Items of some interest:

These are my recent Pin​board​.in links:

  • 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

Items of some interest:

These are my recent Pin​board​.in links:

Items of some interest:

These are my recent Pin​board​.in links:

Items of some interest:

These are my recent Pin​board​.in links:

  • [1203.1644] The B36/​S125 “2×2″ Life-​​Like Cel­lu­lar Automaton

    “The B36/​S125 (or “2x2”) cel­lu­lar automa­ton is one that takes place on a 2D square lat­tice much like Conway’s Game of Life. Although it exhibits high-​​level behav­iour that is sim­i­lar to Life, such as chaotic but even­tu­ally sta­ble evo­lu­tion and the exis­tence of a nat­ural diag­o­nal glider, the indi­vid­ual objects that the rule con­tains gen­er­ally look very dif­fer­ent from their Life coun­ter­parts. In this arti­cle, a his­tory of notable dis­cov­er­ies in the 2×2 rule is pro­vided, and the fun­da­men­tal pat­terns of the automa­ton are described. Some the­o­ret­i­cal results are derived along the way, includ­ing a proof that the speed lim­its for diag­o­nal and orthog­o­nal space­ships in this rule are c/​3 and c/​2, respec­tively. A Mar­go­lus block cel­lu­lar automa­ton that 2×2 emu­lates is inves­ti­gated, and in par­tic­u­lar a fam­ily of oscil­la­tors made up entirely of 2 x 2 blocks are ana­lyzed and used to show that there exist oscil­la­tors with period 2m(2k — 1) for any inte­gers m,k geq 1.”

    cellular-​​automata artificial-​​life discrete-​​mathematics emer­gence mathematical-​​recreations nudge-​​targets
  • [1203.1034] Gen­eral Com­plex Poly­no­mial Root Solver and Its Fur­ther Opti­miza­tion for Binary Microlenses

    “We present a new algo­rithm to solve poly­no­mial equa­tions, and pub­lish its code, which is 1.6−3 times faster than the ZROOTS sub­rou­tine that is com­mer­cially avail­able from Numer­i­cal Recipes, depend­ing on appli­ca­tion. The largest improve­ment, when com­pared to naive solvers, comes from a fail-​​safe pro­ce­dure that per­mits us to skip the major­ity of the cal­cu­la­tions in the great major­ity of cases, with­out risk­ing cat­a­strophic fail­ure in the few cases that these are actu­ally required. Sec­ond, we iden­tify a dis­crim­i­nant that enables a ratio­nal choice between Laguerre’s Method and Newton’s Method (or a new inter­me­di­ate method) on a case-​​by-​​case basis. We briefly review the his­tory of root solv­ing and demon­strate that “Newton’s Method” was dis­cov­ered nei­ther by New­ton (1671) nor by Raph­son (1690), but only by Simp­son (1740). Some of the argu­ments lead­ing to this con­clu­sion were first given by the British his­to­rian of sci­ence Nick Koller­strom in 1992, but these do not appear to have pen­e­trated the astro­nom­i­cal com­mu­nity. Finally, we argue that Numer­i­cal Recipes should vol­un­tar­ily sur­ren­der its copy­right pro­tec­tion for non-​​profit appli­ca­tions, despite the fact that, in this par­tic­u­lar case, such pro­tec­tion was the major stim­u­lant for devel­op­ing our improved algorithm.”

    algo­rithms numerical-​​methods optics nudge-​​targets
  • [1203.1065] Sub­space clus­ter­ing of high-​​dimensional data: a pre­dic­tive approach

    “In sev­eral appli­ca­tion domains, high-​​dimensional obser­va­tions are col­lected and then analysed in search for nat­u­rally occur­ring data clus­ters which might pro­vide fur­ther insights about the nature of the prob­lem. In this paper we describe a new approach for par­ti­tion­ing such high-​​dimensional data. Our assump­tion is that, within each clus­ter, the data can be approx­i­mated well by a lin­ear sub­space esti­mated by means of a prin­ci­pal com­po­nent analy­sis (PCA). The pro­posed algo­rithm, Pre­dic­tive Sub­space Clus­ter­ing (PSC) par­ti­tions the data into clus­ters while simul­ta­ne­ously esti­mat­ing cluster-​​wise PCA para­me­ters. The algo­rithm min­imises an objec­tive func­tion that depends upon a new mea­sure of influ­ence for PCA mod­els. A penalised ver­sion of the algo­rithm is also described for car­ry­ing our simul­ta­ne­ous sub­space clus­ter­ing and vari­able selec­tion. The con­ver­gence of PSC is dis­cussed in detail, and exten­sive sim­u­la­tion results and com­par­isons to com­pet­ing meth­ods are pre­sented. The com­par­a­tive per­for­mance of PSC has been assessed on six real gene expres­sion data sets for which PSC often pro­vides state-​​of-​​art results.”

    ain’t-performance-space sta­tis­tics clus­ter­ing cure-​​for-​​dimensionality algo­rithms
  • [1203.1067] Cor­ti­cal free asso­ci­a­tion dynam­ics: dis­tinct phases of a latch­ing network

    “… The occur­rence and dura­tion of latch­ing dynam­ics is found through sim­u­la­tions to depend crit­i­cally on the strength of local attrac­tor states, expressed in the Potts model by a para­me­ter w. Here we describe with sim­u­la­tions and then ana­lyt­i­cally the bound­aries between dis­tinct phases of no latch­ing, of tran­sient and sus­tained latch­ing, deriv­ing a phase dia­gram in the plane w-​​T, where T param­e­trizes ther­mal noise effects. Impli­ca­tions for real cor­ti­cal dynam­ics are briefly reviewed in the conclusions.”

    neural-​​networks biologically-​​inspired dynamical-​​systems emergent-​​design nudge-​​targets
  • Fright­en­ingly Ambi­tious Startup Ideas

    “One of the more sur­pris­ing things I’ve noticed while work­ing on Y Com­bi­na­tor is how fright­en­ing the most ambi­tious startup ideas are. In this essay I’m going to demon­strate this phe­nom­e­non by describ­ing some. Any one of them could make you a bil­lion­aire. That might sound like an attrac­tive prospect, and yet when I describe these ideas you may notice you find your­self shrink­ing away from them.”

    every-​​idea-​​is-​​born star­tups inno­va­tion
  • [1201.6054] Attain­abil­ity in Repeated Games with Vec­tor Payoffs

    “We intro­duce the con­cept of attain­able sets of pay­offs in two-​​player repeated games with vec­tor pay­offs. A set of pay­off vec­tors is called {em attain­able} if player 1 can ensure that there is a finite hori­zon $T$ such that after time $T$ the dis­tance between the set and the cumu­la­tive pay­off is arbi­trar­ily small, regard­less of what strat­egy player 2 is using. This paper focuses on the case where the attain­able set con­sists of one pay­off vec­tor. In this case the vec­tor is called an attain­able vec­tor. We study prop­er­ties of the set of attain­able vec­tors, and char­ac­ter­ize when a spe­cific vec­tor is attain­able and when every vec­tor is attainable.”

    game-​​theory agent-​​based multiobjective-​​optimization nudge-​​targets
  • [1203.1080] Data Struc­ture Lower Bounds on Ran­dom Access to Grammar-​​Compressed Strings

    “In this paper we inves­ti­gate the prob­lem of build­ing a sta­tic data struc­ture that rep­re­sents a string s using space close to its com­pressed size, and allows fast access to indi­vid­ual char­ac­ters of s. …”

    gram­mars algo­rithms nudge-​​targets

Items of some interest:

These are my recent Pin​board​.in links:

  • Edge Per­spec­tives with John Hagel: Finite and Infi­nite Games — Which Game Shall We Play in the New Year?

    Far bet­ter, if pos­si­ble, to avoid direct con­fronta­tion and find ways to pur­sue infi­nite game play on the mar­gins or edges of finite game insti­tu­tions or in the white spaces not yet occu­pied by finite game insti­tu­tions.  By draw­ing atten­tion to hori­zons that have not yet been explored and demon­strat­ing the abil­ity to make progress in draw­ing out more poten­tial and pos­si­bil­ity, infi­nite game play­ers have a greater chance of shift­ing the game and attract­ing other play­ers. By build­ing par­al­lel insti­tu­tions and prac­tices that pull oth­ers into their game, infi­nite game play­ers can attract enough crit­i­cal mass so that they can pur­sue their quests with lower risk of inter­ven­tion from the finite game play­ers who view such actions as deeply sub­ver­sive.  At our research cen­ter, JSB and I are now explor­ing these kinds of approaches as a way of achiev­ing orga­ni­za­tional change within large institutions.

    what-​​I-​​do
  • [1107.0056] Fixed para­me­ter algo­rithms for restricted col­or­ing problems

    In this paper, we obtain poly­no­mial time algo­rithms to deter­mine the acyclic chro­matic num­ber, the star chro­matic num­ber, the Thue chro­matic num­ber, the har­mo­nious chro­matic num­ber and the clique chro­matic num­ber of $P_4$-tidy graphs and $(q,q-4)$-graphs, for every fixed $q$. These classes include cographs, $P_4$-sparse and $P_4$-lite graphs. All these col­or­ing prob­lems are known to be NP-​​hard for gen­eral graphs. These algo­rithms are fixed para­me­ter tractable on the para­me­ter $q(G)$, which is the min­i­mum $q$ such that $G$ is a $(q,q-4)$-graph. We also prove that every con­nected $(q,q-4)$-graph with at least $q$ ver­tices is 2-​​clique-​​colorable and that every acyclic col­or­ing of a cograph is also nonrepetitive.

    algo­rithms graph-​​theory discrete-​​mathematics nudge-​​targets
  • [1112.6045] Com­par­ing inter­mit­tency and net­work mea­sure­ments of words and their depen­dency on authorship

    Many fea­tures from texts and lan­guages can now be inferred from sta­tis­ti­cal analy­ses using con­cepts from com­plex net­works and dynam­i­cal sys­tems. In this paper we quan­tify how topo­log­i­cal prop­er­ties of word co-​​occurrence net­works and inter­mit­tency (or bursti­ness) in word dis­tri­b­u­tion depend on the style of authors. Our data­base con­tains 40 books from 8 authors who lived in the 19th and 20th cen­turies, for which the fol­low­ing net­work mea­sure­ments were obtained: clus­ter­ing coef­fi­cient, aver­age short­est path lengths, and between­ness. We found that the two fac­tors with stronger depen­dency on the authors were the skew­ness in the dis­tri­b­u­tion of word inter­mit­tency and the aver­age short­est paths. Other fac­tors such as the betwee­ness and the Zipf’s law expo­nent show only weak depen­dency on author­ship. Also assessed was the con­tri­bu­tion from each mea­sure­ment to author­ship recog­ni­tion using three machine learn­ing meth­ods. The best per­for­mance was a ca. 65 % accu­racy upon com­bin­ing com­plex net­work and inter­mit­tency fea­tures with the near­est neigh­bor algo­rithm. From a detailed analy­sis of the inter­de­pen­dence of the var­i­ous met­rics it is con­cluded that the meth­ods used here are com­ple­men­tary for pro­vid­ing short– and long-​​scale per­spec­tives of texts, which are use­ful for appli­ca­tions such as iden­ti­fi­ca­tion of top­i­cal words and infor­ma­tion retrieval.

    natural-​​language-​​processing document-​​clustering clus­ter­ing feature-​​selection algo­rithms nudge-​​targets
  • [1108.1170] Con­vex Opti­miza­tion with­out Pro­jec­tion Steps

    For the gen­eral prob­lem of min­i­miz­ing a con­vex func­tion over a com­pact con­vex domain, we will inves­ti­gate a sim­ple iter­a­tive approx­i­ma­tion algo­rithm based on the method by Frank & Wolfe 1956, that does not need pro­jec­tion steps in order to stay inside the opti­miza­tion domain. Instead of a pro­jec­tion step, the lin­earized prob­lem defined by a cur­rent sub­gra­di­ent is solved, which gives a step direc­tion that will nat­u­rally stay in the domain. Our frame­work gen­er­al­izes the sparse greedy algo­rithm of Frank & Wolfe and its primal-​​dual analy­sis by Clark­son 2010 (and the low-​​rank SDP approach by Hazan 2008) to arbi­trary con­vex domains. We give a con­ver­gence proof guar­an­tee­ing {epsilon}-small dual­ity gap after O(1/{epsilon}) iter­a­tions. The method allows us to under­stand the spar­sity of approx­i­mate solu­tions for any l1-​​regularized con­vex opti­miza­tion prob­lem (and for opti­miza­tion over the sim­plex), expressed as a func­tion of the approx­i­ma­tion qual­ity. We obtain match­ing upper and lower bounds of {Theta}(1/{epsilon}) for the spar­sity for l1-​​problems. The same bounds apply to low-​​rank semi­def­i­nite opti­miza­tion with bounded trace, show­ing that rank O(1/{epsilon}) is best pos­si­ble here as well. As another appli­ca­tion, we obtain sparse matri­ces of O(1/{epsilon}) non-​​zero entries as {epsilon}-approximate solu­tions when opti­miz­ing any con­vex func­tion over a class of diag­o­nally dom­i­nant sym­met­ric matri­ces. We show that our pro­posed first-​​order method also applies to nuclear norm and max-​​norm matrix opti­miza­tion prob­lems. For nuclear norm reg­u­lar­ized opti­miza­tion, such as matrix com­ple­tion and low-​​rank recov­ery, we demon­strate the prac­ti­cal effi­ciency and scal­a­bil­ity of our algo­rithm for large matrix prob­lems, as e.g. the Net­flix dataset. For gen­eral con­vex opti­miza­tion over bounded matrix max-​​norm, our algo­rithm is the first with a con­ver­gence guar­an­tee, to the best of our knowledge.

    operations-​​research opti­miza­tion algo­rithms nudge-​​targets
  • [1112.6235] Detect­ing a Vec­tor Based on Lin­ear Measurements

    We con­sider a sit­u­a­tion where the state of a sys­tem is rep­re­sented by a real-​​valued vec­tor. Under nor­mal cir­cum­stances, the vec­tor is zero, while an event man­i­fests as non-​​zero entries in this vec­tor, pos­si­bly few. Our inter­est is in the design of algo­rithms that can reli­ably detect events (i.e., test whether the vec­tor is zero or not) with the least amount of infor­ma­tion. We place our­selves in a sit­u­a­tion, now com­mon in the sig­nal pro­cess­ing lit­er­a­ture, where infor­ma­tion about the vec­tor comes in the form of noisy lin­ear mea­sure­ments. We derive infor­ma­tion bounds in an active learn­ing setup and exhibit some sim­ple near-​​optimal algo­rithms. In par­tic­u­lar, our results show that the task of detec­tion within this set­ting is at once much eas­ier, sim­pler and dif­fer­ent than the tasks of esti­ma­tion and sup­port recovery.

    signal-​​processing sta­tis­tics algo­rithms nudge-​​targets
  • [1109.2215] Find­ing miss­ing edges and com­mu­ni­ties in incom­plete networks

    Many algo­rithms have been pro­posed for pre­dict­ing miss­ing edges in net­works, but they do not usu­ally take account of which edges are miss­ing. We focus on net­works which have miss­ing edges of the form that is likely to occur in real net­works, and com­pare algo­rithms that find these miss­ing edges. We also inves­ti­gate the effect of this kind of miss­ing data on com­mu­nity detec­tion algorithms.

    network-​​theory algo­rithms infer­ence sta­tis­tics nudge-​​targets
  • [1010.4735] Explor­ing the Energy Land­scapes of Pro­tein Fold­ing Sim­u­la­tions with Bayesian Computation

    Nested sam­pling is a Bayesian sam­pling tech­nique devel­oped to explore prob­a­bil­ity dis­tri­b­u­tions lo– calised in an expo­nen­tially small area of the para­me­ter space. The algo­rithm pro­vides both pos­te­rior sam­ples and an esti­mate of the evi­dence (mar­ginal like­li­hood) of the model. The nested sam­pling algo– rithm also pro­vides an effi­cient way to cal­cu­late free ener­gies and the expec­ta­tion value of ther­mo­dy­namic observ­ables at any tem­per­a­ture, through a sim­ple post-​​processing of the out­put. Pre­vi­ous appli­ca­tions of the algo­rithm have yielded large effi­ciency gains over other sam­pling tech­niques, includ­ing par­al­lel tem­per­ing (replica exchange). In this paper we describe a par­al­lel imple­men­ta­tion of the nested sam­pling algo­rithm and its appli­ca­tion to the prob­lem of pro­tein fold­ing in a Go-​​type force field of empir­i­cal poten­tials that were designed to sta­bi­lize sec­ondary struc­ture ele­ments in room-​​temperature sim­u­la­tions. We demon­strate the method by con­duct­ing fold­ing sim­u­la­tions on a num­ber of small pro­teins which are com­monly used for test­ing pro­tein fold­ing pro­ce­dures: pro­tein G, the SH3 domain of Src tyro­sine kinase and chy­motrypsin inhibitor 2. A topo­log­i­cal analy­sis of the pos­te­rior sam­ples is per­formed to pro­duce energy land­scape charts, which give a high level descrip­tion of the poten­tial energy sur­face for the pro­tein fold­ing sim­u­la­tions. These charts pro­vide qual­i­ta­tive insights into both the fold­ing process and the nature of the model and force field used.

    structural-​​biology bio­chem­istry mod­el­ing algo­rithms sta­tis­tics meta­mod­el­ing
  • [1109.2618] Fast and Accu­rate Mod­el­ing of Mol­e­c­u­lar Atom­iza­tion Ener­gies with Machine Learning

    We intro­duce a machine learn­ing model to pre­dict atom­iza­tion ener­gies of a diverse set of organic mol­e­cules, based on nuclear charges and atomic posi­tions only. The prob­lem of solv­ing the mol­e­c­u­lar Schr“odinger equa­tion is mapped onto a non-​​linear sta­tis­ti­cal regres­sion prob­lem of reduced com­plex­ity. Regres­sion mod­els are trained on and com­pared to atom­iza­tion ener­gies com­puted with hybrid density-​​functional the­ory. Cross-​​validation over more than seven thou­sand small organic mol­e­cules yields a mean absolute error of ~10 kcal/​mol. Applic­a­bil­ity is demon­strated for the pre­dic­tion of mol­e­c­u­lar atom­iza­tion poten­tial energy curves.

    machine-​​learning learning-​​from-​​data bio­chem­istry computational-​​science nudge-​​targets
  • [1101.2135] Bounded con­fi­dence model: addressed infor­ma­tion main­tain diver­sity of opinions

    A com­mu­nity of agents is sub­ject to a stream of mes­sages, which are rep­re­sented as points on a plane of issues. Mes­sages are sent by media and by agents them­selves. Mes­sages from media shape the pub­lic opin­ion. They are unbi­ased, i.e. pos­i­tive and neg­a­tive opin­ions on a given issue appear with equal fre­quen­cies. In our pre­vi­ous work, the only cri­te­rion to receive a mes­sage by an agent is if the dis­tance between this mes­sage and the ones received ear­lier does not exceed the given value of the tol­er­ance para­me­ter. Here we intro­duce a pos­si­bil­ity to address a mes­sage to a given neigh­bour. We show that this option reduces the una­nim­ity effect, what improves the col­lec­tive performance.

    agent-​​based com­mu­ni­ca­tion network-​​theory machine-​​learning diver­sity