digital camera cross correlation similar images co alignment x ray crystallography reconstruct crystal structure diffraction pattern fourier transform ion cyclotron resonance mass spectrometry determine mass ions frequency cyclotron motion magnetic field many forms spectroscopy including infrared nuclear magnetic resonance spectroscopies generation sound spectrograms used analyze sounds passive sonar used classify targets based machinery noise variants fourier analysis ''s'' ''f'' make popular analysis tool continuous fourier transform often unqualified term '''fourier transform''' refers transform


functions continuous real argument produces continuous function frequency known ''frequency distribution'' one function transformed another operation reversible domain input initial function time domain output final function ordinary frequency transform function frequency given complex number math f int infty infty cdot e pi f dt math evaluating quantity values produces ''frequency domain'' function represented recombination complex exponentials

Formal science
Mathematics
Pure mathematics
Analysis
Fourier analysis


possible frequencies math int infty infty f cdot e pi f df math inverse transform formula complex number conveys amplitude phase frequency see fourier transform much information including conventions amplitude normalization frequency scaling units transform properties tabulated transforms specific functions extension generalization functions multiple dimensions images fourier series fourier transform periodic function period becomes dirac comb function modulated sequence complex coefficients math k frac p int p p cdot e pi frac k p dt quad k z math nbsp


nbsp integral interval length ''p'' inverse transform known '''fourier series''' representation terms summation potentially infinite number harmonically related sinusoids complex exponential functions amplitude phase specified one coefficients math p mathcal f left sum k infty infty k delta left f frac k p right right sum k infty infty k cdot e pi frac k p math expressed periodic summation another function math p triangleq sum infty infty mp math coefficients proportional samples discrete intervals


math k frac p cdot left frac k p right math efn ua math int p left sum infty infty mp right cdot e pi frac k p dt underbrace int infty infty cdot e pi frac k p dt triangleq left frac k p right math note whose transform discrete sample values used periodic summation sufficient condition recovering therefore samples ie fourier series non zero portion confined known interval duration frequency domain dual nyquist shannon sampling theorem see fourier series information including historical development discrete time fourier transform


cdot delta nt cdot sum n infty infty delta nt end align math consequently common practice model sampling multiplication dirac comb function course possible purely mathematical sense br br fourier series coefficients inverse transform defined math n triangleq int frac frac f cdot e pi f nt df underbrace int infty infty f cdot e pi f nt df triangleq nt math parameter corresponds sampling interval fourier series recognized form poisson summation formula nbsp thus important result discrete data


sequence proportional samples underlying continuous function one observe periodic summation continuous fourier transform note discrete sample values produces dtft nbsp certain idealized conditions one theoretically recover exactly sufficient condition perfect recovery non zero portion confined known frequency interval width nbsp interval applicable reconstruction formula whittaker shannon interpolation formula cornerstone foundation digital signal


processing another reason interested ''f'' often provides insight amount aliasing caused sampling process applications dtft limited sampled functions see discrete time fourier transform information topics including normalized frequency units windowing finite length sequences transform properties tabulated transforms specific functions discrete fourier transform dft similar fourier series dtft periodic sequence ''n'' period becomes dirac comb function modulated sequence complex coefficients see math k sum n n n cdot e pi frac k n n


quad k z math nbsp nbsp sum sequence length sequence customarily known '''dft''' one cycle also periodic never necessary compute coefficients inverse transform also known discrete fourier series given math n n frac n sum k k cdot e pi frac n n k math nbsp sum sequence length ''n'' expressed periodic summation another function math n n triangleq sum infty infty n mn math nbsp nbsp math n triangleq nt math


equal length non zero portion increasing known ''zero padding'' ''interpolation'' results closely spaced samples one cycle ''f'' decreasing causes overlap adding time domain analogous aliasing corresponds decimation frequency domain see cases practical interest sequence represents longer sequence truncated application finite length window function fir filter array dft computed using fast fourier transform fft algorithm makes practical important transformation computers see discrete


fourier transform much information including transform properties applications tabulated transforms specific functions summary periodic functions fourier transform dtft comprise discrete set frequency components fourier series transforms diverge frequencies one common practice discussed handle divergence via dirac delta dirac comb functions spectral information discerned one cycle periodic function since cycles identical similarly finite duration functions represented fourier series actual loss information


except periodicity inverse transform mere artifact common practice duration ' 's'' limited period nbsp formulas require condition class wikitable style text align left transforms continuous time continuous frequency discrete frequencies transform math f triangleq int infty infty cdot e pi f dt math math overbrace frac p cdot left frac k p right k triangleq frac p int infty infty cdot e pi frac k p dt equiv frac p int p p cdot e pi frac k p dt math inverse math int infty infty f cdot e pi f


df math math underbrace p sum k infty infty k cdot e pi frac k p text poisson summation formula fourier series math class wikitable style text align left transforms discrete time continuous frequency discrete frequencies transform math underbrace frac frac f triangleq sum n infty infty nt cdot e pi f nt text poisson summation formula dtft math math begin align overbrace frac frac left frac k nt right k triangleq sum n infty infty nt cdot e pi frac kn n equiv underbrace sum n p nt cdot e pi frac kn n text dft end align math inverse math nt int frac frac frac f cdot e pi f nt df math math sum n infty infty nt cdot delta nt underbrace int infty infty frac frac f cdot e pi f df text inverse fourier transform math math begin align p nt overbrace frac n sum k k cdot e pi frac kn n text inverse dft tfrac p


sum k frac left frac k p right cdot e pi frac kn n end align math symmetry properties real imaginary parts complex function decomposed even odd parts four components denoted subscripts ro ie io one one mapping four components complex time function four components complex frequency transform ref name proakis math begin array rccccccccc text time domain text text ro text ie underbrace text io bigg updownarrow mathcal f bigg updownarrow mathcal f bigg updownarrow mathcal f


bigg updownarrow mathcal f bigg updownarrow mathcal f text frequency domain text overbrace text io text ie text ro end array math various relationships apparent example transform real valued function ' 's'' even symmetric function ''i'' ''s'' conversely even symmetric transform implies real valued time domain transform imaginary valued function ''i'' ' 's'' odd symmetric function ''i'' ''s'' converse true transform even symmetric function ''i'' ' 's''


compute orbit ref name terras described first formula dft ref name thedft joseph louis lagrange computing coefficients trigonometric series vibrating string ref name thedft technically clairaut 's work cosine series form discrete cosine transform lagrange 's work sine series form discrete sine transform true cosine sine dft used gauss trigonometric interpolation asteroid orbits ref name heideman euler lagrange discretized vibrating string problem using would today called samples ref name thedft early modern development


toward fourier analysis paper ''r flexions sur la r solution alg brique des quations'' lagrange method lagrange resolvents used complex fourier decomposition study solution cubic ref name knapp lagrange transformed roots resolvents math begin align r x x x r x zeta x zeta x r x zeta x zeta x end align math cubic root unity dft order number authors notably jean le rond d'alembert carl friedrich gauss used


trigonometric series study heat equation ref name narasimhan breakthrough development paper ''m moire sur la propagation de la chaleur dans les corps solides'' joseph fourier whose crucial insight model ''all'' functions trigonometric series introducing fourier series historians divided much credit lagrange others development fourier theory daniel bernoulli leonhard euler introduced trigonometric representations functions lagrange given fourier series solution wave equation fourier 's contribution mainly bold claim arbitrary function could


represented fourier series ref name thedft subsequent development field known harmonic analysis also early instance representation theory first fast fourier transform fft algorithm dft discovered around carl friedrich gauss interpolating measurements orbit asteroids juno pallas although particular fft algorithm often attributed modern rediscoverers cooley tukey ref name heideman ref name terras time frequency transforms signal processing terms function time representation signal perfect ''time resolution'' frequency information


fourier transforms arbitrary locally compact abelian topological groups fourier variants also generalized fourier transforms arbitrary locally compact abelian topological groups studied harmonic analysis fourier transform takes functions group functions dual group treatment also allows general formulation convolution theorem relates fourier transforms convolutions see also pontryagin duality generalized underpinnings fourier transform specific fourier analysis done cosets ref name forrest even discrete cosets see also generalized fourier series fourier bessel series fourier related transforms laplace


transform lt two sided laplace transform mellin transform non uniform discrete fourier transform ndft quantum fourier transform qft number theoretic transform least squares spectral analysis basis vectors bispectrum characteristic function probability theory orthogonal functions schwartz space spectral density spectral density estimation spectral music wavelet notes references ref ref name rabiner ref ref name proakis ref ref name forrest forrest brian fourier analysis coset spaces rocky mountain journal mathematics rmjm ref ref name prestini ref ref name rota ref ref name neugebauer ref ref name brack ref ref name terras ref ref name thedft ref ref name heideman ref ref name knapp ref ref name narasimhan ref ref name rudin ref ref name evans ref ref


name conte ref ref name knuth ref reading external links http eqworldipmnetru en auxiliary aux inttranshtm tables integral transforms eqworld world mathematical equations https webarchiveorg web http cns alumnibuedu slehar fourier fourierhtml intuitive explanation fourier theory steven lehar https archiveorg details lectures image processing lectures image processing collection lectures pdf format vanderbilt university lecture fourier transform lectures make use alan peters integral transforms digital signal processing mathematical physics mathematics computing time series joseph fourier acoustics


making humans animals computers modern game theory began idea mixed strategy equilibria two person zero sum game proof john von neumann von neumann 's original proof used brouwer fixed point theorem continuous mappings compact convex sets became standard method game theory mathematical economics paper followed book ''theory games economic behavior'' co written oskar morgenstern considered cooperative games several players second edition book provided axiomatic theory expected utility allowed mathematical statisticians economists treat

Applied science
Military sciences
Game theory


decision making uncertainty game theory developed extensively many scholars explicitly applied evolution although similar developments go back least far game theory widely recognized important tool many fields nobel memorial prize economic sciences going game theorist jean tirole eleven game theorists economics nobel prize john maynard smith awarded crafoord prize application evolutionary game theory history precursors discussions mathematics games began long rise


modern mathematical game theory cardano 's work games chance ''liber de ludo aleae'' ''book games chance'' written around published posthumously formulated field 's basic ideas pascal huygens developed concept expectation reasoning structure games chance huygens published gambling calculus ''de ratiociniis ludo ale '' ''on reasoning games chance'' letter attributed charles waldegrave analyzed game called le active jacobite uncle


james waldegrave british diplomat ref name gt pd ref letter waldegrave provided minimax mixed strategy solution two person version card game le problem known waldegrave problem ''recherches sur les principes math matiques de la th orie des richesses'' ''researches mathematical principles theory wealth'' antoine augustin cournot considered duopoly presented solution nash equilibrium game ernst zermelo published '' ber eine anwendung der mengenlehre auf die theorie des schachspiels'' ''on application set theory theory


two person zero sum games conjecture proved false von neumann birth early developments john von neumann game theory really exist unique field john von neumann published paper ''on theory games strategy'' von neumann 's original proof used brouwer 's fixed point theorem continuous mappings compact convex sets became standard method game theory mathematical economics paper followed book ''theory games economic behavior'' co authored oskar morgenstern second edition book provided axiomatic theory


utility reincarnated daniel bernoulli 's old theory utility money independent discipline von neumann 's work game theory culminated book foundational work contains method finding mutually consistent solutions two person zero sum games subsequent work focused primarily cooperative game theory analyzes optimal strategies groups individuals presuming enforce agreements proper strategies john nash first mathematical discussion prisoner 's dilemma appeared experiment undertaken notable mathematicians merrill flood melvin dresher part


rand corporation 's investigations game theory rand pursued studies possible applications global nuclear strategy ref name stanfordprisoner ref around time john nash developed criterion mutual consistency players' strategies known nash equilibrium applicable wider variety games criterion proposed von neumann morgenstern nash proved every finite n player non zero sum two player zero sum non cooperative game known nash equilibrium mixed strategies game theory experienced flurry activity concepts core extensive form


notion proper equilibrium important graduate text ''game theory analysis conflict'' ref name myerson hurwicz introduced formalized concept incentive compatibility alvin e roth lloyd shapley awarded nobel prize economics theory stable allocations practice market design nobel went game theorist jean tirole game types cooperative non cooperative game ''cooperative'' players able form binding commitments externally enforced eg contract law game ''non cooperative'' players cannot form alliances


agreements need self enforcing eg credible threats cooperative games often analyzed framework ''cooperative game theory'' focuses predicting coalitions form joint actions groups take resulting collective payoffs opposed traditional ''non cooperative game theory'' focuses predicting individual players' actions payoffs analyzing nash equilibria focus individual payoff result phenomenon known tragedy commons resources used collectively inefficient level lack formal negotiation leads deterioration public goods


use provision stems private incentives cooperative game theory provides high level approach describes structure strategies payoffs coalitions whereas non cooperative game theory also looks bargaining procedures affect distribution payoffs within coalition non cooperative game theory general cooperative games analyzed approach non cooperative game theory converse hold provided sufficient assumptions made encompass possible strategies available players due possibility external enforcement cooperation using single theory may


desirable many instances insufficient information available accurately model formal procedures available strategic bargaining process resulting model would complex offer practical tool real world cases cooperative game theory provides simplified approach allows analysis game large without make assumption bargaining powers symmetric asymmetric symmetric game game payoffs playing particular strategy depend strategies employed playing identities


player possible however game identical strategies players yet asymmetric example game pictured section 's graphic asymmetric despite identical strategy sets players zero sum non zero sum zero sum games special case constant sum games choices players neither increase decrease available resources zero sum games total benefit goes players game every combination strategies always adds zero informally player benefits equal expense others poker exemplifies


zero sum game ignoring possibility house 's cut one wins exactly amount one 's opponents lose zero sum games include matching pennies classical board games including go chess many games studied game theorists including famed prisoner 's dilemma non zero sum games outcome net results greater less zero informally non zero sum games gain one player necessarily correspond loss another constant sum games correspond activities like theft gambling fundamental economic situation potential gains


trade possible transform game possibly asymmetric zero sum game adding dummy player often called board whose losses compensate players' net winnings simultaneous sequential simultaneous games games players move simultaneously instead later players unaware earlier players' actions making ''effectively'' simultaneous sequential games dynamic games games later players knowledge earlier actions need perfect information every action earlier players might little knowledge instance player may know


earlier player perform one particular action know available actions first player actually performed difference simultaneous sequential games captured different representations discussed often normal form used represent simultaneous games extensive form used represent sequential ones transformation extensive normal form one way meaning multiple extensive form games correspond normal form consequently notions equilibrium simultaneous games insufficient reasoning sequential games see subgame perfection short differences


aims find profit maximising quantity based believe firm produce behave like monopolies game firms want produce monopoly quantity high incentive deviate produce decreases market clearing price ref name ref example firms may tempted deviate monopoly quantity low monopoly quantity high price aim increasing production maximise profit ref name however option provide highest payoff firm 's ability maximise profits depends


competitors' costs therefore firms incentive deviate equilibrium homogenous product lower price gain market share known cost advantage perfect information imperfect information information set important subset sequential games consists games perfect information game one perfect information players every move game know moves previously made players reality applied firms consumers information price quality available goods


market imperfect information game played players know moves already made opponent simultaneous move game ref name games studied game theory imperfect information games examples perfect information games include tic tac toe checkers infinite chess go many card games games imperfect information poker bridge perfect information often confused complete information similar concept complete information requires every player know strategies payoffs available players necessarily actions taken whereas perfect


information knowledge aspects game players games incomplete information reduced however games imperfect information introducing moves nature bayesian game one assumptions behind concept nash equilibrium every player right beliefs actions players game theory many situations participants fully understand characteristics opponents negotiators may unaware opponent 's valuation object negotiation companies may unaware opponent 's cost functions combatants may unaware


must state every set features player believes may exist example bayesian game example player unsure whether player would rather date get away player understands player 's preferences specific supposing player believes player wants date probability get away probability evaluation comes player 's experience probably faces players want date half time


case players want avoid half time due probability involved analysis situation requires understand player 's preference draw even though people interested pure strategic equilibrium games difficulty finding optimal strategy stems multiplicity possible moves called combinatorial games examples include chess go games involve imperfect information may also strong combinatorial character instance backgammon unified theory addressing combinatorial elements games however


mathematical tools solve particular problems answer general questions ref name bewersdorff games perfect information studied combinatorial game theory developed novel representations eg surreal numbers well combinatorial algebraic sometimes non constructive proof methods solve games certain types including loopy games may result infinitely long sequences moves methods address games higher combinatorial complexity usually considered traditional economic game theory typical game solved way hex related field study drawing computational complexity theory


game complexity concerned estimating computational difficulty finding optimal strategies research artificial intelligence addressed perfect imperfect information games complex combinatorial structures like chess go backgammon provable optimal strategies found practical solutions involve computational heuristics like alpha beta pruning use artificial neural networks trained reinforcement learning make games tractable computing practice ref name bewersdorff ref ref name jones ref infinitely long games games studied economists real world game players generally finished finitely many moves pure mathematicians


descriptive set theory discrete continuous games much game theory concerned finite discrete games finite number players moves events outcomes etc many concepts extended however continuous games allow players choose strategy continuous strategy set instance cournot competition typically modeled players' strategies non negative quantities including fractional quantities differential games differential games continuous pursuit evasion game continuous games evolution players' state variables governed differential equations problem finding optimal strategy


differential game closely related optimal control theory particular two types strategies open loop strategies found using pontryagin maximum principle closed loop strategies found using bellman 's dynamic programming method particular case differential games games random time horizon ref name pm ref games terminal time random variable given probability distribution function therefore players maximize mathematical expectation cost function shown modified optimization problem reformulated discounted differential game


infinite time interval evolutionary game theory evolutionary game theory studies players adjust strategies time according rules necessarily rational farsighted ref name newton renaissance ref general evolution strategies time according rules modeled markov chain state variable current strategy profile game played recent past rules may feature imitation optimization survival fittest biology models represent evolution offspring adopt parents' strategies parents play successful strategies


may different motivators mathematics involved substantially eg using markov decision processes mdp stochastic outcomes also modeled terms game theory adding randomly acting player makes chance moves moves nature player typically considered third player otherwise two player game merely serves provide roll dice required game problems different approaches modeling stochastic outcomes may lead different solutions example difference approach mdps minimax solution


elements stochastic outcomes adversaries partial noisy observability moves players also studied gold standard considered partially observable stochastic game posg realistic problems computationally feasible posg representation ref name mcmahan metagames games play development rules another game target subject game metagames seek maximize utility value rule set developed theory metagames related mechanism design theory term metagame analysis also used refer practical approach


developed nigel howard whereby situation framed strategic game stakeholders try realize objectives means options available subsequent developments led formulation confrontation analysis pooling games games prevailing forms society pooling games repeated plays changing payoff table general experienced path equilibrium strategies usually take form evolutionary social convention economic convention pooling game theory emerges formally recognize interaction optimal choice one play emergence forthcoming


payoff table update path identify invariance existence robustness predict variance time theory based upon topological transformation classification payoff table update time predict variance invariance also within jurisdiction computational law reachable optimality ordered system mean field game theory mean field game theory study strategic decision making large populations small interacting agents class problems considered economics literature boyan jovanovic robert w rosenthal engineering literature peter e caines


employed player profit unilaterally deviating strategy equilibrium strategies determine equilibrium game stable state either one outcome occurs set outcomes occur known probability cooperative games presented characteristic function form extensive normal forms used define noncooperative games extensive form extensive form game extensive form used formalize games time sequencing moves games played trees pictured vertex node represents point choice


ie players know point closed line drawn around see example imperfect information section normal form r u ul ur dl dr normal strategic form game usually represented matrix shows players strategies payoffs see example right generally represented function associates payoff player every possible combination


unity 'empty' speak receive reward origin form found john von neumann oskar morgenstern 's book looking instances guessed union math mathbf c math appears works fraction math left frac mathbf n mathbf c right math two individuals playing normal game balanced payoff c basic function although differing examples help determine coalitional amounts normal games appear function form derived formally


characteristic function seen nv n represents group people math v n mathbf r math normal utility characteristic functions expanded describe games removable utility alternative game representations alternative game representation forms exist used subclasses games adjusted needs interdisciplinary research addition classical game representations alternative representations also encode time related aspects class wikitable sortable name year means type games time congestion game functions subset n person games simultaneous moves


sequential form matrices person games imperfect information timed games functions person games yes gala logic n person games imperfect information local effect games functions subset n person games simultaneous moves gdl logic deterministic n person games simultaneous moves game petri nets petri net deterministic n person games simultaneous moves continuous games functions subset person games imperfect information yes pnsi petri net n person games imperfect information yes action graph games graphs functions n person games simultaneous moves


graphical games graphs functions n person games simultaneous moves general applied uses method applied mathematics game theory used study wide variety human animal behaviors initially developed economics understand large collection economic behaviors including behaviors firms markets consumers first use game theoretic analysis antoine augustin cournot solution cournot duopoly use game theory social sciences expanded game theory applied political sociological psychological behaviors


prescribe behavior ref name camerer ref economics philosophy scholars applied game theory help understanding good proper behavior game theoretic arguments type found far back plato alternative version game theory called chemical game theory represents player 's choices metaphorical chemical reactant molecules called knowlecules nbsp chemical game theory calculates outcomes equilibrium solutions system chemical reactions description modeling four stage centipede game primary use game theory describe model human populations behave scholars believe


models used physicists however empirical work shown classic games centipede game guess average game dictator game people regularly play nash equilibria ongoing debate regarding importance experiments whether analysis experiments fully captures aspects relevant situation ref game theorists following work john maynard smith george r price turned evolutionary game theory order resolve issues models presume either rationality bounded rationality


part players despite name evolutionary game theory necessarily presume natural selection biological sense evolutionary game theory includes biological well cultural evolution also models individual learning example fictitious play dynamics prescriptive normative analysis scholars see game theory predictive tool behavior human beings suggestion people ought behave since strategy corresponding nash equilibrium game constitutes one 's best response actions players provided


general equilibrium mechanism design voting systems across broad areas experimental economics behavioral economics information economics ref name r ref ref name r b ref ref name r c ref ref name r ref industrial organization political economy research usually focuses particular sets strategies known solution concepts equilibria common assumption players act rationally non cooperative games famous nash equilibrium set strategies nash equilibrium represents best response strategies players playing strategies nash equilibrium unilateral incentive deviate


promotes knowledge use game theory within context business procurement cips tws partners conducted series surveys designed explore understanding awareness application game theory among procurement professionals main findings third annual survey include application game theory procurement activity increased time across survey respondents participants predict use game theory applications grow respondents say basic basic understanding game theory


participants undertaken job training game theory respondents said new improved software solutions desirable respondents said software need work project management sensible decision making critical success projects project management game theory used model decision making process players investors project managers contractors sub contractors governments customers quite often players competing interests sometimes interests directly detrimental players making project management scenarios well suited modeled


game theory piraveenan ref name piraveenan px material copied source available https creativecommonsorg licenses creative commons attribution international license ref review provides several examples game theory used model project management scenarios instance investor typically several investment options option likely result different project thus one investment options chosen project charter produced similarly large project involving subcontractors instance construction project complex interplay main contractor project


decisions depend decisions players way competing interests interests decision maker thus ideally modeled using game theory piraveenan ref name piraveenan summarises two player games predominantly used model project management scenarios based identity players five distinct types games used project management government sector private sector games games model public private partnerships contractor contractor games contractor subcontractor games subcontractor subcontractor games games involving players terms types games cooperative well non cooperative normal form well extensive form zero sum


well non zero sum used model various project management scenarios political science application game theory political science focused overlapping areas fair division political economy public choice war bargaining positive political theory social choice theory areas researchers developed game theoretic models players often voters states special interest groups politicians early examples game theory applied political science provided anthony downs book ''an economic theory democracy'' applies hotelling firm location model


political process downsian model political candidates commit ideologies one dimensional policy space downs first shows political candidates converge ideology preferred median voter voters fully informed argues voters choose remain rationally ignorant allows candidate divergence game theory applied cuban missile crisis presidency john f kennedy also proposed game theory explains stability form political government taking simplest case monarchy example king


periods stability citizen find rational move replace sovereign even citizens know would better act collectively game theoretic explanation democratic peace public open debate democracies sends clear reliable information regarding intentions states contrast difficult know intentions nondemocratic leaders effect concessions promises kept thus mistrust unwillingness make concessions least one parties


warfare finally war may result issue indivisibilities game theory could also help predict nation 's responses new rule law applied nation one example peter john wood 's research looking nations could help reduce climate change wood thought could accomplished making treaties nations reduce greenhouse gas emissions however concluded idea could work would create prisoner 's dilemma nations biology unlike economics payoffs games biology often


interpreted corresponding fitness addition focus less equilibria correspond notion rationality ones would maintained evolutionary forces best known equilibrium biology known ''evolutionarily stable strategy'' ess first introduced although initial motivation involve mental requirements nash equilibrium every ess nash equilibrium biology game theory used model understand many different phenomena first used explain evolution stability approximate


exhibit feed forward behavior akin fashion see paul ormerod 's ''butterfly economics'' biologists used game chicken analyze fighting behavior territoriality according maynard smith preface ''evolution theory games'' paradoxically turned game theory readily applied biology field economic behaviour originally designed evolutionary game theory used explain many seemingly incongruous phenomena nature ref name stan egt ref one phenomenon known biological altruism situation organism appears act


chance survival ref name qudzyh ref actions increase overall fitness group occur cost individual evolutionary game theory explains altruism idea kin selection altruists discriminate individuals help favor relatives hamilton 's rule explains evolutionary rationale behind selection equation cost altruist must less benefit recipient multiplied coefficient relatedness closely related two organisms causes incidences altruism increase share many


alleles means altruistic individual ensuring alleles close relative passed survival offspring forgo option offspring number alleles passed example helping sibling diploid animals coefficient average individual shares half alleles sibling 's offspring ensuring enough sibling 's offspring survive adulthood precludes necessity altruistic individual producing offspring ref name qudzyh coefficient values depend heavily scope


playing field example choice favor includes genetic living things relatives assume discrepancy humans accounts approximately diversity playing field coefficient smaller field becomes similarly considered information genetic nature eg epigenetics religion science etc persisted time playing field becomes larger still discrepancies smaller computer science logic game theory come play increasingly important role logic


computer science several logical theories basis game semantics addition computer scientists used games model interactive computations also game theory provides theoretical basis field multi agent systems ref name shohamleyton brown ref separately game theory played role online algorithms particular k server problem past referred ''games moving costs'' ' 'request answer games'' yao 's principle game theoretic technique proving lower bounds computational complexity randomized algorithms especially online algorithms emergence internet motivated development algorithms


finding equilibria games markets computational auctions peer peer systems security information markets algorithmic game theory ref name algorithmic game ref within algorithmic mechanism design combine computational algorithm design analysis complex systems economic theory philosophy game theory put several uses philosophy responding two papers used game theory develop philosophical account convention provided first analysis common knowledge employed analyzing play coordination games addition first suggested one understand meaning terms signaling games


later suggestion pursued several philosophers since lewis following game theoretic account conventions edna ullmann margalit bicchieri developed theories social norms define nash equilibria result transforming mixed motive game coordination game game theory also challenged philosophers think terms interactive epistemology means collective common beliefs knowledge consequences knowledge social outcomes resulting interactions agents philosophers worked area include bicchieri


corresponding animal behaviors authors look several games including prisoner 's dilemma stag hunt nash bargaining game providing explanation emergence attitudes morality see eg retail consumer product pricing game theory applications used heavily pricing strategies retail consumer markets particularly sale inelastic goods retailers constantly competing one another consumer market share become fairly common practice retailers discount certain goods intermittently hopes increasing foot traffic brick


mortar locations websites visits e commerce retailers increasing sales ancillary complimentary products black friday popular shopping holiday us many retailers focus optimal pricing strategies capture holiday shopping market black friday scenario retailers using game theory applications typically ask dominant competitor 's reaction ref name ref scenario game two players retailer consumer retailer focused optimal pricing strategy consumer focused best deal closed system often


dominant strategy players alternative options retailers find different customer consumers shop different retailer ref name given market competition day however dominant strategy retailers lies outperforming competitors open system assumes multiple retailers selling similar goods finite number consumers demanding goods optimal price blog cornell university professor provided example strategy amazon priced samsung tv retail value effectively undercutting competitors amazon made part difference increasing


price hdmi cables found consumers less price discriminatory comes sale secondary items ref name retail markets continue evolve strategies applications game theory comes pricing consumer goods key insights found simulations controlled environment real world retail experiences show applications strategies complex retailer find optimal balance pricing supplier relations brand image potential cannibalize sale profitable items ref name skk marine sfk


seccon language en us access date ref epidemiology since decision take vaccine particular disease often made individuals may consider range factors parameters making decision incidence prevalence disease perceived real risks associated contracting disease mortality rate perceived real risks associated vaccination financial cost vaccination game theory used model predict vaccination uptake society popular culture based book sylvia nasar life story game theorist mathematician john nash


turned biopic ''a beautiful mind'' starring russell crowe nash military science fiction novel ''starship troopers'' robert heinlein mentioned games theory theory games film name character carl jenkins referred military intelligence assignment assigned games theory film ''dr strangelove'' satirizes game theoretic ideas deterrence theory example nuclear deterrence depends threat retaliate catastrophically nuclear attack detected game theorist might argue threats fail ''credible''


sense lead subgame imperfect equilibria movie takes idea one step soviet union irrevocably committing catastrophic nuclear response without making threat public power pop band game theory founded singer songwriter scott miller described band 's name alluding study calculating appropriate action given adversary give minimum amount failure ref name intpacsun ref ''liar game'' japanese manga television series presents main characters episode game problem typically


theory intra household bargaining kingmaker scenario law economics outline artificial intelligence parrondo 's paradox precautionary principle quantum refereed game risk management self confirming equilibrium tragedy commons wilson doctrine economics '''lists''' list cognitive biases list emerging technologies list games game theory notes references reading textbooks general references http pressprincetonedu titles html description suitable undergraduate business students https b okorg book e suitable upper level undergraduates suitable advanced undergraduates published europe presents game theory formal way suitable graduate level joseph e harrington ''games strategies decision


making'' worth textbook suitable undergraduates applied fields numerous examples fewer formalisms concept presentation maschler michael solan eilon zamir shmuel ''game theory'' cambridge university press undergraduate textbook suitable general audience undergraduate textbook modern introduction graduate level leading textbook advanced undergraduate level consistent treatment game types usually claimed different applied fields eg markov decision processes historically important texts reprinted edition shapley ls value n person games contributions theory games volume ii h w kuhn


kaminski http webfilesuciedu mkaminsk www courseshtml game theory politics syllabuses lecture notes game theory political science http wwwsocialcapitalgatewayorg eng gametheoryhtm websites game theory social interactions kesten green 's see http wwwforecastingprinciplescom paperpdf greenforecastinginconflictpdf papers http wwwdecisionworkshopscom graphs findings evidence accuracy forecasts game theory methods mckelvey richard mclennan andrew turocy theodore l '' http gambitsourceforgenet gambit software tools game theory '' benjamin polak http oycyaleedu economics game theory open course game theory yale https webarchiveorg web http wwwyoutubecom view play listp ef e e b videos course benjamin moritz bernhard k nsgen danny bures ronni wiersch '' https webarchiveorg web http wwwspieltheorie softwarede spieltheorie softwarede application game theory implemented java '' antonin


kucera http slideslivecom stochastic twoplayer games stochastic two player games yu chi ho http blogsciencenetcn homephpmod space uid blog id mathematical game theory http blogsciencenetcn homephpmod space uid blog id mathematical game theory http blogsciencenetcn homephpmod space uid blog id mathematical game theory http blogsciencenetcn homephpmod space uid blog id mathematical game theory many person game theory http blogsciencenetcn homephpmod space uid blog id mathematical game theory finale summing view artificial intelligence formal sciences mathematical economics john von neumann


structure commonly observed properties galaxies hubble tuning fork diagram galaxy morphologybecause inability conduct experiments outer space way test theories models galaxy evolution compare observations explanations galaxies formed evolved must able predict observed properties types galaxies edwin hubble created first galaxy classification scheme known hubble tuning fork diagram partitioned galaxies ellipticals normal spirals barred spirals milky way irregulars galaxy types exhibit following properties explained

Natural science
Space science
Numerical simulations
Galaxy formation and evolution


current galaxy evolution theories many properties galaxies including galaxy color magnitude diagram indicate fundamentally two types galaxies groups divide blue star forming galaxies like spiral types red non star forming galaxies like elliptical galaxies spiral galaxies quite thin dense rotate relatively fast stars elliptical galaxies randomly oriented orbits majority giant galaxies contain supermassive black hole centers ranging mass millions billions times mass sun black hole mass


tied host galaxy bulge spheroid mass metallicity positive correlation absolute magnitude luminosity galaxy common misconception hubble believed incorrectly tuning fork diagram described evolutionary sequence galaxies elliptical galaxies lenticulars spiral galaxies case instead tuning fork diagram shows evolution simple complex temporal connotations intended astronomers believe disk galaxies likely formed first evolved elliptical galaxies galaxy mergers current models also predict majority mass galaxies


made dark matter substance directly observable might interact means except gravity observation arises galaxies could formed rotate seen unless contain far mass directly observed formation disk galaxies earliest stage evolution galaxies formation galaxy forms disk shape called spiral galaxy due spiral like arm structures located disk different theories disk like distributions


stars develop cloud matter however present none exactly predicts results observation top theories olin eggen donald lynden bell allan sandage proposed theory disk galaxies form monolithic collapse large gas cloud distribution matter early universe clumps consisted mostly dark matter clumps interacted gravitationally putting tidal torques acted give angular momentum baryonic matter cooled dissipated energy contracted toward center


angular momentum conserved matter near center speeds rotation like spinning ball pizza dough matter forms tight disk disk cools gas gravitationally stable cannot remain singular homogeneous cloud breaks smaller clouds gas form stars since dark matter dissipate interacts gravitationally remains distributed outside disk known dark halo observations show stars located outside disk quite fit pizza dough


model first proposed leonard searle robert zinn galaxies form coalescence smaller progenitors known top formation scenario theory quite simple yet longer widely accepted bottom theories recent theories include clustering dark matter halos bottom process instead large gas clouds collapsing form galaxy gas breaks smaller clouds proposed matter started smaller clumps mass order globular clusters many clumps merged


form galaxies drawn gravitation form galaxy clusters still results disk like distributions baryonic matter dark matter forming halo reasons top theory models using sort process predict small galaxies large ones matches observations astronomers currently know process stops contraction fact theories disk galaxy formation successful producing rotation speed size disk galaxies suggested radiation bright newly formed stars active galactic


comparable mass least percent mass merger likely destroy minimum greatly disrupt disk resulting galaxy expected disk galaxy see next section remains unsolved problem astronomers necessarily mean lambda cdm model completely wrong rather requires refinement accurately reproduce population galaxies universe galaxy mergers formation elliptical galaxies artist 's image firestorm star birth deep inside core young growing elliptical


galaxy ngc mice galaxies example present merger antennae galaxies pair colliding galaxies bright blue knots young stars recently ignited result merger eso g typical elliptical galaxy elliptical galaxies ic among largest known thus far stars orbits randomly oriented within galaxy ie rotating like disk galaxies distinguishing feature elliptical galaxies velocity stars necessarily contribute flattening


galaxy spiral galaxies elliptical galaxies central supermassive black holes masses black holes correlate galaxy 's mass elliptical galaxies two main stages evolution first due supermassive black hole growing accreting cooling gas second stage marked black hole stabilizing suppressing gas cooling thus leaving elliptical galaxy stable state mass black hole also correlated property called sigma dispersion velocities stars orbits relationship


known sigma relation discovered elliptical galaxies mostly lack disks although bulges disk galaxies resemble elliptical galaxies elliptical galaxies likely found crowded regions universe galaxy clusters astronomers see elliptical galaxies evolved systems universe widely accepted main driving force evolution elliptical galaxies mergers smaller galaxies many galaxies universe gravitationally bound galaxies means never escape mutual pull galaxies


similar size resultant galaxy appear similar neither progenitors instead elliptical many types galaxy mergers necessarily result elliptical galaxies result structural change example minor merger event thought occurring milky way magellanic clouds mergers large galaxies regarded violent frictional interaction gas two galaxies cause gravitational shock waves capable forming new stars new elliptical galaxy sequencing several


images different galactic collisions one observe timeline two spiral galaxies merging single elliptical galaxy local group milky way andromeda galaxy gravitationally bound currently approaching high speed simulations show milky way andromeda collision course expected collide less five billion years collision expected sun rest solar system ejected current path around milky way remnant could giant


elliptical galaxy galaxy quenching access date april ref one observation see must explained successful theory galaxy evolution existence two different populations galaxies galaxy color magnitude diagram galaxies tend fall two separate locations diagram red sequence blue cloud red sequence galaxies generally non star forming elliptical galaxies little gas dust blue cloud galaxies tend dusty star forming spiral galaxies described previous sections galaxies tend evolve spiral elliptical structure via mergers however current


galaxy simply use reservoir cold gas ref name ref galaxy evolution models explain hypothesizing physical mechanisms remove shut supply cold gas galaxy mechanisms broadly classified two categories preventive feedback mechanisms stop cold gas entering galaxy stop producing stars ejective feedback mechanisms remove gas cannot form stars one theorized preventive mechanism called strangulation keeps cold gas entering galaxy strangulation likely main mechanism quenching star formation


found centers galaxies simulations shown gas accreting onto supermassive black holes galactic centers produces high energy jets released energy expel enough cold gas quench star formation milky way nearby andromeda galaxy currently appear undergoing quenching transition star forming blue galaxies passive red galaxies gallery gallery young ellipticaljpg ngc shows structure form bright disc implying formed short time ago ngc jpg ngc thin disk galaxy hires stsci prc ajpg image messier


prototypical spiral galaxy seen face warped galaxyjpg spiral galaxy eso g warped result colliding another galaxy galaxy completely absorbed distortion disappear process typically takes millions billions years gallery see also list galaxies red nugget small galaxies packed large amounts red stars reading references external links http wwwnoaoedu image gallery galaxieshtml noao gallery galaxy images http wwwnoaoedu image gallery html im html image andromeda galaxy http wwwastroyaleedu dokkum evocalc javascript passive evolution calculator early type elliptical galaxies http spacegeekorg ep flashshtml video evolution galaxies canadian astrophysicist doctor p formation


evolution stellar evolution concepts astronomy


moon modern geology significantly overlaps earth sciences including hydrology atmospheric sciences treated one major aspect integrated earth system science planetary science yellowstone national park kinney lake mount whitehorn near mount robson canada geology describes structure earth beneath surface processes shaped structure also provides tools determine relative absolute ages rocks found given location also describe histories rocks combining tools geologists able chronicle

Social science
Geography
Physical geography
Geology


geological history earth whole also demonstrate age earth geology provides primary evidence plate tectonics evolutionary history life earth 's past climates geologists use wide variety methods understand earth 's structure evolution including field work rock description geophysical techniques chemical analysis physical experiments numerical modelling practical terms geology important mineral hydrocarbon exploration exploitation evaluating water resources understanding natural hazards remediation environmental problems providing insights past climate change geology major


naturally occurring solid mass aggregate minerals mineraloids research geology associated study rocks provide primary record majority geological history earth three major types rock igneous sedimentary metamorphic rock cycle illustrates relationships among see diagram rock solidifies crystallizes melt magma lava igneous rock rock weathered eroded redeposited lithified sedimentary rock turned metamorphic rock heat


pressure change mineral content resulting characteristic fabric three types may melt happens new magma formed igneous rock may solidify organic matter coal bitumen oil natural gas linked mainly organic rich sedimentary rocks native gold venezuela quartz tibet quartz makes earth 's crust mass tests study three types rock geologists evaluate minerals composed mineral distinct physical properties many tests


geologic history magma unlithified material include sediments magma original unlithified source igneous rocks active flow molten rock closely studied volcanology igneous petrology aims determine history igneous rocks final crystallization original molten source whole earth structure plate tectonics oceanic continental convergence resulting subduction volcanic arcs illustrates one effect plate tectonics major tectonic plates earth discovered earth 's lithosphere includes crust rigid uppermost portion upper mantle separated


tectonic plates move across plastically deforming solid upper mantle called asthenosphere theory supported several types observations including seafloor spreading ref name tde discovery ref global distribution mountain terrain seismicity intimate coupling movement plates surface convection mantle heat transfer caused bulk movement molecules within fluids thus oceanic plates adjoining mantle convection currents always move direction oceanic lithosphere actually rigid upper thermal


boundary layer convecting mantle coupling rigid plates moving surface earth convecting mantle called plate tectonics diagram based seismic tomography subducting slabs blue continental margins plate boundaries red blue blob cutaway section farallon plate subducting beneath north america remnants plate surface earth juan de fuca plate explorer plate northwestern united states southwestern canada cocos plate


alfred wegener 's theory continental drift continents move across surface earth geological time also provided driving force crustal deformation new setting observations structural geology power theory plate tectonics lies ability combine observations single theory lithosphere moves convecting mantle earth structure earth 's layered structure inner core outer core lower mantle upper mantle lithosphere crust part lithosphere earth layered structure typical


crust lithosphere top mantle separated within seismic discontinuities kilometers outer core inner core recently seismologists able create detailed images wave speeds inside earth way doctor images body ct scan images led much detailed view interior earth replaced simplified layered model much dynamic model mineralogists able use pressure temperature data


first life c ga start photosynthesis c ga oxygenated atmosphere first snowball earth megaannum million years ago second snowball earth cambrian explosion vast multiplication hard bodied life first abundant fossils start paleozoic c first vertebrate land animals permian triassic extinction land animals die end paleozoic beginning mesozoic cretaceous paleogene extinction dinosaurs die end mesozoic beginning cenozoic c first hominins appear first australopithecus direct ancestor modern homo sapiens


appear ka kiloannum thousand years ago first modern homo sapiens appear east africa timescale moon timescale mars dating methods relative dating cross cutting relations used determine relative ages rock strata geological structures explanations folded rock strata cut thrust fault b large intrusion cutting c erosional angular unconformity cutting b rock strata deposited volcanic dyke cutting b c e even younger rock strata overlying c f normal


words past history globe must explained seen happening '''the principle intrusive relationships''' concerns crosscutting intrusions geology igneous intrusion cuts across formation sedimentary rock determined igneous intrusion younger sedimentary rock different types intrusions include stocks laccoliths batholiths sills dikes '''the principle cross cutting relationships''' pertains formation faults age sequences cut faults younger rocks cut accordingly fault found


penetrates formations top formations cut older fault ones cut must younger fault finding key bed situations may help determine whether fault normal fault thrust fault ref name steno strat ref '''the principle inclusions components''' states sedimentary rocks inclusions ''clasts'' found formation inclusions must older formation contains example sedimentary rocks common gravel


capitol reef national park canyonlands national park top bottom rounded tan domes navajo sandstone layered red kayenta formation cliff forming vertically jointed red wingate sandstone slope forming purplish chinle formation layered lighter red moenkopi formation white layered cutler formation sandstone picture glen canyon national recreation area utah '''the principle original horizontality''' states deposition sediments occurs essentially horizontal beds observation modern marine non marine sediments wide variety environments supports generalization although cross bedding inclined overall orientation cross bedded units horizontal ref name steno strat '''the principle


superposition''' states sedimentary rock layer tectonically undisturbed sequence younger one beneath older one logically younger layer cannot slip beneath layer previously deposited principle allows sedimentary layers viewed form vertical timeline partial complete record time elapsed deposition lowest layer deposition highest bed ref name steno strat '''the principle faunal succession''' based appearance fossils sedimentary rocks organisms exist period throughout


world presence sometimes absence provides relative age formations appear based principles william smith laid almost hundred years publication charles darwin 's theory evolution principles succession developed independently evolutionary thought principle becomes quite complex however given uncertainties fossilization localization fossil types due lateral changes habitat facies change sedimentary strata fossils formed globally time absolute dating mineral zircon often used radiometric dating geologists also use methods


determine absolute age rock samples geological events dates useful may also used conjunction relative dating methods calibrate relative methods beginning th century advancement geological science facilitated ability obtain accurate absolute dates geological events using radioactive isotopes methods changed understanding geological time previously geologists could use fossils stratigraphic correlation date sections rock relative one another isotopic dates became possible assign absolute ages rock


applications dating lava volcanic ash layers found within stratigraphic sequence provide absolute age data sedimentary rock units contain radioactive isotopes calibrate relative dating techniques methods also used determine ages pluton emplacement thermochemical techniques used determine temperature profiles within crust uplift mountain ranges paleo topography fractionation lanthanide series elements used compute ages since rocks removed mantle methods used recent events optically stimulated luminescence cosmogenic radionuclide dating used


date surfaces erosion rates dendrochronology also used dating landscapes radiocarbon dating used geologically young materials containing organic carbon geological development area originally horizontal sequence sedimentary rocks shades tan affected igneous activity deep surface magma chamber large associated igneous bodies magma chamber feeds volcano sends offshoots magma later crystallize dikes sills magma also advances upwards form intrusive igneous bodies diagram illustrates cinder cone volcano releases ash


composite volcano releases lava ash illustration three types faults br strike slip faults occur rock units slide past one another br b normal faults occur rocks undergoing horizontal extension br c reverse thrust faults occur rocks undergoing horizontal shortening san andreas fault california geology area changes time rock units deposited inserted deformational processes change shapes locations rock units first emplaced either deposition onto surface intrusion overlying rock deposition occur


sediments settle onto surface earth later lithify sedimentary rock volcanic material volcanic ash lava flows blanket surface igneous intrusions batholiths laccoliths dikes sills push upwards overlying rock crystallize intrude initial sequence rocks deposited rock units deformed metamorphosed deformation typically occurs result horizontal shortening horizontal extension side side strike slip motion structural regimes broadly relate convergent boundaries divergent boundaries transform boundaries respectively tectonic plates


rock units placed horizontal compression shorten become thicker rock units muds significantly change volume accomplished two primary ways faulting folding shallow crust brittle deformation occur thrust faults form causes deeper rock move top shallower rock deeper rock often older noted principle superposition result older rocks moving top younger ones movement along faults result folding either faults planar


rock layers dragged along forming drag folds slip occurs along fault deeper earth rocks behave plastically fold instead faulting folds either material center fold buckles upwards creating antiforms buckles downwards creating synforms tops rock units within folds remain pointing upwards called anticlines synclines respectively units fold facing downward structure called overturned anticline syncline rock units


overturned correct direction unknown simply called general terms antiforms synforms diagram folds indicating anticline syncline even higher pressures temperatures horizontal shortening cause folding metamorphism rocks metamorphism causes changes mineral composition rocks creates foliation planar surface related mineral growth stress remove signs original textures rocks bedding sedimentary rocks flow features lavas crystal patterns crystalline rocks


extension causes rock units whole become longer thinner primarily accomplished normal faulting ductile stretching thinning normal faults drop rock units higher lower typically results younger units ending older units stretching units result thinning fact one location within maria fold thrust belt entire sedimentary sequence grand canyon appears length less meter rocks depth ductilely stretched often also metamorphosed


creation topographic gradients causing material rock unit increasing elevation eroded hillslopes channels sediments deposited rock unit going continual motion along fault maintains topographic gradient spite movement sediment continues create accommodation space material deposit deformational events often also associated volcanism igneous activity volcanic ashes lavas accumulate surface igneous intrusions enter dikes long planar igneous intrusions enter along cracks therefore often form


large numbers areas actively deformed result emplacement dike swarms observable across canadian shield rings dikes around lava tube volcano processes necessarily occur single environment necessarily occur single order hawaiian islands example consist almost entirely layered basaltic lava flows sedimentary sequences mid continental united states grand canyon southwestern united states contain almost undeformed stacks sedimentary rocks remained


task hand typical fieldwork could consist geological mapping structural mapping identifying locations major rock units faults folds led placement stratigraphic mapping pinpointing locations sedimentary facies lithofacies biofacies mapping isopachs equal thickness sedimentary rock surficial mapping recording locations soils surficial deposits surveying topographic features compilation topographic maps work understand change across landscapes including patterns erosion deposition river channel change migration avulsion hillslope processes subsurface mapping geophysical methods methods include shallow seismic


surveys ground penetrating radar aeromagnetic surveys electrical resistivity tomography aid hydrocarbon exploration finding groundwater locating buried archaeological artifacts high resolution stratigraphy measuring describing stratigraphic sections surface well drilling logging biogeochemistry geomicrobiology collecting samples determine biochemical pathways identify new species organisms identify new chemical compounds use discoveries understand early life earth functioned metabolized find important compounds use pharmaceuticals paleontology excavation fossil material research past life evolution museums education collection samples geochronology thermochronology glaciology measurement


characteristics glaciers motion petrology addition identifying rocks field lithology petrologists identify rock samples laboratory two primary methods identifying rocks laboratory optical microscopy using electron microprobe optical mineralogy analysis petrologists analyze thin sections rock samples using petrographic microscope minerals identified different properties plane polarized cross polarized light including birefringence pleochroism twinning interference properties conoscopic lens electron microprobe individual locations analyzed exact chemical


compositions variation composition within individual crystals stable radioactive isotope studies provide insight geochemical evolution rock units petrologists also use fluid inclusion data perform high temperature pressure physical experiments understand temperatures pressures different mineral phases appear change igneous metamorphic processes research extrapolated field understand metamorphic processes conditions crystallization igneous rocks work also help explain processes occur within earth subduction magma chamber evolution rock strata


history rock deformation area addition perform analog numerical experiments rock deformation large small settings analysis structures often accomplished plotting orientations various features onto stereonets stereonet stereographic projection sphere onto plane planes projected lines lines projected points used find locations fold axes relationships faults relationships geological structures among well known experiments structural geology involving orogenic wedges


use data reconstruct ancient processes occurring surface earth interpret past environments locate areas water coal hydrocarbon extraction laboratory biostratigraphers analyze rock samples outcrop drill cores fossils found ref name hodell ref fossils help scientists date core understand depositional environment rock units formed geochronologists precisely date rocks within stratigraphic section provide better absolute bounds timing rates deposition magnetic stratigraphers look signs magnetic reversals igneous rock units within


drill cores ref name hodell scientists perform stable isotope studies rocks gain information past climate ref name hodell planetary geology surface mars photographed viking lander december advent space exploration twentieth century geologists begun look planetary bodies ways developed study earth new field study called planetary geology sometimes known astrogeology relies known geological principles study bodies solar system although greek language origin prefix ''geo'' refers


phoenix lander analyzed martian polar soil water chemical mineralogical constituents related biological processes applied geology man panning gold mokelumne harper 's weekly got gold california economic geology economic geology branch geology deals aspects economic minerals humankind uses fulfill various needs economic minerals extracted profitably various practical uses economic geologists help locate manage earth 's natural resources petroleum coal well mineral resources include metals iron copper uranium mining geology


mining geology consists extractions mineral resources earth resources economic interests include gemstones metals gold copper many minerals asbestos perlite mica phosphates zeolites clay pumice quartz silica well elements sulfur chlorine helium petroleum geology mud log process common way study lithology drilling oil wells petroleum geologists study locations subsurface earth contain extractable hydrocarbons especially petroleum natural gas many reservoirs found sedimentary basins study


formation basins well sedimentary tectonic evolution present day positions rock units engineering geology engineering geology application geological principles engineering practice purpose assuring geological factors affecting location design construction operation maintenance engineering works properly addressed engineering geology distinct geological engineering particularly north america child drinks water well built part hydrogeological humanitarian project kenya field civil engineering geological principles analyses used order


ascertain mechanical principles material structures built allows tunnels built without collapsing bridges skyscrapers built sturdy foundations buildings built settle clay mud hydrology geology geological principles applied various environmental problems stream restoration restoration brownfields understanding interaction natural habitat geological environment groundwater hydrology hydrogeology used locate groundwater ref name hamilton pixie ref often provide ready supply uncontaminated water


especially important arid regions monitor spread contaminants groundwater wells ref name hamilton pixie paleoclimatology geologists also obtain data stratigraphy boreholes core samples ice cores ice cores sediment cores used paleoclimate reconstructions tell geologists past present temperature precipitation sea level across globe datasets primary source information global climate change outside instrumental data natural hazards rockfall grand canyon geologists geophysicists study natural hazards order enact safe building codes warning systems


used prevent loss property life examples important natural hazards pertinent geology opposed mainly pertinent meteorology history william smith 's geological map england wales southern scotland completed second national scale geologic map far accurate time ref name map ref study physical material earth dates back least ancient greece theophrastus bce wrote work ''peri lithon'' ''on stones'' roman period pliny elder wrote detail


many minerals metals practical use even correctly noting origin amber additionally th century bce aristotle made critical observations slow rate geological change observed composition land formulated theory earth changes slow rate changes cannot observed one person 's lifetime aristotle developed one first evidence based concepts connected geological realm regarding rate earth physically changes modern scholars fielding h garrison opinion origin


science geology traced persia muslim conquests come end abu al rayhan al biruni ce one earliest persian geologists whose works included earliest writings geology india hypothesizing indian subcontinent sea drawing greek indian scientific literature destroyed muslim conquests persian scholar ibn sina avicenna proposed detailed explanations formation mountains origin earthquakes topics central modern geology provided essential foundation later


introduced fixed term horace b n dict de saussure word derived greek ''g '' meaning earth ''logos'' meaning speech according another source word geology comes norwegian mikkel peders n escholt priest scholar escholt first used definition book titled ''geologia norvegica'' william smith drew first geological maps began process ordering rock strata layers examining fossils contained ref name map mikhail lomonosov published treatise ''on


turn raised become dry land hutton published two volume version ideas followers hutton known ''plutonists'' believed rocks formed ''vulcanism'' deposition lava volcanoes opposed ''neptunists'' led abraham werner believed rocks settled large ocean whose level gradually dropped time first geological map us produced william maclure ref name maclure ref maclure commenced self imposed task making geological survey


united states almost every state union traversed mapped allegheny mountains crossed recrossed times results unaided labours submitted american philosophical society memoir entitled ''observations geology united states explanatory geological map'' published ''society 's transactions'' together nation 's first geological map antedates william smith 's geological map england six years although constructed using different classification rocks sir charles lyell first published famous book ''principles geology''


earth 's age estimated two billion years awareness vast amount time opened door new theories processes shaped planet significant advances th century geology development theory plate tectonics refinement estimates planet 's age plate tectonics theory arose two separate geological observations seafloor spreading continental drift theory revolutionized earth sciences today earth known approximately billion years old ref name book gallery file hutton james portrait


raeburnjpg james hutton scottish geologist father modern geology file john tuzo wilson jpg john tuzo wilson canadian geophysicist father plate tectonics file msh david johnston camp med cropped jpg volcanologist david johnston hours death br eruption mount st helens gallery fields related disciplines earth system science economic geology mining geology petroleum geology engineering geology environmental geology environmental science geoarchaeology geochemistry biogeochemistry isotope geochemistry geochronology geodetics geography geological engineering geological modelling geometallurgy geomicrobiology geomorphology geomythology geophysics glaciology historical geology hydrogeology meteorology mineralogy oceanography marine geology paleoclimatology paleontology micropaleontology palynology petrology petrophysics physical


geography plate tectonics regional geology sedimentology seismology soil science pedology soil study speleology stratigraphy biostratigraphy chronostratigraphy lithostratigraphy structural geology systems geology tectonics volcanology see also glossary geology geoprofessions geotourism glossary geology terms index geology articles international union geological sciences iugs outline geology timeline geology references external links http wwwonegeologyorg one geology interactive geological map world international initiative geological surveys around globe groundbreaking project launched contributed 'international year planet earth' becoming one flagship projects http geologycom ''earth science


'''genetics''' branch biology concerned study genes genetic variation heredity organisms ref name griffiths sect ref ref name hartl jones hartl jones e ref though heredity observed millennia gregor mendel moravian scientist augustinian friar working th century brno first study genetics scientifically mendel studied trait inheritance patterns way traits handed parents offspring time observed organisms pea plants inherit traits way discrete units inheritance term still used today somewhat ambiguous definition referred


gene trait inheritance molecular inheritance mechanisms genes still primary principles genetics st century modern genetics expanded beyond inheritance studying function behavior genes gene structure function variation distribution studied within context cell organism eg dominance within context population genetics given rise number subfields including molecular genetics epigenetics population genetics organisms studied within broad field span domains life archaea bacteria eukarya genetic processes work combination


water nutrients environment etymology word ''genetics'' stems ancient greek '''' meaning genitive generative turn derives '''' meaning origin history observation living things inherit traits parents used since prehistoric times improve crop plants animals selective breeding ref name publishing ref modern science genetics seeking understand process began work augustinian friar gregor mendel mid th century ref name weiling ref prior mendel imre festetics hungarian noble lived k szeg mendel first used


word genetics described several rules genetic inheritance work ''the genetic law nature'' die genetische ges tze der natur second law mendel published third law developed basic principles mutation considered forerunner hugo de vries blending inheritance leads averaging every characteristic engineer fleeming jenkin pointed makes evolution natural selection impossible theories inheritance preceded mendel 's work popular theory th century implied charles darwin 's


''on origin species'' blending inheritance idea individuals inherit smooth blend traits parents ref name hamilton ref mendel 's work provided examples traits definitely blended hybridization showing traits produced combinations distinct genes rather continuous blend blending traits progeny explained action multiple genes quantitative effects another theory support time inheritance acquired characteristics belief individuals inherit traits strengthened parents theory commonly associated jean baptiste lamarck


known wrong experiences individuals affect genes pass children theories included pangenesis charles darwin acquired inherited aspects francis galton 's reformulation pangenesis particulate inherited mendelian classical genetics sex linked inheritance mutation causing white eyes ''drosophila'' led hypothesis genes located upon chromosomes modern genetics started mendel 's studies nature inheritance plants paper ''versuche ber pflanzenhybriden'' experiments plant hybridization presented ''naturforschender verein'' society


research nature br nn mendel traced inheritance patterns certain traits pea plants described mathematically ref name mendel ref although pattern inheritance could observed traits mendel 's work suggested heredity particulate acquired inheritance patterns many traits could explained simple rules ratios importance mendel 's work gain wide understanding death hugo de vries scientists rediscovered research william bateson proponent mendel 's work coined word ''genetics'' adjective


''genetic'' derived greek word ''genesis'' origin predates noun first used biological sense bateson acted mentor aided significantly work scientists newnham college cambridge specifically work becky saunders nora darwin barlow muriel wheldale onslow bateson popularized usage word ''genetics'' describe study inheritance inaugural address third international conference plant hybridization london ref name bateson genetics initially titled international conference hybridisation plant breeding title changed


result bateson 's speech see ref rediscovery mendel 's work scientists tried determine molecules cell responsible inheritance nettie stevens began studying mealworm ref name net ref next years discovered females x chromosome males x chromosomes ref name net able conclude sex chromosomal factor determined male ref name net thomas hunt morgan argued genes chromosomes based observations sex linked white eye mutation


fruit flies student alfred sturtevant used phenomenon genetic linkage show genes arranged linearly chromosome molecular genetics dna molecular basis biological inheritance strand dna chain nucleotides matching center form look like rungs twisted ladder although genes known exist chromosomes chromosomes composed protein dna scientists know two responsible inheritance frederick griffith discovered phenomenon transformation see griffith 's experiment dead


bacteria could transfer genetic material transform still living bacteria sixteen years later avery macleod mccarty experiment identified dna molecule responsible transformation ref name avery et al reprint ref role nucleus repository genetic information eukaryotes established h mmerling work single celled alga ''acetabularia'' hershey chase experiment confirmed dna rather protein genetic material viruses infect bacteria providing evidence dna molecule responsible inheritance james watson francis crick determined structure dna


using x ray crystallography work rosalind franklin maurice wilkins indicated dna helical structure ie shaped like corkscrew ref name watsoncrick ref double helix model two strands dna nucleotides pointing inward matching complementary nucleotide strand form look like rungs twisted ladder ref name watsoncrick b ref structure showed genetic information exists sequence nucleotides strand dna structure also suggested simple method replication strands separated new partner strands reconstructed based


read nucleotide sequence dna molecule ref name sanger et al ref kary banks mullis developed polymerase chain reaction providing quick way isolate amplify specific section dna mixture ref name saiki et al ref efforts human genome project department energy nih parallel private efforts celera genomics led sequencing human genome ref name human genome project features inheritance discrete inheritance mendel 's laws punnett square depicting cross two pea plants heterozygous purple b white b blossoms fundamental level inheritance organisms


occurs passing discrete heritable units called genes parents offspring ref name griffiths sect ref property first observed gregor mendel studied segregation heritable traits pea plants ref name mendel ref name griffiths sect ref experiments studying trait flower color mendel observed flowers pea plant either purple white never intermediate two colors different discrete versions gene called alleles case pea diploid species individual plant two copies gene one copy inherited


observed alleles complete dominance instead incomplete dominance expressing intermediate phenotype codominance expressing alleles ref name griffiths sect ref pair organisms reproduce sexually offspring randomly inherit one two alleles parent observations discrete inheritance segregation alleles collectively known mendel 's first law law segregation notation diagrams genetic pedigree charts help track inheritance patterns traits geneticists use diagrams symbols describe inheritance gene represented one


letters often symbol used mark usual non mutant allele gene fertilization breeding experiments especially discussing mendel 's laws parents referred p generation offspring f first filial generation f offspring mate offspring called f second filial generation one common diagrams used predict result cross breeding punnett square studying human genetic diseases geneticists often use pedigree charts represent inheritance traits ref name griffiths sect ref charts map


inheritance trait family tree multiple gene interactions human height trait complex genetic causes francis galton 's data shows relationship offspring height function mean parent height organisms thousands genes sexually reproducing organisms genes generally assort independently means inheritance allele yellow green pea color unrelated inheritance alleles white purple flowers phenomenon known mendel 's second law law independent assortment means alleles


different genes get shuffled parents form offspring many different combinations genes assort independently demonstrating genetic linkage topic discussed later article often different genes interact way influences trait blue eyed mary ''omphalodes verna'' example exists gene alleles determine color flowers blue magenta another gene however controls whether flowers color white plant two copies white allele flowers white regardless whether first gene blue


influence total variation trait example human height trait complex causes heritability united states nigeria however people experience variable access good nutrition health care height heritability molecular basis inheritance dna chromosomes molecular structure dna bases pair arrangement hydrogen bonding strands dna sequence molecular basis genes deoxyribonucleic acid dna dna composed chain nucleotides four types adenine


strand pairs c pairs g thus two stranded form strand effectively contains necessary information redundant partner strand structure dna physical basis inheritance dna replication duplicates genetic information splitting strands using strand template synthesis new partner strand ref name griffiths sect ref genes arranged linearly along long chains dna base pair sequences bacteria cell usually contains single circular genophore eukaryotic organisms plants animals dna arranged multiple linear chromosomes


nonchromosomal genes found outside nucleus ref name ruth ref plants often found chloroplasts organisms mitochondria ref name ruth nonchromosomal genes still passed either partner sexual reproduction control variety hereditary characteristics replicate remain active throughout generations ref name ruth haploid organisms one copy chromosome animals many plants diploid containing two chromosome thus two copies every gene ref name griffiths sect ref two alleles gene located identical loci


genes said mary frances lyon discovered x chromosome inactivation reproduction avoid passing twice many genes offspring ref name lyon ref lyon 's discovery led discovery things including x linked diseases ref name lyon x chromosomes form strongly heterogeneous pair reproduction cells divide full genome copied daughter cell inherits one copy process called mitosis simplest form reproduction basis asexual reproduction asexual reproduction also occur multicellular organisms producing offspring inherit genome


single parent offspring genetically identical parents called clones eukaryotic organisms often use sexual reproduction generate offspring contain mixture genetic material inherited two different parents process sexual reproduction alternates forms contain single copies genome haploid double copies diploid ref name griffiths sect haploid cells fuse combine genetic material create diploid cell paired chromosomes diploid organisms form haploids dividing without replicating dna create daughter cells randomly inherit one pair chromosomes animals many plants diploid


lifespan haploid form reduced single cell gametes sperm eggs although use haploid diploid method sexual reproduction bacteria many methods acquiring new genetic information bacteria undergo conjugation transferring small circular piece dna another bacterium ref name griffiths sect ref bacteria also take raw dna fragments found environment integrate genomes phenomenon known transformation ref name griffiths sect ref processes result horizontal gene transfer transmitting fragments genetic information organisms would otherwise unrelated natural


bacterial transformation occurs many bacterial species regarded sexual process transferring dna one cell another cell usually species ref name bernstein ref transformation requires action numerous bacterial gene products primary adaptive function appears repair dna damages recipient cell ref name bernstein recombination genetic linkage thomas hunt morgan 's illustration double crossover chromosomes diploid nature chromosomes allows genes different chromosomes assort independently separated homologous pair sexual reproduction


wherein haploid gametes formed way new combinations genes occur offspring mating pair genes chromosome would theoretically never recombine however via cellular process chromosomal crossover crossover chromosomes exchange stretches dna effectively shuffling gene alleles chromosomes ref name griffiths sect ref process chromosomal crossover generally occurs meiosis series cell divisions creates haploid cells meiotic recombination particularly microbial eukaryotes appears serve adaptive function repair dna damages ref name bernstein first cytological demonstration


genes demonstrate genetic linkage alleles two genes tend inherited together amounts linkage series genes combined form linear linkage map roughly describes arrangement genes along chromosome ref name griffiths sect ref gene expression genetic code genetic code using triplet code dna messenger rna intermediary specifies protein genes generally express functional effect production proteins complex molecules responsible functions cell proteins made one polypeptide chains


composed sequence amino acids dna sequence gene rna intermediate used produce specific amino acid sequence process begins production rna molecule sequence matching gene 's dna sequence process called transcription messenger rna molecule serves produce corresponding amino acid sequence process called translation group three nucleotides sequence called codon corresponds either one twenty possible amino acids protein instruction end amino acid


sequence correspondence called genetic code flow information unidirectional information transferred nucleotide sequences amino acid sequence proteins never transfers protein back sequence dna phenomenon francis crick called central dogma molecular biology ref name crick ref specific sequence amino acids results unique three dimensional structure protein three dimensional structures proteins related functions simple structural molecules like fibers formed protein collagen proteins bind proteins simple molecules sometimes acting


enzymes facilitating chemical reactions within bound molecules without changing structure protein protein structure dynamic protein hemoglobin bends slightly different forms facilitates capture transport release oxygen molecules within mammalian blood single nucleotide difference within dna cause change amino acid sequence protein protein structures result amino acid sequences changes dramatically change properties protein destabilizing structure changing surface protein way changes


interaction proteins molecules example sickle cell anemia human genetic disease results single base difference within coding region globin section hemoglobin causing single amino acid change changes hemoglobin 's physical properties sickle cell versions hemoglobin stick stacking form fibers distort shape red blood cells carrying protein sickle shaped cells longer flow smoothly blood vessels tendency clog degrade causing medical problems associated disease dna sequences transcribed rna


translated protein products rna molecules called non coding rna cases products fold structures involved critical cell functions eg ribosomal rna transfer rna rna also regulatory effects hybridization interactions rna molecules microrna nature nurture siamese cats temperature sensitive pigment production mutation although genes contain information organism uses function environment plays important role determining ultimate phenotypes organism displays phrase nature nurture refers complementary relationship phenotype organism depends


interaction genes environment interesting example coat coloration siamese cat case body temperature cat plays role environment cat 's genes code dark hair thus hair producing cells cat make cellular proteins resulting dark hair dark hair producing proteins sensitive temperature ie mutation causing temperature sensitivity denature higher temperature environments failing produce dark hair pigment areas cat higher body temperature low temperature environment however protein 's structure stable


produces dark hair pigment normally protein remains functional areas skin coldersuch legs ears tail faceso cat dark hair extremities environment plays major role effects human genetic disease phenylketonuria mutation causes phenylketonuria disrupts ability body break amino acid phenylalanine causing toxic build intermediate molecule turn causes severe symptoms progressive intellectual disability seizures however someone phenylketonuria mutation follows strict diet avoids amino acid remain normal


healthy common method determining genes environment nature nurture contribute phenotype involves studying identical fraternal twins siblings multiple births identical siblings genetically since come zygote meanwhile fraternal twins genetically different one another normal siblings comparing often certain disorder occurs pair identical twins often occurs pair fraternal twins scientists determine whether disorder caused genetic postnatal environmental factors one famous example involved


study genain quadruplets identical quadruplets diagnosed schizophrenia ref name genain ref however tests cannot separate genetic factors environmental factors affecting fetal development gene regulation genome given organism contains thousands genes genes need active given moment gene expressed transcribed mrna exist many cellular methods controlling expression genes proteins produced needed cell transcription factors regulatory proteins bind dna either promoting inhibiting


transcription gene within genome ''escherichia coli'' bacteria example exists series genes necessary synthesis amino acid tryptophan however tryptophan already available cell genes tryptophan synthesis longer needed presence tryptophan directly affects activity genes tryptophan molecules bind tryptophan repressor transcription factor changing repressor 's structure repressor binds genes tryptophan repressor blocks transcription expression genes thereby creating negative feedback regulation tryptophan synthesis process


transcription factors bind dna influencing transcription associated genes differences gene expression especially clear within multicellular organisms cells contain genome different structures behaviors due expression different sets genes cells multicellular organism derive single cell differentiating variant cell types response external intercellular signals gradually establishing different patterns gene expression create different behaviors single gene responsible development structures within multicellular organisms patterns arise complex


exceptions general rule dna basis inheritance genetic change mutations gene duplication allows diversification providing redundancy one gene mutate lose original function without harming organism process dna replication errors occasionally occur polymerization second strand errors called mutations affect phenotype organism especially occur within protein coding sequence gene error rates usually low error every nbsp million bases due proofreading ability dna polymerases ref name griffiths sect ref ref name kunkel ref processes increase rate


changes dna called mutagenic mutagenic chemicals promote errors dna replication often interfering structure base pairing uv radiation induces mutations causing damage dna structure ref name griffiths sect ref chemical damage dna occurs naturally well cells use dna repair mechanisms repair mismatches breaks repair however always restore original sequence particularly important source dna damages appears reactive oxygen species ref name pmid ref produced cellular aerobic respiration lead mutations ref name pmid ref organisms use chromosomal crossover exchange dna recombine


genes errors alignment meiosis also cause mutations ref name griffiths sect ref errors crossover especially likely similar sequences cause partner chromosomes adopt mistaken alignment makes regions genomes prone mutating way errors create large structural changes dna sequence duplications inversions deletions entire regions accidental exchange whole parts sequences different chromosomes chromosomal translocation diagram showing mutations rna sequence figure normal rna sequence consisting codons figure shows missense single point non silent mutation figures


show frameshift mutations grouped together figure shows deletion second base pair second codon figure shows insertion third base pair second codon figure shows repeat expansion entire codon duplicated natural selection evolution mutations alter organism 's genotype occasionally causes different phenotypes appear mutations little effect organism 's phenotype health reproductive fitness mutations effect usually detrimental occasionally beneficial ref name calverlymbery ref


studies fly ''drosophila melanogaster'' suggest mutation changes protein produced gene percent mutations harmful remainder either neutral weakly beneficial evolutionary tree eukaryotic organisms constructed comparison several orthologous gene sequences population genetics studies distribution genetic differences within populations distributions change time ref name griffiths sect ref changes frequency allele population mainly influenced natural selection given allele provides selective reproductive advantage organism ref name griffiths sect ref