 0 b2b3   2.407670e+015  800000 0 b2b4   2.410392e+015  800000 0 a2a3   1.822743e+015  800000 0 a2a4   2.575083e+015  800000 0 g1h3   2.132846e+015  800000 0 g1f3   2.702652e+015  800000 0 b1c3   2.734292e+015  800000 0 b1a3   2.099795e+015  800000 Perft 6.284513e+016 ------------ 17 -------------- 0 h2h3   1.815288e+015  850000 0 h2h4   2.619383e+015  850000 0 g2g3   2.500610e+015  850000 0 g2g4   2.213982e+015  850000 0 f2f3   1.552783e+015  850000 0 f2f4   2.051022e+015  850000 0 e2e3   7.150560e+015  850000 0 e2e4   7.260795e+015  850000 0 d2d3   4.588434e+015  850000 0 d2d4   6.326281e+015  850000 0 c2c3   2.754893e+015  850000 0 c2c4   3.122189e+015  850000 0 b2b3   2.408502e+015  850000 0 b2b4   2.409861e+015  850000 0 a2a3   1.823433e+015  850000 0 a2a4   2.575755e+015  850000 0 g1h3   2.133033e+015  850000 0 g1f3   2.703218e+015  850000 0 b1c3   2.735026e+015  850000 0 b1a3   2.102021e+015  850000 Perft 6.284707e+016 ------------ 18 -------------- 0 h2h3   1.815656e+015  900000 0 h2h4   2.619418e+015  900000 0 g2g3   2.500655e+015  900000 0 g2g4   2.214291e+015  900000 0 f2f3   1.553066e+015  900000 0 f2f4   2.051256e+015  900000 0 e2e3   7.149329e+015  900000 0 e2e4   7.259226e+015  900000 0 d2d3   4.588728e+015  900000 0 d2d4   6.327667e+015  900000 0 c2c3   2.754532e+015  900000 0 c2c4   3.121963e+015  900000 0 b2b3   2.409020e+015  900000 0 b2b4   2.409387e+015  900000 0 a2a3   1.823615e+015  900000 0 a2a4   2.576327e+015  900000 0 g1h3   2.132703e+015  900000 0 g1f3   2.703474e+015  900000 0 b1c3   2.735448e+015  900000 0 b1a3   2.101198e+015  900000 Perft 6.284696e+016 ------------ 19 -------------- 0 h2h3   1.816246e+015  950000 0 h2h4   2.618368e+015  950000 0 g2g3   2.500863e+015  950000 0 g2g4   2.214835e+015  950000 0 f2f3   1.553202e+015  950000 0 f2f4   2.049946e+015  950000 0 e2e3   7.147544e+015  950000 0 e2e4   7.264825e+015  950000 0 d2d3   4.587508e+015  950000 0 d2d4   6.327325e+015  950000 0 c2c3   2.753856e+015  950000 0 c2c4   3.122839e+015  950000 0 b2b3   2.408637e+015  950000 0 b2b4   2.409409e+015  950000 0 a2a3   1.824127e+015  950000 0 a2a4   2.576294e+015  950000 0 g1h3   2.132834e+015  950000 0 g1f3   2.703278e+015  950000 0 b1c3   2.734808e+015  950000 0 b1a3   2.100417e+015  950000 Perft 6.284716e+016 ------------ 20 -------------- 0 h2h3   1.816109e+015  1000000 0 h2h4   2.617712e+015  1000000 0 g2g3   2.501489e+015  1000000 0 g2g4   2.216040e+015  1000000 0 f2f3   1.553030e+015  1000000 0 f2f4   2.049958e+015  1000000 0 e2e3   7.151964e+015  1000000 0 e2e4   7.264583e+015  1000000 0 d2d3   4.585124e+015  1000000 0 d2d4   6.324209e+015  1000000 0 c2c3   2.752492e+015  1000000 0 c2c4   3.121799e+015  1000000 0 b2b3   2.408474e+015  1000000 0 b2b4   2.409765e+015  1000000 0 a2a3   1.824919e+015  1000000 0 a2a4   2.575964e+015  1000000 0 g1h3   2.133127e+015  1000000 0 g1f3   2.702962e+015  1000000 0 b1c3   2.736287e+015  1000000 0 b1a3   2.100308e+015  1000000 Perft 6.284632e+016

And using the formula I proposed above. It seems to perform well in the earlier iterations but I am not sure if it is better overall. Infact after 13 million simulations it got 5 significant digist right but may have ended up worse.. (need to investigate it) The number of visits of each node seems to exactly match the node proportions as expected. BTW we don't use weights in the tree part of the search since we just add up all the sub-trees so that should be forgotten.

 Code: 0 d2d3   4.595497e+015  657923 0 d2d4   6.316675e+015  904338 0 c2c3   2.750965e+015  393847 0 c2c4   3.117351e+015  446302 0 b2b3   2.408188e+015  344772 0 b2b4   2.405799e+015  344430 0 a2a3   1.830297e+015  262038 0 a2a4   2.578775e+015  369195 0 g1h3   2.137554e+015  306028 0 g1f3   2.705512e+015  387340 0 b1c3   2.732411e+015  391191 0 b1a3   2.097368e+015  300273 Perft 6.286372e+016 ------------ 10 -------------- 0 h2h3   1.813059e+015  288428 0 h2h4   2.620649e+015  416901 0 g2g3   2.504079e+015  398357 0 g2g4   2.218685e+015  352956 0 f2f3   1.549584e+015  246513 0 f2f4   2.047378e+015  325704 0 e2e3   7.167063e+015  1140160 0 e2e4   7.262421e+015  1155331 0 d2d3   4.592701e+015  730622 0 d2d4   6.317081e+015  1004942 0 c2c3   2.752083e+015  437810 0 c2c4   3.117873e+015  496001 0 b2b3   2.409631e+015  383333 0 b2b4   2.405647e+015  382698 0 a2a3   1.832156e+015  291465 0 a2a4   2.579491e+015  410354 0 g1h3   2.137038e+015  339968 0 g1f3   2.705199e+015  430352 0 b1c3   2.727891e+015  433962 0 b1a3   2.100427e+015  334143 Perft 6.286013e+016 ------------ 11 -------------- 0 h2h3   1.813997e+015  317488 0 h2h4   2.621098e+015  458748 0 g2g3   2.503788e+015  438217 0 g2g4   2.219913e+015  388532 0 f2f3   1.549072e+015  271121 0 f2f4   2.047491e+015  358354 0 e2e3   7.167173e+015  1254408 0 e2e4   7.258842e+015  1270453 0 d2d3   4.593822e+015  804017 0 d2d4   6.317270e+015  1105657 0 c2c3   2.751479e+015  481567 0 c2c4   3.117819e+015  545686 0 b2b3   2.408365e+015  421516 0 b2b4   2.406613e+015  421208 0 a2a3   1.828823e+015  320083 0 a2a4   2.577085e+015  451045 0 g1h3   2.135356e+015  373734 0 g1f3   2.703714e+015  473207 0 b1c3   2.727331e+015  477341 0 b1a3   2.100421e+015  367618 Perft 6.284947e+016 ------------ 12 -------------- 0 h2h3   1.812292e+015  346021 0 h2h4   2.622347e+015  500685 0 g2g3   2.502575e+015  477817 0 g2g4   2.219905e+015  423847 0 f2f3   1.549419e+015  295830 0 f2f4   2.046605e+015  390759 0 e2e3   7.168725e+015  1368726 0 e2e4   7.258829e+015  1385929 0 d2d3   4.592223e+015  876793 0 d2d4   6.318268e+015  1206347 0 c2c3   2.751836e+015  525408 0 c2c4   3.117031e+015  595135 0 b2b3   2.409042e+015  459959 0 b2b4   2.405685e+015  459318 0 a2a3   1.828049e+015  349029 0 a2a4   2.576190e+015  491872 0 g1h3   2.136554e+015  407933 0 g1f3   2.705915e+015  516640 0 b1c3   2.726956e+015  520658 0 b1a3   2.101784e+015  401294 Perft 6.285023e+016 ------------ 13 -------------- 0 h2h3   1.811803e+015  374729 0 h2h4   2.618846e+015  541646 0 g2g3   2.504188e+015  517930 0 g2g4   2.220471e+015  459252 0 f2f3   1.548924e+015  320359 0 f2f4   2.046215e+015  423211 0 e2e3   7.169890e+015  1482923 0 e2e4   7.261306e+015  1501830 0 d2d3   4.594948e+015  950356 0 d2d4   6.316519e+015  1306423 0 c2c3   2.752095e+015  569206 0 c2c4   3.118487e+015  644985 0 b2b3   2.409069e+015  498259 0 b2b4   2.405068e+015  497432 0 a2a3   1.828397e+015  378161 0 a2a4   2.574745e+015  532525 0 g1h3   2.136591e+015  441903 0 g1f3   2.704993e+015  559465 0 b1c3   2.728415e+015  564308 0 b1a3   2.103684e+015  435097 Perft 6.285465e+016 ------------ 14 -------------- 0 h2h3   1.813291e+015  403891 0 h2h4   2.620117e+015  583601 0 g2g3   2.502080e+015  557310 0 g2g4   2.220889e+015  494678 0 f2f3   1.548103e+015  344823 0 f2f4   2.045591e+015  455633 0 e2e3   7.171794e+015  1597435 0 e2e4   7.263690e+015  1617904 0 d2d3   4.592061e+015  1022829 0 d2d4   6.318092e+015  1407278 0 c2c3   2.751921e+015  612959 0 c2c4   3.116581e+015  694183 0 b2b3   2.409730e+015  536740 0 b2b4   2.403458e+015  535343 0 a2a3   1.827671e+015  407094 0 a2a4   2.575980e+015  573770 0 g1h3   2.137585e+015  476123 0 g1f3   2.705148e+015  602542 0 b1c3   2.727396e+015  607496 0 b1a3   2.102771e+015  468368 Perft 6.285395e+016 ------------ 15 -------------- 0 h2h3   1.813036e+015  432652 0 h2h4   2.622403e+015  625795 0 g2g3   2.503675e+015  597463 0 g2g4   2.220766e+015  529950 0 f2f3   1.550062e+015  369898 0 f2f4   2.045958e+015  488236 0 e2e3   7.170076e+015  1711025 0 e2e4   7.261934e+015  1732945 0 d2d3   4.593117e+015  1096074 0 d2d4   6.317087e+015  1507471 0 c2c3   2.751558e+015  656616 0 c2c4   3.117043e+015  743832 0 b2b3   2.410570e+015  575244 0 b2b4   2.402488e+015  573316 0 a2a3   1.828604e+015  436367 0 a2a4   2.574928e+015  614466 0 g1h3   2.137888e+015  510173 0 g1f3   2.705798e+015  645696 0 b1c3   2.728363e+015  651080 0 b1a3   2.102386e+015  501701 Perft 6.285774e+016 ------------ 16 -------------- 0 h2h3   1.814018e+015  461744 0 h2h4   2.623417e+015  667770 0 g2g3   2.503974e+015  637367 0 g2g4   2.221177e+015  565383 0 f2f3   1.551175e+015  394840 0 f2f4   2.046955e+015  521037 0 e2e3   7.167191e+015  1824351 0 e2e4   7.264443e+015  1849106 0 d2d3   4.593504e+015  1169240 0 d2d4   6.316697e+015  1607865 0 c2c3   2.750663e+015  700160 0 c2c4   3.116618e+015  793310 0 b2b3   2.411340e+015  613787 0 b2b4   2.402587e+015  611559 0 a2a3   1.828773e+015  465500 0 a2a4   2.573638e+015  655099 0 g1h3   2.137460e+015  544074 0 g1f3   2.706000e+015  688791 0 b1c3   2.726595e+015  694033 0 b1a3   2.101748e+015  534984 Perft 6.285798e+016 ------------ 17 -------------- 0 h2h3   1.813638e+015  490492 0 h2h4   2.624576e+015  709807 0 g2g3   2.503000e+015  676927 0 g2g4   2.221308e+015  600744 0 f2f3   1.552404e+015  419842 0 f2f4   2.046949e+015  553589 0 e2e3   7.167069e+015  1938306 0 e2e4   7.264421e+015  1964635 0 d2d3   4.593359e+015  1242256 0 d2d4   6.319374e+015  1709050 0 c2c3   2.749583e+015  743615 0 c2c4   3.115050e+015  842454 0 b2b3   2.411415e+015  652158 0 b2b4   2.404495e+015  650286 0 a2a3   1.826844e+015  494064 0 a2a4   2.572587e+015  695747 0 g1h3   2.137674e+015  578126 0 g1f3   2.705651e+015  731733 0 b1c3   2.727820e+015  737728 0 b1a3   2.101865e+015  568441 Perft 6.285908e+016 ------------ 18 -------------- 0 h2h3   1.815725e+015  519894 0 h2h4   2.625884e+015  751866 0 g2g3   2.502382e+015  716504 0 g2g4   2.221896e+015  636192 0 f2f3   1.553130e+015  444706 0 f2f4   2.048007e+015  586402 0 e2e3   7.168234e+015  2052470 0 e2e4   7.264676e+015  2080084 0 d2d3   4.593371e+015  1315213 0 d2d4   6.319948e+015  1809581 0 c2c3   2.748922e+015  787095 0 c2c4   3.115832e+015  892151 0 b2b3   2.412455e+015  690755 0 b2b4   2.404762e+015  688552 0 a2a3   1.826525e+015  522986 0 a2a4   2.572899e+015  736694 0 g1h3   2.136722e+015  611804 0 g1f3   2.705012e+015  774522 0 b1c3   2.726329e+015  780625 0 b1a3   2.102156e+015  601904 Perft 6.286487e+016 ------------ 19 -------------- 0 h2h3   1.815107e+015  548552 0 h2h4   2.625603e+015  793495 0 g2g3   2.501708e+015  756052 0 g2g4   2.222109e+015  671553 0 f2f3   1.553298e+015  469429 0 f2f4   2.049418e+015  619364 0 e2e3   7.167926e+015  2166250 0 e2e4   7.266628e+015  2196080 0 d2d3   4.593653e+015  1388268 0 d2d4   6.320792e+015  1910234 0 c2c3   2.748679e+015  830690 0 c2c4   3.115870e+015  941661 0 b2b3   2.412186e+015  728997 0 b2b4   2.405768e+015  727058 0 a2a3   1.826682e+015  552050 0 a2a4   2.572771e+015  777528 0 g1h3   2.136955e+015  645818 0 g1f3   2.705180e+015  817545 0 b1c3   2.726352e+015  823943 0 b1a3   2.102589e+015  635433 Perft 6.286927e+016 ------------ 20 -------------- 0 h2h3   1.815710e+015  577626 0 h2h4   2.625207e+015  835150 0 g2g3   2.502826e+015  796217 0 g2g4   2.221826e+015  706823 0 f2f3   1.553493e+015  494208 0 f2f4   2.048690e+015  651743 0 e2e3   7.167533e+015  2280186 0 e2e4   7.267550e+015  2312004 0 d2d3   4.593755e+015  1461397 0 d2d4   6.320145e+015  2010608 0 c2c3   2.748152e+015  874261 0 c2c4   3.115947e+015  991267 0 b2b3   2.410237e+015  766761 0 b2b4   2.406517e+015  765579 0 a2a3   1.826718e+015  581128 0 a2a4   2.573466e+015  818684 0 g1h3   2.136368e+015  679636 0 g1f3   2.704945e+015  860516 0 b1c3   2.726488e+015  867369 0 b1a3   2.102422e+015  668837 Perft 6.286800e+016

And the visit allocation at iteration 20 are exact as the last two columns show.
 Code: % node   % visit 0   h2h3   1.82E+15   577626       0   h2h4   2.63E+15   835150   4.1757   4.1758 0   g2g3   2.50E+15   796217   3.9811   3.9811 0   g2g4   2.22E+15   706823   3.5341   3.5341 0   f2f3   1.55E+15   494208   2.4710   2.4710 0   f2f4   2.05E+15   651743   3.2587   3.2587 0   e2e3   7.17E+15   2280186   11.4009   11.4009 0   e2e4   7.27E+15   2312004   11.5600   11.5600 0   d2d3   4.59E+15   1461397   7.3070   7.3070 0   d2d4   6.32E+15   2010608   10.0530   10.0530 0   c2c3   2.75E+15   874261   4.3713   4.3713 0   c2c4   3.12E+15   991267   4.9563   4.9563 0   b2b3   2.41E+15   766761   3.8338   3.8338 0   b2b4   2.41E+15   765579   3.8279   3.8279 0   a2a3   1.83E+15   581128   2.9056   2.9056 0   a2a4   2.57E+15   818684   4.0934   4.0934 0   g1h3   2.14E+15   679636   3.3982   3.3982 0   g1f3   2.70E+15   860516   4.3026   4.3026 0   b1c3   2.73E+15   867369   4.3368   4.3368 0   b1a3   2.10E+15   668837   3.3442   3.3442                    Total   6.29E+16   20000000   97.1119   97.1119

Daniel
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Daniel Shawul Fri Jul 15, 2011 3:04 pm
Daniel Shawul Fri Jul 15, 2011 5:48 pm
Michel Van den Bergh Fri Jul 15, 2011 6:15 pm
Daniel Shawul Fri Jul 15, 2011 6:28 pm
H.G.Muller Fri Jul 15, 2011 6:40 pm
Daniel Shawul Fri Jul 15, 2011 6:52 pm
Daniel Shawul Fri Jul 15, 2011 7:45 pm
Uri Blass Fri Jul 15, 2011 8:58 pm
Daniel Shawul Fri Jul 15, 2011 10:14 pm
Uri Blass Sat Jul 16, 2011 2:27 am
Daniel Shawul Sat Jul 16, 2011 2:33 pm
Daniel Shawul Sat Jul 16, 2011 5:53 pm
Uri Blass Sat Jul 16, 2011 7:23 pm
Daniel Shawul Sat Jul 16, 2011 11:55 pm
Michel Van den Bergh Sun Jul 17, 2011 1:36 am
Daniel Shawul Sun Jul 17, 2011 11:16 am
Daniel Shawul Sun Jul 17, 2011 4:26 pm
Michel Van den Bergh Mon Jul 18, 2011 2:31 am
Daniel Shawul Mon Jul 18, 2011 11:38 am
Michel Van den Bergh Mon Jul 18, 2011 1:21 pm
Daniel Shawul Mon Jul 18, 2011 2:49 pm
Daniel Shawul Fri Jul 22, 2011 2:21 pm
Sven Schüle Fri Jul 22, 2011 2:46 pm
Daniel Shawul Fri Jul 22, 2011 3:08 pm
Michel Van den Bergh Fri Jul 22, 2011 11:24 pm
Daniel Shawul Fri Jul 22, 2011 11:50 pm
Daniel Shawul Sat Jul 23, 2011 5:11 am
Michel Van den Bergh Sat Jul 23, 2011 8:56 am
Daniel Shawul Sat Jul 23, 2011 12:02 pm
Daniel Shawul Fri Jul 22, 2011 11:14 pm
Sven Schüle Sat Jul 23, 2011 10:56 pm
Daniel Shawul Sat Jul 23, 2011 11:42 pm
Michel Van den Bergh Sat Jul 23, 2011 11:53 pm
Daniel Shawul Sun Jul 24, 2011 12:07 am
Michel Van den Bergh Sun Jul 24, 2011 12:31 am
Daniel Shawul Sun Jul 24, 2011 12:49 am
Michel Van den Bergh Sun Jul 24, 2011 3:03 am
Uri Blass Sun Jul 24, 2011 5:46 am
Michel Van den Bergh Sun Jul 24, 2011 6:07 am
Daniel Shawul Sun Jul 24, 2011 12:00 am
Uri Blass Mon Jul 25, 2011 12:16 pm
Daniel Shawul Mon Jul 25, 2011 12:21 pm
Uri Blass Mon Jul 25, 2011 12:40 pm
Peter Österlund Thu Jul 14, 2011 10:52 am
Daniel Shawul Thu Jul 14, 2011 3:24 pm
Peter Österlund Thu Jul 14, 2011 5:54 pm
Daniel Shawul Thu Jul 14, 2011 6:41 pm
Daniel Shawul Thu Jul 14, 2011 7:47 pm
Peter Österlund Thu Jul 14, 2011 9:08 pm
Daniel Shawul Thu Jul 14, 2011 9:37 pm
Daniel Shawul Thu Jul 14, 2011 10:41 pm
Peter Österlund Thu Jul 14, 2011 10:58 pm
Daniel Shawul Fri Jul 15, 2011 1:23 am
Daniel Shawul Fri Jul 15, 2011 12:45 pm
H.G.Muller Fri Jul 15, 2011 8:13 am
Daniel Shawul Fri Jul 15, 2011 12:35 pm
Steven Edwards Sat Jul 30, 2011 1:43 am
Peter Österlund Sat Jul 30, 2011 7:25 am
Steven Edwards Sat Jul 30, 2011 7:43 am
Peter Österlund Sat Jul 30, 2011 8:43 am
H.G.Muller Sat Jul 30, 2011 11:29 am
Michel Van den Bergh Sat Jul 30, 2011 12:59 pm
H.G.Muller Sat Jul 30, 2011 1:29 pm
Michel Van den Bergh Sat Jul 30, 2011 1:44 pm
H.G.Muller Sat Jul 30, 2011 1:57 pm
Michel Van den Bergh Sat Jul 30, 2011 2:41 pm
Michel Van den Bergh Sat Jul 30, 2011 3:43 pm
Michel Van den Bergh Sat Jul 30, 2011 4:35 pm
H.G.Muller Sat Jul 30, 2011 5:51 pm
Michel Van den Bergh Sat Jul 30, 2011 7:06 pm
H.G.Muller Sat Jul 30, 2011 7:39 pm
Michel Van den Bergh Sun Jul 31, 2011 1:36 am
Michel Van den Bergh Sun Jul 31, 2011 12:11 pm
Michel Van den Bergh Sun Jul 31, 2011 12:38 pm
Daniel Shawul Sun Jul 31, 2011 4:33 pm
Re: Defect of a node? Daniel Shawul Sun Jul 31, 2011 8:34 pm
Michel Van den Bergh Sun Jul 31, 2011 10:09 pm
Daniel Shawul Sun Jul 31, 2011 10:53 pm
Michel Van den Bergh Mon Aug 01, 2011 2:05 am
Daniel Shawul Mon Aug 01, 2011 10:08 am
Daniel Shawul Mon Aug 01, 2011 11:23 am
Daniel Shawul Mon Aug 01, 2011 1:28 pm
Daniel Shawul Mon Aug 01, 2011 3:24 pm
Daniel Shawul Mon Aug 01, 2011 5:20 pm
Daniel Shawul Sat Aug 06, 2011 11:23 am
Daniel Shawul Sat Aug 06, 2011 5:27 pm
Daniel Shawul Sat Aug 06, 2011 9:53 pm
Daniel Shawul Sun Aug 07, 2011 1:39 am
Daniel Shawul Sun Aug 07, 2011 3:18 am
H.G.Muller Sun Aug 07, 2011 8:13 am
Daniel Shawul Sun Aug 07, 2011 11:20 am
H.G.Muller Sun Aug 07, 2011 2:08 pm
Daniel Shawul Sun Aug 07, 2011 3:02 pm
H.G.Muller Sun Aug 07, 2011 3:51 pm
Daniel Shawul Sun Aug 07, 2011 4:35 pm
Michel Van den Bergh Sun Aug 07, 2011 4:58 pm
Daniel Shawul Sun Aug 07, 2011 6:36 pm
H.G.Muller Sun Aug 07, 2011 5:38 pm
Daniel Shawul Sun Aug 07, 2011 6:41 pm
H.G.Muller Sun Aug 07, 2011 8:51 pm
Daniel Shawul Mon Aug 08, 2011 1:08 pm
Daniel Shawul Sun Aug 07, 2011 11:35 am
Peter Österlund Sun Aug 07, 2011 10:57 pm
Daniel Shawul Mon Aug 08, 2011 1:00 pm
Daniel Shawul Mon Aug 08, 2011 2:23 pm
Daniel Shawul Mon Aug 08, 2011 4:51 pm
Peter Österlund Mon Aug 08, 2011 5:49 pm
Daniel Shawul Mon Aug 08, 2011 8:39 pm
Peter Österlund Mon Aug 08, 2011 9:49 pm
Daniel Shawul Mon Aug 08, 2011 11:26 pm
Daniel Shawul Tue Aug 09, 2011 10:28 am
Michel Van den Bergh Tue Aug 09, 2011 6:17 am
Daniel Shawul Tue Aug 09, 2011 10:40 am
Daniel Shawul Tue Aug 09, 2011 1:03 pm
Michel Van den Bergh Tue Aug 09, 2011 1:17 pm
Michel Van den Bergh Tue Aug 09, 2011 3:07 pm
Daniel Shawul Tue Aug 09, 2011 4:24 pm
Daniel Shawul Tue Aug 09, 2011 7:55 pm
Daniel Shawul Tue Aug 09, 2011 4:02 pm
Daniel Shawul Tue Aug 09, 2011 9:24 pm
Michel Van den Bergh Wed Aug 10, 2011 6:47 am
Daniel Shawul Wed Aug 10, 2011 10:57 am
Daniel Shawul Wed Aug 10, 2011 11:10 am
Michel Van den Bergh Wed Aug 10, 2011 11:22 am
Daniel Shawul Wed Aug 10, 2011 11:58 am
Michel Van den Bergh Wed Aug 10, 2011 12:30 pm
Daniel Shawul Wed Aug 10, 2011 2:16 pm
Michel Van den Bergh Wed Aug 10, 2011 2:23 pm
Daniel Shawul Wed Aug 10, 2011 2:29 pm
Daniel Shawul Wed Aug 10, 2011 2:53 pm
Michel Van den Bergh Wed Aug 10, 2011 3:00 pm
Daniel Shawul Wed Aug 10, 2011 3:34 pm
Michel Van den Bergh Wed Aug 10, 2011 3:55 pm
Daniel Shawul Wed Aug 10, 2011 4:08 pm
Michel Van den Bergh Thu Aug 11, 2011 3:14 am
Daniel Shawul Thu Aug 11, 2011 11:20 am
Michel Van den Bergh Thu Aug 11, 2011 11:39 am
Daniel Shawul Thu Aug 11, 2011 11:49 am
Michel Van den Bergh Thu Aug 11, 2011 1:28 pm
Daniel Shawul Thu Aug 11, 2011 3:19 pm
Michel Van den Bergh Fri Aug 12, 2011 10:42 am
Michel Van den Bergh Fri Aug 12, 2011 11:24 am
Sven Schüle Fri Aug 12, 2011 11:58 am
Sven Schüle Fri Aug 12, 2011 12:15 pm
Michel Van den Bergh Fri Aug 12, 2011 12:27 pm
Sven Schüle Fri Aug 12, 2011 1:28 pm
H.G.Muller Fri Aug 12, 2011 12:20 pm
H.G.Muller Fri Aug 12, 2011 2:53 pm
Michel Van den Bergh Fri Aug 12, 2011 3:07 pm
Daniel Shawul Fri Aug 12, 2011 3:18 pm
Michel Van den Bergh Fri Aug 12, 2011 3:29 pm
Daniel Shawul Fri Aug 12, 2011 3:38 pm
Sven Schüle Fri Aug 12, 2011 4:22 pm
Michel Van den Bergh Fri Aug 12, 2011 4:26 pm
Sven Schüle Fri Aug 12, 2011 4:37 pm
H.G.Muller Fri Aug 12, 2011 4:49 pm
Daniel Shawul Fri Aug 12, 2011 1:42 pm
Sven Schüle Fri Aug 12, 2011 2:10 pm
H.G.Muller Fri Aug 12, 2011 2:17 pm
Daniel Shawul Fri Aug 12, 2011 2:29 pm
Michel Van den Bergh Fri Aug 12, 2011 2:36 pm
Daniel Shawul Fri Aug 12, 2011 2:45 pm
H.G.Muller Wed Aug 10, 2011 11:59 am
Michel Van den Bergh Wed Aug 10, 2011 12:21 pm
H.G.Muller Wed Aug 10, 2011 1:29 pm
Michel Van den Bergh Wed Aug 10, 2011 1:41 pm
H.G.Muller Wed Aug 10, 2011 1:52 pm
Daniel Shawul Wed Aug 10, 2011 2:07 pm
H.G.Muller Wed Aug 10, 2011 3:18 pm
Daniel Shawul Wed Aug 10, 2011 3:36 pm
Peter Österlund Wed Aug 10, 2011 7:55 pm
H.G.Muller Wed Aug 10, 2011 8:39 pm
Daniel Shawul Wed Aug 10, 2011 10:54 pm
Daniel Shawul Thu Aug 11, 2011 11:28 am
Daniel Shawul Fri Aug 12, 2011 5:27 pm
Daniel Shawul Fri Aug 12, 2011 5:52 pm
Daniel Shawul Fri Aug 12, 2011 6:25 pm
Michel Van den Bergh Fri Aug 12, 2011 7:23 pm
Daniel Shawul Fri Aug 12, 2011 7:43 pm
H.G.Muller Fri Aug 12, 2011 8:22 pm
Daniel Shawul Fri Aug 12, 2011 8:55 pm
Daniel Shawul Fri Aug 12, 2011 9:45 pm
Michel Van den Bergh Fri Aug 12, 2011 11:49 pm
Michel Van den Bergh Wed Aug 10, 2011 2:08 pm
Daniel Shawul Wed Aug 10, 2011 12:28 pm
Daniel Shawul Thu Aug 11, 2011 11:37 am
Peter Österlund Tue Aug 09, 2011 6:56 pm
Daniel Shawul Tue Aug 09, 2011 8:32 pm
Daniel Shawul Tue Aug 09, 2011 8:33 pm
Daniel Shawul Tue Aug 02, 2011 12:12 am
Steven Edwards Fri Aug 05, 2011 6:08 am
Sven Schüle Fri Aug 05, 2011 10:51 pm
Peter Österlund Fri Aug 05, 2011 11:21 pm
Michel Van den Bergh Sat Aug 06, 2011 6:59 am
Steven Edwards Sat Aug 06, 2011 6:18 am
Steven Edwards Sat Aug 06, 2011 6:21 am
Steven Edwards Sat Aug 06, 2011 6:19 pm
H.G.Muller Sat Aug 06, 2011 8:03 pm
H.G.Muller Sat Aug 06, 2011 7:06 pm
Steven Edwards Sun Aug 07, 2011 1:49 pm
Steven Edwards Mon Aug 08, 2011 1:04 am
Jesús Muñoz Tue Aug 09, 2011 11:41 am
Sven Schüle Tue Aug 09, 2011 3:59 pm
Jesús Muñoz Tue Aug 09, 2011 4:25 pm
Sven Schüle Tue Aug 09, 2011 5:22 pm
Jesús Muñoz Tue Aug 09, 2011 5:49 pm
Sven Schüle Tue Aug 09, 2011 6:35 pm
Steven Edwards Tue Aug 09, 2011 6:04 pm
Peter Österlund Mon Aug 15, 2011 6:35 pm
Peter Österlund Sat Aug 13, 2011 1:31 am
Michel Van den Bergh Sat Aug 13, 2011 8:05 am
H.G.Muller Sat Aug 13, 2011 8:55 am
Daniel Shawul Sat Aug 13, 2011 1:08 pm
Michel Van den Bergh Sat Aug 13, 2011 1:44 pm
Daniel Shawul Sat Aug 13, 2011 1:54 pm
Daniel Shawul Sat Aug 13, 2011 2:06 pm
Michel Van den Bergh Sat Aug 13, 2011 2:08 pm
Michel Van den Bergh Sat Aug 13, 2011 2:12 pm
Daniel Shawul Sat Aug 13, 2011 2:13 pm
H.G.Muller Sat Aug 13, 2011 2:10 pm
Daniel Shawul Sat Aug 13, 2011 2:15 pm
Daniel Shawul Sat Aug 13, 2011 2:32 pm
Peter Österlund Sat Aug 13, 2011 2:47 pm
Daniel Shawul Sat Aug 13, 2011 2:53 pm
Daniel Shawul Sat Aug 13, 2011 3:24 pm
Michel Van den Bergh Sat Aug 13, 2011 3:33 pm
Daniel Shawul Sat Aug 13, 2011 3:45 pm
Daniel Shawul Sat Aug 13, 2011 4:41 pm
Michel Van den Bergh Sat Aug 13, 2011 4:54 pm
Daniel Shawul Sat Aug 13, 2011 5:16 pm
Michel Van den Bergh Sat Aug 13, 2011 5:27 pm
Daniel Shawul Sat Aug 13, 2011 5:58 pm
Daniel Shawul Sat Aug 13, 2011 6:17 pm
Michel Van den Bergh Sat Aug 13, 2011 6:26 pm
Daniel Shawul Sat Aug 13, 2011 6:31 pm
Daniel Shawul Sat Aug 13, 2011 6:34 pm
Michel Van den Bergh Sat Aug 13, 2011 7:16 pm
Daniel Shawul Sat Aug 13, 2011 8:32 pm
Michel Van den Bergh Sat Aug 13, 2011 8:55 pm
Daniel Shawul Sat Aug 13, 2011 9:01 pm
Michel Van den Bergh Sat Aug 13, 2011 9:26 pm
Daniel Shawul Sat Aug 13, 2011 9:51 pm
Michel Van den Bergh Sat Aug 13, 2011 10:05 pm
Daniel Shawul Sat Aug 13, 2011 10:22 pm
Michel Van den Bergh Sat Aug 13, 2011 10:42 pm
Daniel Shawul Sat Aug 13, 2011 10:57 pm
Michel Van den Bergh Sat Aug 13, 2011 11:11 pm
Daniel Shawul Sat Aug 13, 2011 11:24 pm
Michel Van den Bergh Sat Aug 13, 2011 11:16 pm
Daniel Shawul Sat Aug 13, 2011 11:30 pm
Michel Van den Bergh Sun Aug 14, 2011 7:22 am
Michel Van den Bergh Sun Aug 14, 2011 8:32 am
Daniel Shawul Sun Aug 14, 2011 10:34 am
Michel Van den Bergh Sun Aug 14, 2011 10:45 am
Daniel Shawul Sun Aug 14, 2011 10:55 am
H.G.Muller Sat Aug 13, 2011 9:07 pm
Peter Österlund Sat Aug 13, 2011 9:56 pm
Michel Van den Bergh Wed Aug 17, 2011 4:44 am
Peter Österlund Wed Aug 17, 2011 5:20 am
Michel Van den Bergh Wed Aug 17, 2011 9:22 am
Michel Van den Bergh Wed Aug 17, 2011 10:41 am
Michel Van den Bergh Wed Aug 17, 2011 11:19 am
Michel Van den Bergh Wed Aug 17, 2011 11:53 am
Michel Van den Bergh Wed Aug 17, 2011 3:18 pm
Daniel Shawul Wed Aug 17, 2011 3:43 pm
Daniel Shawul Wed Aug 17, 2011 8:56 pm
Michel Van den Bergh Thu Aug 18, 2011 9:56 am
Daniel Shawul Thu Aug 18, 2011 3:51 pm
Daniel Shawul Fri Aug 19, 2011 2:25 pm
Michel Van den Bergh Sat Aug 13, 2011 9:58 pm
Peter Österlund Sun Aug 14, 2011 10:35 am
Michel Van den Bergh Sun Aug 14, 2011 10:42 am
Daniel Shawul Sat Aug 13, 2011 12:55 pm
Peter Österlund Sat Aug 13, 2011 2:14 pm
Michel Van den Bergh Sat Aug 13, 2011 2:41 pm
Peter Österlund Sat Aug 13, 2011 3:04 pm
Peter Österlund Sat Aug 13, 2011 7:08 pm
Daniel Shawul Mon Aug 15, 2011 1:17 pm
Peter Österlund Mon Aug 15, 2011 5:29 pm
ethan ara Mon Aug 15, 2011 6:31 pm
Daniel Shawul Mon Aug 15, 2011 8:12 pm
Daniel Shawul Tue Aug 16, 2011 2:36 am
Michel Van den Bergh Tue Aug 16, 2011 5:01 am
Michel Van den Bergh Tue Aug 16, 2011 5:33 am
Michel Van den Bergh Tue Aug 16, 2011 8:27 am
Daniel Shawul Tue Aug 16, 2011 11:07 am
Michel Van den Bergh Tue Aug 16, 2011 11:17 am
Michel Van den Bergh Tue Aug 16, 2011 11:19 am
Daniel Shawul Tue Aug 16, 2011 11:31 am
Michel Van den Bergh Tue Aug 16, 2011 11:49 am
Daniel Shawul Tue Aug 16, 2011 12:50 pm
Michel Van den Bergh Tue Aug 16, 2011 2:09 pm
Daniel Shawul Tue Aug 16, 2011 3:42 pm
Michel Van den Bergh Tue Aug 16, 2011 4:02 pm
Daniel Shawul Tue Aug 16, 2011 4:15 pm
Michel Van den Bergh Tue Aug 16, 2011 4:38 pm
Michel Van den Bergh Tue Aug 16, 2011 4:55 pm
Daniel Shawul Tue Aug 16, 2011 5:02 pm
Michel Van den Bergh Tue Aug 16, 2011 5:43 pm
Daniel Shawul Tue Aug 16, 2011 6:34 pm
Michel Van den Bergh Tue Aug 16, 2011 6:38 pm
Daniel Shawul Tue Aug 16, 2011 6:56 pm
Michel Van den Bergh Tue Aug 16, 2011 9:02 pm
Daniel Shawul Sat Aug 20, 2011 2:45 pm
Daniel Shawul Tue Aug 16, 2011 4:04 pm
Michel Van den Bergh Tue Aug 16, 2011 4:14 pm
Daniel Shawul Tue Aug 16, 2011 4:22 pm
Daniel Shawul Tue Aug 16, 2011 5:21 pm
Daniel Shawul Tue Aug 16, 2011 5:40 pm
Daniel Shawul Tue Aug 16, 2011 7:32 pm
Daniel Shawul Tue Aug 16, 2011 10:53 am
Michel Van den Bergh Tue Aug 16, 2011 11:07 am
Daniel Shawul Tue Aug 16, 2011 11:10 am
Steven Edwards Mon Aug 15, 2011 5:41 am
Michel Van den Bergh Mon Aug 15, 2011 9:27 am
Sven Schüle Mon Aug 15, 2011 11:13 am
Sven Schüle Mon Aug 15, 2011 12:42 pm
Sven Schüle Mon Aug 15, 2011 2:08 pm
Michel Van den Bergh Mon Aug 15, 2011 2:31 pm
Sven Schüle Mon Aug 15, 2011 3:12 pm
Michel Van den Bergh Mon Aug 15, 2011 3:29 pm
Sven Schüle Mon Aug 15, 2011 3:51 pm
Steven Edwards Mon Aug 15, 2011 12:47 pm
Daniel Shawul Mon Aug 15, 2011 1:32 pm
Steven Edwards Mon Aug 15, 2011 2:32 pm
Peter Österlund Mon Aug 15, 2011 6:13 pm
Steven Edwards Wed Aug 17, 2011 6:11 am
Steven Edwards Wed Aug 17, 2011 4:37 pm
Steven Edwards Fri Aug 19, 2011 7:37 pm
Steven Edwards Tue Aug 23, 2011 10:04 pm

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