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  • [1205.0349] Euclid­ean dis­tance geom­e­try and applications

    “Euclid­ean dis­tance geom­e­try is the study of Euclid­ean geom­e­try based on the con­cept of dis­tance. This is use­ful in sev­eral appli­ca­tions where the input data con­sists of an incom­plete set of dis­tances, and the out­put is a set of points in Euclid­ean space that real­izes the given dis­tances. We sur­vey some of the the­ory of Euclid­ean dis­tance geom­e­try and some of the most impor­tant appli­ca­tions: mol­e­c­u­lar con­for­ma­tion, local­iza­tion of sen­sor net­works and statics.”

    algo­rithms nudge-​​targets mod­el­ing inverse-​​problems

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  • Logic gate — Wikipedia, the free encyclopedia

    For an input of 2 boolean vari­ables, there are 16 pos­si­ble boolean alge­braic func­tions. These 16 func­tions are enu­mer­ated below, together with their out­puts for each com­bi­na­tion of input variables.

    Boolean-​​logic logic-​​gates pragmatic-​​gp for-​​the-​​book Game-​​of-​​Life
  • [0812.4170] Find­ing Still Lifes with Memetic/​Exact Hybrid Algorithms

    “The max­i­mum den­sity still life prob­lem (MDSLP) is a hard con­straint opti­miza­tion prob­lem based on Conway’s game of life. It is a prime exam­ple of weighted con­strained opti­miza­tion prob­lem that has been recently tack­led in the constraint-​​programming com­mu­nity. Bucket elim­i­na­tion (BE) is a com­plete tech­nique com­monly used to solve this kind of con­straint sat­is­fac­tion prob­lem. When the mem­ory required to apply BE is too high, a heuris­tic method based on it (denom­i­nated mini-​​buckets) can be used to cal­cu­late bounds for the opti­mal solu­tion. Nev­er­the­less, the curse of dimen­sion­al­ity makes these tech­niques unprac­ti­cal for large size prob­lems. In response to this sit­u­a­tion, we present a memetic algo­rithm for the MDSLP in which BE is used as a mech­a­nism for recom­bin­ing solu­tions, pro­vid­ing the best pos­si­ble child from the parental set. Sub­se­quently, a multi-​​level model in which this exact/​metaheuristic hybrid is fur­ther hybridized with branch-​​and-​​bound tech­niques and mini-​​buckets is stud­ied. Exten­sive exper­i­men­tal results ana­lyze the per­for­mance of these mod­els and multi-​​parent recom­bi­na­tion. The result­ing algo­rithm con­sis­tently finds opti­mal pat­terns for up to date solved instances in less time than cur­rent approaches. More­over, it is shown that this pro­posal pro­vides new best known solu­tions for very large instances.”

    prag­mat­icGP game-​​of-​​life cellular-​​automata opti­miza­tion discrete-​​mathematics via:jj

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  • Attrac­tive Mod­els — Kieran Healy

    “Now, if you write a paper describ­ing neg­a­tive results—a model where noth­ing is significant—then you may have a hard time get­ting it pub­lished. In the absence of some spe­cific con­tro­versy, neg­a­tive results are bor­ing. For the same rea­son, though, if your results just barely cross the thresh­old of con­ven­tional sig­nif­i­cance, they may stand a dis­pro­por­tion­ately bet­ter chance of get­ting pub­lished than an oth­er­wise quite sim­i­lar paper where the results just failed to make the thresh­old. And this is what the graph above shows, for papers pub­lished in the Amer­i­can Polit­i­cal Sci­ence Review. It’s a his­togram of p-​​values for coef­fi­cients in regres­sions reported in the jour­nal. The dashed line is the con­ven­tional thresh­old for sig­nif­i­cance. The tall red bar to the right of the dashed line is the num­ber of coef­fi­cients that just made it over the thresh­old, while the short red bar is the num­ber of coef­fi­cients that just failed to do so. If there were no bias in the pub­li­ca­tion process, the shape of the his­togram would approx­i­mate the right-​​hand side of a bell curve. The gap between the big and the small red bars is a con­se­quence of two things: the unwill­ing­ness of jour­nals to report neg­a­tive results, and the efforts of authors to search for (and write up) results that cross the con­ven­tional threshold.”

    sta­tis­tics academic-​​culture pub­lish­ing meta-​​analysis