value function point given points extrapolation similar interpolation except value unknown function point outside given points must found regression also similar takes account data imprecise given points measurement value function points error unknown function found least squares method one way achieve solving equations systems equations another fundamental problem computing


solution given equation two cases commonly distinguished depending whether equation linear instance equation math x math linear math x math much effort put development methods solving systems linear equations standard direct methods ie methods use matrix decomposition gaussian elimination lu decomposition cholesky decomposition symmetric hermitian positive definite matrix qr decomposition non square matrices iterative methods jacobi method gauss seidel method successive relaxation conjugate gradient method usually preferred large systems general iterative methods

Formal science
Mathematics
Numerical analysis


also concerned computing approximate way solution differential equations ordinary differential equations partial differential equations partial differential equations solved first discretizing equation bringing finite dimensional subspace done finite element method finite difference method particularly engineering finite volume method theoretical justification methods often involves theorems functional analysis reduces problem solution algebraic equation software since late twentieth century algorithms implemented variety programming languages netlib


hrebicek j eds solving problems scientific computing using maple matlab springer science business media ref ref name bf barnes b fulford g r mathematical modelling case studies differential equations approach using maple matlab chapman hall crc ref tk solver plus idl well free open source alternatives freemat scilab gnu octave similar matlab c library also programming languages r similar plus julia python libraries numpy scipy sympy performance varies widely vector matrix operations


usually fast scalar loops may vary speed order magnitude many computer algebra systems mathematica also benefit availability arbitrary precision arithmetic provide accurate results also spreadsheet software used solve simple problems relating numerical analysis excel example hundreds available functions including matrices may used conjunction built solver see also analysis algorithms computational science interval arithmetic list numerical analysis topics local linearization method numerical differentiation numerical recipes probabilistic numerics symbolic numeric computation validated numerics


notes references citations sources examples importance accurate arithmetic trefethen lloyd n http peoplemathsoxacuk trefethen naessaypdf numerical analysis pages timothy gowers june barrow green editors ''princeton companion mathematics'' princeton university press external links journals http www gdzsubuni goettingende cgi bin digbibcgippn gdzsubuni goettingen ''numerische mathematik'' volumes springer searchable pages images ''numerische mathematik'' volumes springer ''journal numerical analysis'' volumes siam online texts https webarchiveorg web http wwwnrcom oldverswitcherhtml ''numerical recipes'' william h press free downloadable previous editions https webarchiveorg web http krcsaitacth radok math mat stepsahtm ''first steps numerical analysis'' archived rjhosking sjoe dcjoyce jcturner https webarchiveorg web http wwwphyornlgov csep csep textochtml ''csep'' computational science education project us department energy archived https dlmfnistgov


numerical methods ch ''digital library mathematical functions'' https personalmathubcca cbm aands page htm numerical interpolation differentiation integration ch ''handbook mathematical functions'' abramowitz stegun online course material http wwwdamtpcamacuk user fdl people sd lectures nummeth indexhtm l title page numerical methods stuart dalziel university cambridge http wwwmathupennedu wilf deturckwilfpdf lectures numerical analysis dennis deturck herbert wilf university pennsylvania http johndfentoncom lectures numerical methods numerical methodspdf numerical methods john fenton university karlsruhe http www teachingphysicsoxacuk computing numericalmethods nmfppdf numerical methods physicists anthony hare oxford university https webarchiveorg web http krcsaitacth radok math mat stepsahtm lectures numerical analysis archived r radok mahidol university http ocwmitedu courses mechanical engineering j introduction numerical analysis engineering j spring introduction numerical analysis engineering henrik schmidt massachusetts institute technology http eceuwaterlooca dwharder numericalanalysis ''numerical analysis engineering''


w harder university waterloo https wwwmathumdedu diom courses amsc levy notespdf introduction numerical analysis doron levy university maryland https webarchiveorg web http mathfullertonedu mathews n numericalundergradmodhtml numerical analysis numerical methods archived john h mathews california state university fullerton mathematical physics computational science


fullerene nanogears gpn jpg '''nanotechnology''' also shortened '''nanotech''' use matter atomic molecular supramolecular scale industrial purposes earliest widespread description nanotechnology referred particular technological goal precisely manipulating atoms molecules fabrication macroscale products also referred molecular nanotechnology ref name engines ref ref name nanotsystems ref generalized description nanotechnology subsequently established national nanotechnology initiative defined nanotechnology manipulation matter least one dimension sized nanometers definition reflects fact quantum mechanical effects

Natural science
Chemistry
Nanotechnology


important quantum realm scale definition shifted particular technological goal research category inclusive types research technologies deal special properties matter occur given size threshold therefore common see plural form nanotechnologies well nanoscale technologies refer broad range research applications whose common trait size nanotechnology defined size naturally broad including fields science diverse surface science organic chemistry molecular biology semiconductor physics energy storage engineering microfabrication


molecular engineering associated research applications equally diverse ranging extensions conventional device physics completely new approaches based upon molecular self assembly developing new materials dimensions nanoscale direct control matter atomic scale scientists currently debate future implications nanotechnology nanotechnology may able create many new materials devices vast range applications nanomedicine nanoelectronics biomaterials energy production consumer products hand nanotechnology raises many issues new technology including concerns toxicity


environmental impact nanomaterials potential effects global economics well speculation various doomsday scenarios concerns led debate among advocacy groups governments whether special regulation nanotechnology warranted origins concepts seeded nanotechnology first discussed renowned physicist richard feynman talk ''there 's plenty room bottom'' described possibility synthesis via direct manipulation atoms comparison nanomaterials sizes term nano technology first used norio taniguchi though widely known


inspired feynman 's concepts k eric drexler used term nanotechnology book ''engines creation coming era nanotechnology'' proposed idea nanoscale assembler would able build copy items arbitrary complexity atomic control also drexler co founded foresight institute longer affiliated help increase public awareness understanding nanotechnology concepts implications emergence nanotechnology field occurred convergence drexler 's theoretical public work developed


popularized conceptual framework nanotechnology high visibility experimental advances drew additional wide scale attention prospects atomic control matter two major breakthroughs sparked growth nanotechnology modern era first invention scanning tunneling microscope provided unprecedented visualization individual atoms bonds successfully used manipulate individual atoms microscope 's developers gerd binnig heinrich rohrer ibm zurich research laboratory received nobel prize physics ref name binnig ref binnig quate gerber also invented analogous atomic force microscope


year buckminsterfullerene c sub sub also known buckyball representative member carbon structures known fullerenes members fullerene family major subject research falling nanotechnology umbrella second fullerenes discovered harry kroto richard smalley robert curl together nobel prize chemistry c sub sub initially described nanotechnology term used regarding subsequent work related carbon nanotubes sometimes called graphene tubes bucky tubes suggested potential applications nanoscale electronics devices discovery carbon nanotubes largely


attributed sumio iijima nec ref name carbon ref iijima inaugural kavli prize nanoscience nanolayer base metal semiconductor junction junction transistor initially proposed rose fabricated l geppert mohamed atalla dawon kahng decades later advances multi gate technology enabled scaling metal oxide semiconductor field effect transistor mosfet devices nano scale levels smaller nbsp nm gate length starting finfet fin field effect transistor three dimensional non planar double gate mosfet uc berkeley team researchers including digh hisamoto chenming hu tsu jae king liu jeffrey bokor


others fabricated finfet devices nm process nm nm ref name liu ref early field garnered increased scientific political commercial attention led controversy progress controversies emerged regarding definitions potential implications nanotechnologies exemplified royal society 's report nanotechnology ref name royalsociety ref challenges raised regarding feasibility applications envisioned advocates molecular nanotechnology culminated public debate drexler smalley ref name counterpoint ref meanwhile commercialization products based advancements nanoscale technologies


began emerging products limited bulk applications nanomaterials involve atomic control matter examples include silver nano platform using silver nanoparticles antibacterial agent nanoparticle based transparent sunscreens carbon fiber strengthening using silica nanoparticles carbon nanotubes stain resistant textiles ref name americanelements ref ref name emergingnano ref governments moved promote fund research nanotechnology us national nanotechnology initiative formalized size based definition nanotechnology established funding research nanoscale europe via european framework programmes research technological development


r funding coming corporations based united states japan germany top five organizations filed intellectual patents nanotechnology r samsung electronics first patents nippon steel first patents ibm first patents toshiba first patents canon first patents top five organizations published scientific papers nanotechnology research chinese academy sciences russian academy sciences centre national de la recherche scientifique university tokyo osaka university ref name wipo fundamental concepts


nanotechnology engineering functional systems molecular scale covers current work concepts advanced original sense nanotechnology refers projected ability construct items bottom using techniques tools developed today make complete high performance products one nanometer nm one billionth sup sup meter comparison typical carbon carbon bond lengths spacing atoms molecule range dna double helix diameter around nbsp nm hand smallest cellular life forms


bacteria genus ''mycoplasma'' around nbsp nm length convention nanotechnology taken scale range following definition used national nanotechnology initiative us lower limit set size atoms hydrogen smallest atoms approximately quarter nm kinetic diameter since nanotechnology must build devices atoms molecules upper limit less arbitrary around size phenomena observed larger structures start become apparent made use


nano device new phenomena make nanotechnology distinct devices merely miniaturised versions equivalent macroscopic device devices larger scale come description microtechnology put scale another context comparative size nanometer meter marble size earth ref name nationalg ref another way putting nanometer amount average man 's beard grows time takes raise razor face ref name nationalg two main approaches


used nanotechnology bottom approach materials devices built molecular components assemble chemically principles molecular recognition ref name referencea ref top approach nano objects constructed larger entities without atomic level control areas physics nanoelectronics nanomechanics nanophotonics nanoionics evolved last decades provide basic scientific foundation nanotechnology larger smaller materials perspective reconstruction clean gold surface visualized using scanning tunneling microscopy positions individual atoms composing surface visible several phenomena become pronounced size


system decreases include statistical mechanical effects well quantum mechanical effects example quantum size effect electronic properties solids altered great reductions particle size effect come play going macro micro dimensions however quantum effects become significant nanometer size range reached typically distances nanometers less called quantum realm additionally number physical mechanical electrical optical etc properties change compared macroscopic systems one example increase surface area volume ratio


altering mechanical thermal catalytic properties materials diffusion reactions nanoscale nanostructures materials nanodevices fast ion transport generally referred nanoionics ''mechanical'' properties nanosystems interest nanomechanics research catalytic activity nanomaterials also opens potential risks interaction biomaterials materials reduced nanoscale show different properties compared exhibit macroscale enabling unique applications instance opaque substances become transparent copper stable materials turn combustible aluminium insoluble materials may become soluble gold material gold chemically inert


normal scales serve potent chemical catalyst nanoscales much fascination nanotechnology stems quantum surface phenomena matter exhibits nanoscale simple complex molecular perspective modern synthetic chemistry reached point possible prepare small molecules almost structure methods used today manufacture wide variety useful chemicals pharmaceuticals commercial polymers ability raises question extending kind control next larger level seeking methods assemble single molecules supramolecular assemblies


consisting many molecules arranged well defined manner approaches utilize concepts molecular self assembly supramolecular chemistry automatically arrange useful conformation bottom approach concept molecular recognition especially important molecules designed specific configuration arrangement favored due non covalent intermolecular forces watson crick basepairing rules direct result specificity enzyme targeted single substrate specific folding protein thus two components designed


complementary mutually attractive make complex useful whole bottom approaches capable producing devices parallel much cheaper top methods could potentially overwhelmed size complexity desired assembly increases useful structures require complex thermodynamically unlikely arrangements atoms nevertheless many examples self assembly based molecular recognition biology notably watson crick basepairing enzyme substrate interactions challenge nanotechnology whether principles used engineer new constructs addition natural ones molecular nanotechnology


referred future manufacturing technology based molecular machine systems premise molecular scale biological analogies traditional machine components demonstrated molecular machines possible countless examples found biology known sophisticated stochastically optimized biological machines produced hoped developments nanotechnology make possible construction means perhaps using biomimetic principles however drexler researchers proposed advanced nanotechnology although perhaps initially implemented biomimetic means ultimately could based mechanical engineering principles namely manufacturing technology based mechanical functionality


components gears bearings motors structural members would enable programmable positional assembly atomic specification physics engineering performance exemplar designs analyzed drexler 's book ''nanosystems'' general difficult assemble devices atomic scale one position atoms atoms comparable size stickiness another view put forth carlo montemagno future nanosystems hybrids silicon technology biological molecular machines richard smalley argued mechanosynthesis impossible due difficulties mechanically manipulating individual molecules led


exchange letters acs publication chemical engineering news though biology clearly demonstrates molecular machine systems possible non biological molecular machines today infancy leaders research non biological molecular machines dr alex zettl colleagues lawrence berkeley laboratories uc berkeley http researchphysicsberkeleyedu zettl constructed least three distinct molecular devices whose motion controlled desktop changing voltage nanotube nanomotor molecular actuator nanoelectromechanical relaxation oscillator see nanotube nanomotor examples experiment indicating positional molecular assembly possible


rotating view c sub sub one kind fullerene device transfers energy nano thin layers quantum wells nanocrystals causing nanocrystals emit visible light nanomaterials nanomaterials field includes subfields develop study materials unique properties arising nanoscale dimensions interface colloid science given rise many materials may useful nanotechnology carbon nanotubes fullerenes various nanoparticles nanorods nanomaterials fast ion transport related also nanoionics nanoelectronics nanoscale materials also used bulk applications present commercial


nanotechnology utilizes specificity watson crick basepairing construct well defined structures dna nucleic acids approaches field classical chemical synthesis inorganic organic synthesis also aim designing molecules well defined shape eg bis peptides ref name levins ref generally molecular self assembly seeks use concepts supramolecular chemistry molecular recognition particular cause single molecule components automatically arrange useful conformation atomic force microscope tips used nanoscale write head deposit chemical upon surface desired pattern process called dip pen nanolithography


received nobel prize physics discovery giant magnetoresistance contributions field spintronics solid state techniques also used create devices known nanoelectromechanical systems nems related microelectromechanical systems mems focused ion beams directly remove material even deposit material suitable precursor gasses applied time example technique used routinely create sub nbsp nm sections material analysis transmission electron microscopy atomic force microscope tips used nanoscale write head deposit resist


followed etching process remove material top method functional approaches seek develop components desired functionality without regard might assembled magnetic assembly synthesis anisotropic superparamagnetic materials recently presented magnetic nano chains ref name referencea molecular scale electronics seeks develop molecules useful electronic properties could used single molecule components nanoelectronic device example see rotaxane synthetic chemical methods also used create synthetic molecular motors called nanocar biomimetic approaches bionics


created molecular nanotechnology proposed approach involves manipulating single molecules finely controlled deterministic ways theoretical subfields many proposed techniques beyond current capabilities nanorobotics centers self sufficient machines functionality operating nanoscale hopes applying nanorobots medicine nevertheless progress innovative materials methodologies demonstrated patents granted new nanomanufacturing devices future commercial applications also progressively helps development towards nanorobots use embedded nanobioelectronics concepts productive nanosystems systems nanosystems


complex nanosystems produce atomically precise parts nanosystems necessarily using novel nanoscale emergent properties well understood fundamentals manufacturing discrete ie atomic nature matter possibility exponential growth stage seen basis another industrial revolution mihail roco one architects usa 's national nanotechnology initiative proposed four states nanotechnology seem parallel technical progress industrial revolution progressing passive nanostructures active nanodevices complex nanomachines ultimately productive nanosystems programmable matter seeks design materials


whose properties easily reversibly externally controlled though fusion information science materials science due popularity media exposure term nanotechnology words picotechnology femtotechnology coined analogy although used rarely informally dimensionality nanomaterials nanomaterials classified nanomaterials dimensionality play major role determining characteristic nanomaterials including physical chemical biological characteristics decrease dimensionality increase surface volume ratio observed indicate smaller dimensional nanomaterials


two early versions scanning probes launched nanotechnology types scanning probe microscopy although conceptually similar scanning confocal microscope developed marvin minsky scanning acoustic microscope sam developed calvin quate coworkers newer scanning probe microscopes much higher resolution since limited wavelength sound light tip scanning probe also used manipulate nanostructures process called positional assembly feature oriented scanning methodology may promising way implement nanomanipulations automatic mode ref


name feature ref ref name fospm ref however still slow process low scanning velocity microscope various techniques nanolithography optical lithography x ray lithography dip pen nanolithography electron beam lithography nanoimprint lithography also developed lithography top fabrication technique bulk material reduced size nanoscale pattern another group nanotechnological techniques include used fabrication nanotubes nanowires used semiconductor fabrication deep ultraviolet lithography electron beam lithography focused ion beam machining nanoimprint lithography atomic layer deposition molecular vapor deposition including molecular


thin films another variation bottom approach molecular beam epitaxy mbe researchers bell telephone laboratories like john r arthur alfred cho art c gossard developed implemented mbe research tool late samples made mbe key discovery fractional quantum hall effect nobel prize physics awarded mbe allows scientists lay atomically precise layers atoms process build complex structures important research semiconductors mbe also widely used make


samples devices newly emerging field spintronics however new therapeutic products based responsive nanomaterials ultradeformable stress sensitive transfersome vesicles development already approved human use countries research development variety potential applications including industrial military governments invested billions dollars nanotechnology research prior usa invested billion using national nanotechnology initiative european union invested billion japan invested million sixty countries created nanotechnology research development r programs


us eu invested nanotechnology research followed japan global investment reached government funding exceeded corporate r spending nanotechnology research largest corporate r spenders us japan germany accounted combined ref name wipo ref class wikitable sortable top nanotechnology research organizations patents ref name wipo rank organization country first patents samsung electronics south korea nippon steel sumitomo metal japan ibm united states toshiba japan


canon inc japan hitachi japan university california berkeley united states panasonic japan hewlett packard united states tdk japan class wikitable sortable top nanotechnology research organizations scientific publications ref name wipo rank organization country scientific publications chinese academy sciences china russian academy sciences russia centre national de la recherche scientifique france university tokyo japan osaka university japan tohoku university japan


university california berkeley united states spanish national research council spain university illinois united states mit united states applications one major applications nanotechnology area nanoelectronics mosfet 's made small nanowires nm length simulation nanowire nanostructures provide surface superhydrophobicity lets water droplets roll inclined plane nanowire lasers ultrafast transmission information light pulses august project emerging nanotechnologies estimates


tennis balls last longer golf balls fly straighter even bowling balls become durable harder surface trousers socks infused nanotechnology last longer keep people cool summer bandages infused silver nanoparticles heal cuts faster ref name nnin ref video game consoles personal computers may become cheaper faster contain memory thanks nanotechnology also build structures chip computing light example chip optical quantum information processing picosecond transmission information nanotechnology may


ability make existing medical applications cheaper easier use places like general practitioner 's office home cars manufactured nanomaterials may need fewer metals less fuel operate future scientists turning nanotechnology attempt develop diesel engines cleaner exhaust fumes platinum currently used diesel engine catalyst engines catalyst cleans exhaust fume particles first reduction catalyst employed take nitrogen atoms nox molecules order free oxygen next oxidation


catalyst oxidizes hydrocarbons carbon monoxide form carbon dioxide water platinum used reduction oxidation catalysts using platinum though inefficient expensive unsustainable danish company innovationsfonden invested dkk million search new catalyst substitutes using nanotechnology goal project launched autumn maximize surface area minimize amount material required objects tend minimize surface energy two drops water example join form one drop decrease surface area


catalyst 's surface area exposed exhaust fumes maximized efficiency catalyst maximized team working project aims create nanoparticles merge every time surface optimized material saved thus creating nanoparticles increase effectiveness resulting diesel engine catalyst turn leading cleaner exhaust fumes decrease cost successful team hopes reduce platinum use nanotechnology also prominent role fast developing field tissue engineering designing scaffolds researchers attempt mimic nanoscale features


electronics began production nm process ref name tomshardware ref tsmc began production nbsp nm process ref name tsmc nm ref samsung began production nbsp nm process samsung announced plans commercial production nm gaafet process commercial production nanoelectronic semiconductor memory also began sk hynix began mass production nm nand flash memory ref name hynix samsung began production nm multi level cell mlc nand flash memory ref name tomshardware tsmc began production sram memory using nbsp nm process ref name tsmc nm implications area concern


effect industrial scale manufacturing use nanomaterials would human health environment suggested nanotoxicology research reasons groups advocate nanotechnology regulated governments others counter overregulation would stifle scientific research development beneficial innovations public health research agencies national institute occupational safety health actively conducting research potential health effects stemming exposures nanoparticles ref name niosh ref ref name nioshnano ref nanoparticle products may unintended consequences researchers discovered bacteriostatic silver nanoparticles used socks reduce foot odor released


wash particles flushed waste water stream may destroy bacteria critical components natural ecosystems farms waste treatment processes public deliberations risk perception us uk carried center nanotechnology society found participants positive nanotechnologies energy applications health applications health applications raising moral ethical dilemmas cost availability ref name harthorn harthorn barbara herr january http nanotechnologytodayblogspotcom people us uk show stronghtml people us uk show strong similarities attitudes toward nanotechnologies nanotechnology


pulmonary diseases eg fibrosis researchers found rats breathed nanoparticles particles settled brain lungs led significant increases biomarkers inflammation stress response nanoparticles induce skin aging oxidative stress hairless mice two year study ucla 's school public health found lab mice consuming nano titanium dioxide showed dna chromosome damage degree linked big killers man namely cancer heart disease neurological disease aging major study published recently nature nanotechnology suggests forms carbon nanotubes


poster child nanotechnology revolution could harmful asbestos inhaled sufficient quantities anthony seaton institute occupational medicine edinburgh scotland contributed article carbon nanotubes said know probably potential cause mesothelioma sorts materials need handled carefully absence specific regulation forthcoming governments paull lyons called exclusion engineered nanoparticles food newspaper article reports workers paint factory developed serious lung


disease nanoparticles found lungs ref name bbcfibre https wwwbbccouk news health nanofibres 'may pose health risk' bbc ref regulation calls tighter regulation nanotechnology occurred alongside growing debate related human health safety risks nanotechnology significant debate responsible regulation nanotechnology regulatory agencies currently cover nanotechnology products processes varying degrees bolting nanotechnology existing regulations clear gaps regimes davies proposed regulatory road map describing steps deal shortcomings stakeholders concerned


lack regulatory framework assess control risks associated release nanoparticles nanotubes drawn parallels bovine spongiform encephalopathy mad cow disease thalidomide genetically modified food nuclear energy reproductive technologies biotechnology asbestosis dr andrew maynard chief science advisor woodrow wilson center 's project emerging nanotechnologies concludes insufficient funding human health safety research result currently limited understanding human health safety risks associated nanotechnology result academics called stricter application precautionary principle


energy health applications suggesting public calls nano regulations may differ technology sector ref name harthorn see also carbon nanotube electrostatic deflection molecular physics nanotechnology energy applications nanotechnology ethics nanotechnologies ion implantation induced nanoparticle formation gold nanoparticle list emerging technologies list nanotechnology organizations list software nanostructures modeling magnetic nanochains materiomics nano thermite molecular design software molecular mechanics nanobiotechnology nanoelectromechanical relay nanoengineering nanofluidics nanohub nanometrology nanoparticle nanoscale networks nanotechnology education nanotechnology fiction nanotechnology water treatment nanoweapons national nanotechnology initiative self assembly nanoparticles top bottom translational research wet nanotechnology references external links


http wwwvegaorguk video programme nanotechnology vega bbc ou video discussion introductions introductions articles containing video clips emerging technologies neologisms neologisms


'''nutrition''' biochemical physiological process organism uses food support life includes ingestion absorption assimilation biosynthesis catabolism excretion science studies physiological process nutrition called nutritional science also ''nutrition science'' nutritional groups organisms primarily provide carbon one two ways autotrophy self production organic food heterotrophy consumption existing organic carbon combined source energy either light phototrophy chemical chemotrophy four primary nutritional groups organisms nutrients ''nutrients'' substances used


food necessary support human life good health humans poor nutrition cause deficiency related diseases blindness anemia scurvy preterm birth stillbirth cretinism ref name whitney rolfes lead ref nutrient excess health threatening conditions obesity metabolic syndrome common chronic systemic diseases cardiovascular disease diabetes osteoporosis undernutrition lead wasting acute cases stunting marasmus chronic cases malnutrition ref name whitney rolfes lead animal nutrition ''animal nutrition'' focuses dietary nutrients needs animals often comparison contrast organisms like plants carnivore herbivore diets


contrasting basic nitrogen carbon proportions vary particular foods many herbivores rely bacterial fermentation create digestible nutrients indigestible plant cellulose obligate carnivores must eat animal meats obtain certain vitamins nutrients bodies cannot otherwise synthesize animals generally higher requirement energy comparison plants plant nutrition ''plant nutrition'' study chemical elements necessary plant growth several principles apply plant nutrition elements directly involved plant metabolism however principle account called beneficial


elements whose presence required clear positive effects plant growth nutrient limit plant growth according liebig 's law minimum considered essential plant nutrient plant cannot complete full life cycle without essential plant soil nutrients besides three major elemental nutrients carbon oxygen obtained photosynthetic plants carbon dioxide air hydrogen obtained water plants uptake essential elements soil roots air consisting mainly nitrogen oxygen


leaves green plants obtain carbohydrate supply carbon dioxide air process photosynthesis carbon oxygen absorbed air nutrients absorbed soil nutrient uptake soil achieved cation exchange wherein root hairs pump hydrogen ions h sup sup soil proton pumps hydrogen ions displace cations attached negatively charged soil particles cations available uptake root leaves stomata open take carbon dioxide expel oxygen carbon dioxide molecules used


carbon source photosynthesis although nitrogen plentiful earth 's atmosphere plants use directly plants therefore require nitrogen compounds present soil grow made possible fact largely inert atmospheric nitrogen changed nitrogen fixation process biologically usable forms soil bacteria plant nutrition difficult subject understand completely partially variation different plants even different species individuals given clone elements present low levels may cause


deficiency symptoms toxicity possible levels high furthermore deficiency one element may present symptoms toxicity another element vice versa see also auxology exercise nutrition psychology physical fitness references bibliography curley mark ''the natural guide good health'' lafayette louisiana supreme publishing external links https wwwwhoint nutrition topics dietnutrition chronicdiseases en diet nutrition prevention chronic diseases joint fao expert consultation http wwwunscnorg un standing committee nutrition english french portuguese self care


distribution prime numbers central point study number theory ulam spiral serves illustrate hinting particular conditional independence prime value certain quadratic polynomials '''number theory''' '''arithmetic''' '''higher arithmetic''' older usage branch pure mathematics devoted primarily study integers integer valued functions german mathematician carl friedrich gauss said mathematics queen sciences number theory queen mathematics ref group note german original die mathematik ist die k nigin der wissenschaften und die arithmetik

Formal science
Mathematics
Pure mathematics
Number theory


ist die k nigin der mathematik ref number theorists study prime numbers well properties mathematical objects made integers example rational numbers defined generalizations integers example algebraic integers integers considered either solutions equations diophantine geometry questions number theory often best understood study analytical objects example riemann zeta function encode properties integers primes number theoretic objects fashion analytic number theory one may also study real numbers relation rational numbers


use term ''arithmetic'' ''number theory'' regained ground second half th century arguably part due french influence ref group note take example davenport still specify meant ''the higher arithmetic'' hardy wright wrote introduction ''an introduction theory numbers'' proposed one time change title ''an introduction arithmetic'' novel ways appropriate title pointed might lead misunderstandings content


book ref particular ''arithmetical'' commonly preferred adjective ''number theoretic'' history origins dawn arithmetic plimpton tablet earliest historical find arithmetical nature fragment table broken clay tablet plimpton larsa mesopotamia ca bce contains list pythagorean triples integers math abc math math b c math triples many large obtained brute force heading first column reads ''takiltum'' diagonal subtracted width table 's layout suggests


constructed means amounts modern language identity math left frac left x frac x right right left frac left x frac x right right math implicit routine old babylonian exercises method used triples first constructed reordered math c math presumably actual use table example view applications known applications may whether could babylonian astronomy example truly came later suggested instead


takes issue notion scribe produced plimpton work living would belonged leisured middle class could motivated idle curiosity absence market new mathematics ref babylonian number theory survives babylonian mathematics called thus consists single striking fragment babylonian algebra secondary school sense algebra exceptionally well developed late neoplatonic sources ref name vanderw iamblichus ''life pythagoras'' trans example cited see also porphyry ''life pythagoras'' paragraph


van der waerden sustains view thales knew babylonian mathematics ref state pythagoras learned mathematics babylonians much earlier sources ref name stanencyc herodotus ii isocrates ''busiris'' cited thales see eudemus ap proclus example cited proclus using work eudemus rhodes lost ''catalogue geometers'' see also introduction proclus 's reliability ref state thales pythagoras traveled studied egypt euclid ix probably pythagorean ref name becker cited ref simple material odd times even even


terms numbers could irrational discovery seems provoked first foundational crisis mathematical history proof divulgation sometimes credited hippasus expelled split pythagorean sect forced distinction ''numbers'' integers rationals subjects arithmetic one hand ''lengths'' ''proportions'' would identify real numbers whether rational hand pythagorean tradition spoke also called polygonal figurate numbers square numbers cubic numbers etc seen natural triangular numbers


pentagonal numbers etc study sums triangular pentagonal numbers would prove fruitful early modern period th early th century know clearly arithmetical material ancient egyptian vedic sources though algebra chinese remainder theorem appears exercise ''sunzi suanjing'' rd th th century ce ref name yongse date text narrowed ce yan dunjie ce wang ling internal evidence taxation systems assumed text see ref one important step


glossed sunzi 's solution ref group note ''sunzi suanjing'' ch problem blockquote unknown number things count threes remainder count fives remainder count sevens remainder find number things ''answer'' br ''method'' count threes remainder put count fives remainder put count sevens remainder


put add obtain subtract get answer count threes remainder put count fives remainder put count sevens remainder put number exceeds result obtained subtracting blockquote ref problem later solved ryabha 's ku aka see also numerical mysticism chinese mathematics ref group note see example ''sunzi suanjing'' ch problem


male remainder even sex female blockquote last problem sunzi 's otherwise matter fact treatise ref unlike pythagoreans seems led nowhere like pythagoreans' perfect numbers magic squares passed superstition recreation classical greece early hellenistic period aside fragments mathematics classical greece known us either reports contemporary non mathematicians mathematical works early hellenistic period case number theory means large ''plato'' ''euclid'' respectively asian


mathematics influenced greek hellenistic learning seems case greek mathematics also indigenous tradition eusebius pe x chapter mentions pythagoras blockquote fact said pythagoras busily studying wisdom nation visited babylon egypt persia instructed magi priests addition related studied brahmans indian philosophers gathered astrology others geometry arithmetic music others different things different nations wise


men greece get nothing wedded poverty dearth wisdom contrary became author instruction greeks learning procured abroad blockquote aristotle claimed philosophy plato closely followed teachings pythagoreans cicero repeats claim ''platonem ferunt didicisse pythagorea omnia'' say plato learned things pythagorean plato keen interest mathematics distinguished clearly arithmetic calculation ''arithmetic'' meant part theorising number rather ''arithmetic''


elements particular gave algorithm computing greatest common divisor two numbers euclidean algorithm ''elements'' prop vii first known proof infinitude primes ''elements'' prop ix lessing published epigram found manuscript work librarian claimed letter sent archimedes eratosthenes epigram proposed become known archimedes 's cattle problem solution absent manuscript requires solving indeterminate quadratic equation reduces would later misnamed pell 's equation far


invariably find rational solutions system polynomial equations usually form math f xy z math math f xyz w math thus nowadays speak ''diophantine equations'' speak polynomial equations rational integer solutions must found one may say diophantus studying rational points points whose coordinates rational curves algebraic varieties however unlike greeks classical period would call basic algebra geometrical terms diophantus would call basic algebraic geometry purely algebraic terms modern language diophantus


find rational parametrizations varieties given equation form say math f x x x math aim find essence three rational functions math g g g math values math r math math math setting math x g rs math math math gives solution math f x x x math diophantus also studied equations non rational curves rational parametrisation possible managed find rational points curves elliptic curves happens seems first known occurrence means amounts tangent construction


translated coordinate geometry exist diophantus 's time method would visualised drawing tangent curve known rational point finding point intersection tangent curve point new rational point diophantus also resorted could called special case secant construction diophantus concerned largely rational solutions assumed results integer numbers particular every integer sum four squares though never stated much explicitly ryabha brahmagupta


bh skara greek astronomy probably influenced indian learning point introducing trigonometry seems case indian mathematics otherwise indigenous tradition ref name plofbab early contact babylonian indian mathematics remains conjectural ref particular evidence euclid 's elements reached india th century ryabha ce showed pairs simultaneous congruences math n equiv bmod math math n equiv bmod math could solved method called ''ku aka'' ''pulveriser'' procedure close generalisation euclidean algorithm probably discovered independently


century indian mathematics remained largely unknown europe late eighteenth century brahmagupta bh skara 's work translated english henry colebrooke arithmetic islamic golden age al haytham seen west frontispiece ''selenographia'' alhasen represents knowledge reason galileo knowledge senses early ninth century caliph al ma'mun ordered translations many greek mathematical works least one sanskrit work ''sindhind'' may may ref name plofnot cited ref brahmagupta 's br hmasphu asiddh nta diophantus 's main work ''arithmetica'' translated


little interest nowadays true medieval times whether west arab speaking world due part importance given neopythagorean hence mystical nicomachus ca ce wrote primitive influential introduction arithmetic see ref topics led work integer divisors beginning among subjects correspondence onwards put touch mathematical community day fermat claimed without proof whole numbers expressed


sum four squares fewer fermat 's little theorem ''a'' divisible prime ''p'' math p equiv bmod p math ref group note usual given two integers ''a'' ''b'' non zero integer ''m'' write math equiv b bmod math read ''a'' congruent ''b'' modulo ''m'' mean ''m'' divides ''a'' nbsp nbsp ''b'' ''a'' ''b'' leave residue divided ''m'' notation actually much later fermat 's first appears section gauss 's disquisitiones arithmeticae fermat 's little theorem consequence


fact order element group divides order group modern proof would within fermat 's means indeed given later euler even though modern concept group came long fermat euler helps know inverses exist modulo ''p'' given ''a'' divisible prime ''p'' integer ''x'' math x equiv bmod p math fact modern language makes residues mod ''p'' group already known


ryabha see familiar fermat thanks rediscovery bachet weil goes say fermat would recognised bachet 's argument essentially euclid 's algorithm ref ''a'' ''b'' coprime math b math divisible prime congruent modulo every prime congruent modulo written form math b math two statements also date fermat stated huygens proven latter statement method infinite descent fermat posed


problem solving math x n math challenge english mathematicians problem solved months wallis brouncker fermat considered solution valid pointed provided algorithm without proof jayadeva bhaskara though fermat n't aware stated proof could found infinite descent fermat stated proved infinite descent appendix ''observations diophantus'' obs xlv math x z math non trivial solutions integers fermat also mentioned


correspondents math x z math non trivial solutions could also proven infinite descent first known proof due euler indeed infinite descent fermat claimed fermat 's last theorem shown solutions math x n n z n math math n geq math claim appears annotations margins copy diophantus euler leonhard euler interest leonhard euler number theory first spurred friend amateur ref group note second half


seventeenth century academic positions rare mathematicians scientists earned living way already recognisable features professional ''practice'' viz seeking correspondents visiting foreign colleagues building private libraries matters started shift late th century scientific academies founded england royal society france acad mie des sciences russia euler offered position last one accepted arriving st petersburg context term ''amateur'' usually applied


goldbach well defined makes sense described man letters earned living spy cited notice however goldbach published works mathematics sometimes held academic positions ref goldbach pointed towards fermat 's work subject called rebirth modern number theory fermat 's relative lack success getting contemporaries' attention subject euler 's work number theory includes following ''proofs fermat 's statements'' includes fermat 's little theorem generalised euler non prime moduli


research question primes expressed form math x n math prefiguring quadratic reciprocity ''diophantine equations'' euler worked diophantine equations genus particular studied diophantus 's work tried systematise time yet ripe endeavour algebraic geometry still infancy notice connection diophantine problems elliptic integrals whose study initiated wgbh access date march ref sir andrew wiles proof fermat 's last theorem lagrange legendre


gauss carl friedrich gauss 's disquisitiones arithmeticae first edition joseph louis lagrange first give full proofs fermat 's euler 's work observations instance four square theorem basic theory misnamed pell 's equation algorithmic solution found fermat contemporaries also jayadeva bhaskara ii also studied quadratic forms full generality opposed math x n math defining equivalence relation showing put reduced form etc adrien marie legendre first state law


quadratic reciprocity also conjectured amounts prime number theorem dirichlet 's theorem arithmetic progressions gave full treatment equation math x b c z math worked quadratic forms along lines later developed fully gauss old age first prove fermat 's last theorem math n math completing work peter gustav lejeune dirichlet crediting sophie germain carl friedrich gauss ''disquisitiones arithmeticae'' carl friedrich gauss proved law quadratic reciprocity developed theory


quadratic forms particular defining composition also introduced basic notation congruences devoted section computational matters including primality tests last section ''disquisitiones'' established link roots unity number theory blockquote theory division circlewhich treated sec belong arithmetic principles drawn higher arithmetic blockquote way gauss arguably made first foray towards variste galois 's work algebraic number theory maturity division subfields ernst kummer peter gustav lejeune dirichlet


starting early nineteenth century following developments gradually took place rise self consciousness number theory ''higher arithmetic'' field study development much modern mathematics necessary basic modern number theory complex analysis group theory galois theory accompanied greater rigor analysis abstraction algebra rough subdivision number theory modern subfields particular analytic algebraic number theory algebraic number theory may said start study reciprocity cyclotomy truly came development abstract algebra early


ideal theory valuation theory see conventional starting point analytic number theory dirichlet 's theorem arithmetic progressions whose proof introduced l functions involved asymptotic analysis limiting process real variable first use analytic ideas number theory actually goes back euler used formal power series non rigorous implicit limiting arguments use ''complex'' analysis number theory comes later work bernhard riemann zeta function canonical starting point jacobi 's four square theorem predates belongs


initially different strand taken leading role analytic number theory modular forms history subfield briefly addressed section see main article subfield fuller treatments many interesting questions area remain open actively worked main subdivisions elementary number theory term ''elementary'' generally denotes method use complex analysis example prime number theorem first proven using complex analysis elementary proof found


erd selberg term somewhat ambiguous example proofs based complex tauberian theorems example wiener ikehara often seen quite enlightening elementary spite using fourier analysis rather complex analysis elsewhere ''elementary'' proof may longer difficult readers non elementary one number theorists paul erd terence tao erd tao number theory reputation field many whose results stated layperson time


proofs results particularly accessible part range tools use anything unusually broad within mathematics analytic number theory riemann zeta function ' 's'' complex plane color point ' 's'' gives value ' 's'' dark colors denote values close zero hue gives value 's argument action modular group upper half plane region grey standard fundamental domain ''analytic number theory'' may defined terms tools study integers means


tools real complex analysis terms concerns study within number theory estimates size density opposed identities subjects generally considered part analytic number theory example sieve theory ref group note sieve theory figures one main subareas analytic number theory many standard treatments see instance ref better covered second rather first definition sieve theory instance uses little analysis ref group note case small sieves particular combinatorial sieves


brun sieve rather large sieves study latter includes ideas harmonic functional analysis ref yet belong analytic number theory following examples problems analytic number theory prime number theorem goldbach conjecture twin prime conjecture hardy littlewood conjectures waring problem riemann hypothesis important tools analytic number theory circle method sieve methods l functions rather study properties theory modular forms generally automorphic forms also occupies


example general procedure analytic number theory deriving information distribution sequence prime ideals prime numbers analytic behavior appropriately constructed complex valued function algebraic number theory ''algebraic number'' complex number solution polynomial equation math f x math rational coefficients example every solution math x math math x x x math say algebraic number fields algebraic numbers also called ''algebraic number fields'' shortly ''number fields'' algebraic number theory studies algebraic number fields


thus analytic algebraic number theory overlap former defined methods latter objects study could argued simplest kind number fields viz quadratic fields already studied gauss discussion quadratic forms ''disquisitiones arithmeticae'' restated terms ideals norms quadratic fields ''quadratic field'' consists numbers form math b sqrt math math math math b math rational numbers math math fixed rational number whose square root rational


matter th century chakravala method amounts modern terms algorithm finding units real quadratic number field however neither bh skara gauss knew number fields grounds subject know set late nineteenth century ''ideal numbers'' ''theory ideals'' ''valuation theory'' developed three complementary ways dealing lack unique factorisation algebraic number fields example field generated rationals math sqrt math number math math factorised math


cdot math math sqrt sqrt math math math math math math sqrt math math sqrt math irreducible thus na sense analogous primes among integers initial impetus development ideal numbers kummer seems come study higher reciprocity laws generalisations quadratic reciprocity number fields often studied extensions smaller number fields field ''l'' said ''extension'' field ''k'' ''l'' contains ''k'' example complex


numbers ''c'' extension reals ''r'' reals ''r'' extension rationals ''q'' classifying possible extensions given number field difficult partially open problem abelian extensions extensions ''l'' ''k'' galois group ref group note galois group extension ''l k'' consists operations isomorphisms send elements l elements l leaving elements k fixed thus instance ''gal c r '' consists two elements identity element taking every element ''x'' nbsp nbsp ''iy'' ''c'' complex conjugation


map taking element ''x'' nbsp nbsp ''iy'' ''x'' nbsp nbsp ''iy'' galois group extension tells us many crucial properties study galois groups started variste galois modern language main outcome work equation ''f'' ''x'' nbsp nbsp solved radicals ''x'' expressed terms four basic operations together square roots cubic roots etc extension rationals roots equation ''f'' ''x'' nbsp nbsp galois group solvable sense group theory solvable


sense group theory simple property checked easily finite groups ref gal ''l'' ''k'' ''l'' ''k'' abelian group relatively well understood classification object programme class field theory initiated late th century partly kronecker eisenstein carried largely example active area research algebraic number theory iwasawa theory langlands program one main current large scale research plans mathematics sometimes described attempt generalise class field theory non abelian


extensions number fields diophantine geometry central problem ''diophantine geometry'' determine diophantine equation solutions many approach taken think solutions equation geometric object example equation two variables defines curve plane generally equation system equations two variables defines curve surface object ''n'' dimensional space diophantine geometry one asks whether ''rational points'' points whose coordinates rationals


''integral points'' points whose coordinates integers curve surface points next step ask many distributed basic question direction finitely infinitely many rational points given curve surface pythagorean equation math x math would like study rational solutions solutions math xy math ''x'' ''y'' rational asking integer solutions math b


c math solution latter equation gives us solution math x c math math b c math former also asking points rational coordinates curve described math x math curve happens circle radius around origin two examples elliptic curve curve genus least one rational point either graph seen slice torus four dimensional space rephrasing questions equations terms points


curves turns felicitous finiteness number rational integer points algebraic curve rational integer solutions equation math f xy math math f math polynomial two variables turns depend crucially ''genus'' curve ''genus'' defined follows ref group note want study curve math x math allow ''x'' ''y'' complex numbers math b c math effect set two equations four


variables since real imaginary part side must match result get surface two dimensional four dimensional space choose convenient hyperplane project surface meaning say choose ignore coordinate ''a'' plot resulting projection surface ordinary three dimensional space becomes clear result torus loosely speaking surface doughnut somewhat stretched doughnut one hole hence genus ref allow variables math f xy math complex numbers


math f xy math defines dimensional surface projective dimensional space since two complex variables decomposed four real variables four dimensions count number doughnut holes surface call number ''genus'' math f xy math geometrical notions turn crucial also closely linked area diophantine approximations given number math x math finding well approximated rationals looking approximations good relative amount space takes write rational call math q math


based older material example explained matter algorithms number theory old sense older concept proof time modern study computability dates computational complexity theory probabilistic number theory much probabilistic number theory seen important special case study variables almost quite mutually independent example event random integer one million divisible


two event divisible three almost independent quite sometimes said probabilistic combinatorics uses fact whatever happens probability greater math math must happen sometimes one may say equal justice many applications probabilistic number theory hinge fact whatever unusual must rare certain algebraic objects say rational integer solutions certain equations shown tail certain sensibly defined distributions follows must concrete


non probabilistic statement following probabilistic one times non rigorous probabilistic approach leads number heuristic algorithms open problems notably cram r 's conjecture arithmetic combinatorics begin fairly thick infinite set math math contain many elements arithmetic progression math math math b b b ldots b math say possible write large integers sums elements math math questions characteristic ''arithmetic combinatorics'' presently coalescing field subsumes ''additive number theory'' concerns certain specific sets math math arithmetic significance


primes squares arguably ''geometry numbers'' together rapidly developing new material focus issues growth distribution accounts part developing links ergodic theory finite group theory model theory fields term ''additive combinatorics'' also used however sets math math studied need sets integers rather subsets non commutative groups multiplication symbol addition symbol traditionally used also subsets rings case growth math math math math math math


number prime split prime factors rapidly another matter know fast algorithms testing primality spite much work theoretical practical truly fast algorithm factoring difficulty computation useful modern protocols encrypting messages example rsa depend functions known whose inverses known chosen would take one long time figure one 's example functions


inverses computed certain large integers factorized many difficult computational problems outside number theory known working encryption protocols nowadays based difficulty number theoretical problems things may computable fact proven instances instance proven solution hilbert 's th problem turing machine solve diophantine equations particular means given computably enumerable set axioms diophantine equations


proof starting axioms whether set equations integer solutions would necessarily speaking diophantine equations integer solutions since given diophantine equation least one solution solution provides proof fact solution exists cannot prove particular diophantine equation kind since would imply solutions applications number theorist leonard dickson said thank god number theory unsullied application view


longer applicable number theory donald knuth said virtually every theorem elementary number theory arises natural motivated way connection problem making computers high speed numerical calculations elementary number theory taught discrete mathematics courses computer scientists hand number theory also applications continuous numerical analysis well well known applications cryptography also applications many areas mathematics prizes american mathematical society awards ''cole prize number theory'' moreover number theory one three


book euclid 's elements publisher princeton university press isbn url https booksgooglecom booksid jzehj femqac pg pa last neugebauer first otto e last sachs first abraham joseph last g tze first albrecht year author link otto e neugebauer author link abraham sachs title mathematical cuneiform texts series american oriental series volume publisher american oriental society etc last pingree first david last ya'qub first ibn tariq author link david pingree author link ya q b ibn riq year title fragments works ya'qub ibn tariq journal journal near eastern studies volume last pingree first last al fazari year author link al fazari title fragments works al fazari journal journal near eastern studies volume last tannery first paul author link paul tannery last henry first charles eds author link charles henry librarian year last fermat first pierre de author link pierre de fermat


language fr la title oeuvres de fermat series vols location paris publisher imprimerie gauthier villars et fils url https archiveorg details oeuvresdefermat ferm https archiveorg details oeuvresdefermat ferm volume https archiveorg details oeuvresdefermat ferm volume https archiveorg details oeuvresdefermat ferm volume https archiveorg details oeuvresdefermat ferm volume last taylor first thomas trans author link thomas taylor neoplatonist year author iamblichus author link iamblichus title life pythagoras pythagoric life location london publisher jm watkins url http wwwaurumsolisinfo indexphpoption com phocadownload view category download aiamblichus pythagorean life id awritings founders itemid lang en url status bot unknown archive url https webarchiveorg web http wwwaurumsolisinfo indexphpoption com phocadownload view category download aiamblichus pythagorean life id awritings founders itemid lang en archive date editions see iamblichus list editions translations google books preview ''elements algebra'' lacks truesdell 's intro reprinted slightly abridged following book last van der waerden first bartel l last dresden first arnold trans year author link bartel leendert van der waerden title science awakening volume vol vol


location new york publisher oxford university press reading two popular introductions subject hardy wright 's book comprehensive classic though clarity sometimes suffers due authors' insistence elementary methods apostol nd vinogradov 's main attraction consists set problems quickly lead vinogradov 's research interests text basic close minimal popular first introductions popular choices second textbook include external links https encyclopediaofmathorg wiki number theory number theory entry encyclopedia mathematics http wwwnumbertheoryorg number theory web


'''nanoengineering''' practice engineering nanoscale derives name nanometre unit measurement equalling one billionth meter nanoengineering largely synonym nanotechnology emphasizes engineering rather pure science aspects field history th century rome lycurgus cup crafted using dichroic glass product nanoengineering th th centuries stained glass windows created european cathedrals contained nanoparticles gold chloride metal oxides chlorides nanoparticles give glass vibrant colors th th centuries

Applied science
Engineering and technology
Mechanical Engineering
Nanoengineering


atoms carbon nanotube discovered sumio iijima became important due strength electrical thermal conductivity suny albany started first college program focused nanoengineering united states called college nanoscale science engineering robotic nanoscale assembly devices created nadrian seeman colleagues devices would used create dna structures using dna crystals degree programs first nanoengineering program started university toronto within engineering science program one options study


final years lund institute technology started program nanoengineering college nanoscale science engineering suny polytechnic institute established campus university albany university waterloo established unique program offers full degree nanotechnology engineering louisiana tech university started first program us university duisburg essen started bachelor master program nanoengineering unlike early nanoengineering programs first nanoengineering department world offering undergraduate graduate degrees


established university california san diego university toronto began offering options study engineering science degrees bringing second nanoengineering degree canada rice university established department materials science nanoengineering msne dtu nanotech department micro nanotechnology department technical university denmark established wayne state university began offering nanoengineering undergraduate certificate program funded nanoengineering undergraduate education nue grant national science foundation


primary goal offer specialized undergraduate training nanotechnology goals teach emerging technologies undergraduate level train new adaptive workforce retrain working engineers professionals techniques scanning tunneling microscope stm used image manipulate structures small single atom molecular self assembly arbitrary sequences dna synthesized cheaply bulk used create custom proteins regular patterns amino acids similarly dna strands bind dna strands allowing simple structures


created see also list nanoengineering topics nanotechnology picoengineering molecular engineering references external links http wwwnanoengineeringcom nanoengineering http wwwnanofraunhoferde english indexhtm alliance fraunhofer society nanotechnology engineering disciplines


well categorize organize documents challenges natural language processing frequently involve speech recognition natural language understanding natural language generation history natural language processing roots already alan turing published article titled computing machinery intelligence proposed called turing test criterion intelligence though time articulated problem separate artificial intelligence proposed test includes task involves automated interpretation generation natural language symbolic nlp

Humanities
Languages and literature
Linguistics
Natural language processing


time included research rule based parsing eg development hpsg computational operationalization generative grammar morphology eg two level morphology semantics eg lesk algorithm reference eg within centering theory areas natural language understanding eg rhetorical structure theory lines research continued eg development chatterbots racter jabberwacky important development eventually led statistical turn rising importance quantitative evaluation period statistical nlp natural language processing systems based complex


sets hand written rules starting late however revolution natural language processing introduction machine learning algorithms language processing due steady increase computational power see moore 's law gradual lessening dominance chomskyan theories linguistics eg transformational grammar whose theoretical underpinnings discouraged sort corpus linguistics underlies machine learning approach language processing ''' s''' many notable early successes statistical methods nlp occurred field machine translation due especially work


limited amounts data ''' s''' growth web increasing amounts raw unannotated language data become available since mid research thus increasingly focused unsupervised semi supervised learning algorithms algorithms learn data hand annotated desired answers using combination annotated non annotated data generally task much difficult supervised learning typically produces less accurate results given amount input data however enormous amount non annotated data available including among things


entire content world wide web often make inferior results algorithm used low enough time complexity practical neural nlp present representation learning deep neural network style machine learning methods became widespread natural language processing popularity due partly flurry results showing techniques ref name goldberg nnlp ref ref name goodfellow book ref achieve state art results many natural language tasks eg language modeling ref name jozefowicz lm ref parsing ref name choe emnlp ref ref name vinyals nips ref increasingly important medicine healthcare nlp helps analyze notes


text electronic health records would otherwise inaccessible study seeking improve care methods rules statistics neural networks early days many language processing systems designed symbolic methods ie hand coding set rules coupled dictionary lookup ref name winograd shrdlu ref ref name schank ref writing grammars devising heuristic rules stemming recent systems based machine learning algorithms many advantages hand produced rules learning procedures used machine learning automatically focus common cases whereas writing rules hand often


rules made accurate increasing complexity rules much difficult task particular limit complexity systems based handwritten rules beyond systems become unmanageable however creating data input machine learning systems simply requires corresponding increase number man hours worked generally without significant increases complexity annotation process despite popularity machine learning nlp research symbolic methods still commonly used amount training data insufficient


successfully apply machine learning methods eg machine translation low resource languages provided apertium system preprocessing nlp pipelines eg tokenization postprocessing transforming output nlp pipelines eg knowledge extraction syntactic parses statistical methods since called statistical revolution ref name johnson eacl ilcl http wwwaclweborg anthology w mark johnson statistical revolution changes computational linguistics proceedings eacl workshop interaction linguistics computational linguistics ref ref name resnik langlog http languagelogldcupennedu nll p philip resnik four revolutions language log february ref late mid much natural language processing research


relied heavily machine learning machine learning paradigm calls instead using statistical inference automatically learn rules analysis large ''corpora'' plural form ''corpus'' set documents possibly human computer annotations typical real world examples many different classes machine learning algorithms applied natural language processing tasks algorithms take input large set features generated input data increasingly however research focused statistical models make soft probabilistic decisions based attaching real valued weights input feature complex valued embeddings neural


networks general also proposed eg speech models advantage express relative certainty many different possible answers rather one producing reliable results model included component larger system earliest used machine learning algorithms decision trees produced systems hard rules similar existing hand written rules however part speech tagging introduced use hidden markov models natural language processing increasingly research focused statistical models make soft probabilistic decisions based


new paradigm distinct statistical natural language processing instance term ''neural machine translation'' nmt emphasizes fact deep learning based approaches machine translation directly learn sequence sequence transformations obviating need intermediate steps word alignment language modeling used statistical machine translation smt latest works tend use non technical structure given task build proper neural network common nlp tasks following list commonly researched tasks natural language processing tasks direct real world applications


others commonly serve subtasks used aid solving larger tasks though natural language processing tasks closely intertwined subdivided categories convenience coarse division given text speech processing optical character recognition ocr given image representing printed text determine corresponding text speech recognition given sound clip person people speaking determine textual representation speech opposite text speech one extremely difficult problems colloquially termed ai complete see


natural speech hardly pauses successive words thus speech segmentation necessary subtask speech recognition see spoken languages sounds representing successive letters blend process termed coarticulation conversion analog signal discrete characters difficult process also given words language spoken people different accents speech recognition software must able recognize wide variety input identical terms textual equivalent


speech segmentation given sound clip person people speaking separate words subtask speech recognition typically grouped text speech given text transform units produce spoken representation text speech used aid visually impaired word segmentation tokenization separate chunk continuous text separate words language like english fairly trivial since words usually separated spaces however written languages like chinese japanese thai mark word boundaries fashion


grounds rules dictionary syntactic analysis grammar induction generate formal grammar describes language 's syntax sentence breaking also known sentence boundary disambiguation given chunk text find sentence boundaries sentence boundaries often marked periods punctuation marks characters serve purposes ''eg'' marking abbreviations parsing determine parse tree grammatical analysis given sentence grammar natural languages ambiguous typical sentences multiple possible analyses perhaps surprisingly typical sentence may thousands potential


parses seem completely nonsensical human two primary types parsing ' 'dependency parsing'' ''constituency parsing'' dependency parsing focuses relationships words sentence marking things like primary objects predicates whereas constituency parsing focuses building parse tree using probabilistic context free grammar pcfg see also ' 'stochastic grammar'' lexical semantics individual words context lexical semantics computational meaning individual words context distributional semantics learn semantic representations data named entity recognition ner given


arabic capitalization even languages capitalization may consistently use distinguish names example german capitalizes nouns regardless whether names french spanish capitalize names serve adjectives sentiment analysis see also multimodal sentiment analysis extract subjective information usually set documents often using online reviews determine polarity specific objects especially useful identifying trends public opinion social media marketing terminology extraction goal terminology extraction automatically


extract relevant terms given corpus word sense disambiguation wsd many words one meaning select meaning makes sense context problem typically given list words associated word senses eg dictionary online resource wordnet entity linking many words typically proper names refer named entities select entity famous individual location company etc referred context relational semantics semantics individual


sentences relationship extraction given chunk text identify relationships among named entities eg married semantic parsing given piece text typically sentence produce formal representation semantics either graph eg amr parsing accordance logical formalism eg drt parsing challenge typically includes aspects several elementary nlp tasks semantics eg semantic role labelling word sense disambiguation extended include full fledged discourse analysis eg discourse analysis coreference see natural language understanding semantic role


labelling see also implicit semantic role labelling given single sentence identify disambiguate semantic predicates eg verbal frames identify classify frame elements semantic roles discourse semantics beyond individual sentences coreference resolution given sentence larger chunk text determine words mentions refer objects entities anaphora resolution specific example task specifically concerned matching pronouns nouns names refer general task coreference resolution also includes identifying called bridging relationships involving referring expressions


example sentence entered john 's house front door front door referring expression bridging relationship identified fact door referred front door john 's house rather structure might also referred discourse analysis rubric includes several related tasks one task discourse parsing ie identifying discourse structure connected text ie nature discourse relationships sentences eg elaboration explanation contrast another possible task recognizing


classifying speech acts chunk text eg yes question content question statement assertion etc given single sentence identify disambiguate semantic predicates eg verbal frames explicit semantic roles current sentence see semantic role labelling identify semantic roles explicitly realized current sentence classify arguments explicitly realized elsewhere text specified resolve former local text closely related task zero anaphora resolution ie extension coreference resolution pro drop languages


recognizing textual entailment given two text fragments determine one true entails entails 's negation allows either true false ref name rte pascal recognizing textual entailment challenge rte https tacnistgov rte ref topic segmentation recognition given chunk text separate segments devoted topic identify topic segment argument mining goal argument mining automatic extraction identification argumentative structures natural language text aid computer programs argumentative structures include premise conclusions


argument scheme relationship main subsidiary argument main counter argument within discourse higher level nlp applications automatic summarization text summarization produce readable summary chunk text often used provide summaries text known type research papers articles financial section newspaper book generation nlp task proper extension natural language generation nlp tasks creation full fledged books first machine generated book created rule based system


racter ''the policeman 's beard half constructed'' first published work neural network published '' road'' marketed novel contains sixty million words systems basically elaborate non sensical semantics free language models first machine generated science book published beta writer ''lithium ion batteries'' springer cham unlike ''racter'' '' road'' grounded factual knowledge based text summarization dialogue management computer systems intended converse human document ai document ai platform sits top nlp technology enabling users


shared tasks since far orthography morphology syntax certain aspects semantics concerned due development powerful neural language models gpt considered largely solved problem marketed various commercial applications machine translation automatically translate text one human language another one difficult problems member class problems colloquially termed ai complete ie requiring different types knowledge humans possess grammar semantics facts real world


etc solve properly natural language generation nowiki nlg nowiki convert information computer databases semantic intents readable human language natural language understanding nlu convert chunks text formal representations first order logic structures easier computer programs manipulate natural language understanding involves identification intended semantic multiple possible semantics derived natural language expression usually takes form organized notations natural language concepts introduction creation language metamodel ontology efficient however empirical solutions explicit formalization


natural language semantics without confusions implicit assumptions closed world assumption cwa vs open world assumption subjective yes vs objective true false expected construction basis semantics formalization question answering given human language question determine answer typical questions specific right answer capital canada sometimes open ended questions also considered meaning life general tendencies possible future directions based long standing trends field possible extrapolate future directions nlp


three trends among topics long standing series conll shared tasks observed interest increasingly abstract cognitive aspects natural language shallow parsing named entity recognition dependency syntax semantic role labelling coreference discourse parsing semantic parsing increasing interest multilinguality potentially multimodality english since spanish dutch since german since bulgarian danish japanese portuguese slovenian swedish turkish since basque catalan chinese greek hungarian italian turkish since czech since arabic since languages languages elimination symbolic representations rule based


supervised towards weakly supervised methods representation learning end end systems cognition nlp higher level nlp applications involve aspects emulate intelligent behaviour apparent comprehension natural language broadly speaking technical operationalization increasingly advanced aspects cognitive behaviour represents one developmental trajectories nlp see trends among conll shared tasks cognition refers mental action process acquiring knowledge understanding thought experience senses cognitive science interdisciplinary scientific study mind processes cognitive linguistics interdisciplinary branch linguistics combining


knowledge research psychology linguistics especially age symbolic nlp area computational linguistics maintained strong ties cognitive studies example george lakoff offers methodology build natural language processing nlp algorithms perspective cognitive science along findings cognitive linguistics two defining aspects apply theory conceptual metaphor explained lakoff understanding one idea terms another provides idea intent author example consider english word '' big '' used comparison


although rarely made explicit see also '' road'' automated essay scoring biomedical text mining compound term processing computational linguistics computer assisted reviewing controlled natural language deep learning deep linguistic processing distributional semantics foreign language reading aid foreign language writing aid information extraction information retrieval language communication technologies language technology latent semantic indexing native language identification natural language programming natural language understanding natural language search outline natural language processing query expansion query understanding reification linguistics speech processing spoken dialogue systems text proofing text simplification transformer machine learning model truecasing question answering word vec references reading steven


bird ewan klein edward loper ''natural language processing python'' o'reilly media daniel jurafsky james h martin ''speech language processing'' nd edition pearson prentice hall mohamed zakaria kurdi ''natural language processing computational linguistics speech morphology syntax'' volume iste wiley mohamed zakaria kurdi ''natural language processing computational linguistics semantics discourse applications'' volume iste wiley christopher manning prabhakar raghavan hinrich sch tze ''introduction information retrieval'' cambridge university press http nlpstanfordedu ir book official html pdf versions available without charge christopher manning hinrich sch tze


''foundations statistical natural language processing'' mit press david w powers christopher c r turk ''machine learning natural language'' springer verlag external links computational linguistics speech recognition computational fields study artificial intelligence


'''neurosurgery''' '''neurological surgery''' known common parlance '''brain surgery''' medical specialty concerned prevention diagnosis surgical treatment rehabilitation disorders affect portion nervous system including brain spinal cord central peripheral nervous system cerebrovascular system education context different countries different requirements individual legally practice neurosurgery varying methods must educated countries neurosurgeon training requires minimum period seven years graduating medical school united states united states

Applied science
Medicine and health
Surgery
Neurosurgery


neurosurgeon must generally complete four years undergraduate education four years medical school seven years residency pgy ref name preul ref residency programs component basic science clinical research neurosurgeons may pursue additional training form fellowship residency cases senior resident form enfolded fellowship fellowships include pediatric neurosurgery trauma neurocritical care functional stereotactic surgery surgical neuro oncology radiosurgery neurovascular surgery skull base surgery peripheral nerve complex spinal surgery ref name pmid ref fellowships typically span one two years us


neurosurgery small specialty constituting percent physicians united kingdom united kingdom students must gain entry medical school mbbs qualification bachelor medicine bachelor surgery takes four six years depending student 's route newly qualified physician must complete foundation training lasting two years paid training program hospital clinical setting covering range medical specialties including surgery junior doctors apply enter neurosurgical pathway unlike surgical specialties currently independent training pathway takes around


eight years st able sit consultant exams sufficient amounts experience practice behind neurosurgery remains consistently amongst competitive medical specialties obtain entry history neurosurgery premeditated incision head pain relief around thousands years notable advancements neurosurgery come within last hundred years thumb ancient incas appear practiced procedure known trepanation since european colonization middle ages al andalus ad al zahrawi performed surgical treatments head


injuries skull fractures spinal injuries hydrocephalus subdural effusions headache china hua tuo created first general anaesthesia called mafeisan used surgical procedures brain modern '''history tumor removal''' locating via neurological signs alone scottish surgeon william macewen performed first successful brain tumor removal ref name preul november english physician '''alexander hughes bennett''' used macewen 's technique locate english surgeon rickman godlee performed first primary brain tumor removal ref name pmid differs macewen 's operation bennett operated exposed


brain whereas macewen operated outside brain proper via trepanation ref name uakron gage surgery ref march austrian surgeon hermann schloffer became first successfully remove pituitary tumor ref name neurosurgeryorg cybermuseum microneurohall jhardy ref '''lobotomy''' also known '''leucotomy''' form psychosurgery neurosurgical treatment mental disorders involves severing connections brain 's prefrontal cortexthe originator procedure portuguese neurologist ant nio egas moniz shared nobel prize physiology medicine patients improved ways operation complications impairmentssometimes severewere frequent procedure controversial


initial use part due balance benefits risks mostly rejected humane form treatment preserve patients' rights '''history electrodes brain''' richard caton discovered electrical signals transmitted animal 's brain dr jose delgado invented first electrode implanted animal 's brain bull using make run change direction cochlear implant neurological prosthetic allowed deaf people hear marketed commercial use researcher philip kennedy implanted first


hand held power saws robots recently commonly used inside neurological operating room example university utah developed device computer aided design computer aided manufacturing cad cam uses image guided system define cutting tool path robotic cranial drill organised neurosurgery world academy neurological surgery 's conference '''world federation neurosurgical societies''' '''wfns''' founded switzerland professional scientific non governmental organization composed member societies consisting continental associations aans aasns caans eans flanc


affiliate societies national neurosurgical societies representing neurosurgeons worldwide consultative status united nations official journal organization world neurosurgery ref name journal ref ref name elsevier ref global organisations world academy neurological surgery wans world federation skull base societies wfsbs main divisions general neurosurgery involves neurosurgical conditions including neuro trauma neuro emergencies intracranial hemorrhage level hospitals kind practice specialized branches developed cater special difficult conditions specialized branches co exist general neurosurgery


sophisticated hospitals practice advanced specialization within neurosurgery additional higher fellowship training one two years expected neurosurgeon divisions neurosurgery vascular neurosurgery includes clipping aneurysms performing carotid endarterectomy cea stereotactic neurosurgery functional neurosurgery epilepsy surgery latter includes partial total corpus callosotomy severing part corpus callosum stop lessen seizure spread activity surgical removal functional physiological anatomical pieces divisions brain called epileptic foci operable causing seizures


also radical rare partial total lobectomy even hemispherectomy removal part one lobes one cerebral hemispheres brain two procedures possible also rarely used oncological neurosurgery treat severe neurological trauma stab gunshot wounds brain oncological neurosurgery also called neurosurgical oncology includes pediatric oncological neurosurgery treatment benign malignant central peripheral nervous system cancers pre cancerous lesions adults children including among others glioblastoma multiforme


include muscle fibers nervous tissue common applications neuropathology include studying samples tissue patients parkinson 's disease alzheimer 's disease dementia huntington 's disease amyotrophic lateral sclerosis mitochondria disease disorder neural deterioration brain spinal cord history pathology studied millennia within last hundred years medicine focused tissue organ based approach tissue disease thomas hodgkin started look damaged tissue cause conjoined emergence microscopy started current understanding


tissue human body studied neuroanesthesia neuroanesthesia field anesthesiology focuses neurosurgery anesthesia used middle awake brain surgery awake brain surgery patient conscious middle procedure sedated beginning end procedure used tumor clear boundaries surgeon wants know invading critical regions brain involve functions like talking cognition vision hearing also conducted procedures surgeon


trying combat epileptic seizures history physician hippocrates bce made accounts using different wines sedate patients trepanning ce dioscorides physician pharmacologist botanist detailed mandrake henbane opium alcohol used put patients sleep trepanning ce two brother surgeons paramara india used samohine sedate patient removing small tumor awoke patient pouring onion vinegar patient 's mouth combination carbon dioxide hydrogen nitrogen form neuroanesthesia adopted th century


introduced humphry davy neurosurgery methods icd meshid ops othercodes hcpcslevel neuroradiology methods used modern neurosurgery diagnosis treatment include computer assisted imaging computed tomography ct magnetic resonance imaging mri positron emission tomography pet magnetoencephalography meg stereotactic radiosurgery neurosurgery procedures involve use intra operative mri functional mri ''conventional open surgery'' neurosurgeon opens skull creating large opening


mobile global positioning system gps image guided surgery systems like '''curve image guided''' surgery stealthstation use cameras electromagnetic fields capture relay patient anatomy surgeon precise movements relation patient computer monitors operating room sophisticated computerized systems used surgery help orient surgeon three dimensional images patient anatomy including tumor real time functional brain mapping employed identify specific functional regions using electrocorticography ecog minimally invasive ''endoscopic surgery'' commonly utilized neurosurgeons appropriate techniques endoscopic endonasal


surgery used pituitary tumors craniopharyngiomas chordomas repair cerebrospinal fluid leaks ventricular endoscopy used treatment intraventricular bleeds hydrocephalus colloid cyst neurocysticercosis endonasal endoscopy times carried neurosurgeons ent surgeons working together team repair craniofacial disorders disturbance cerebrospinal fluid circulation done neurosurgeons also occasionally team maxillofacial plastic surgeons cranioplasty craniosynostosis performed pediatric neurosurgeons without plastic surgeons neurosurgeons involved ' 'stereotactic radiosurgery'' along radiation oncologists tumor avm treatment radiosurgical


thoracic lumbar spine indications spine surgery include spinal cord compression resulting trauma arthritis spinal discs spondylosis cervical cord compression patients may difficulty gait balance issues numbness tingling hands feet spondylosis condition spinal disc degeneration arthritis may compress spinal canal condition often result bone spurring disc herniation power drills special instruments often used correct compression problems spinal canal disc herniations spinal vertebral discs removed special rongeurs


procedure known '''' 'discectomy''''' generally disc removed replaced implant create bony fusion vertebral bodies instead mobile disc could implanted disc space maintain mobility commonly used cervical disc surgery times instead disc removal laser discectomy could used decompress nerve root method mainly used lumbar discs ''laminectomy'' removal lamina vertebrae spine order make room compressed nerve


stenosis hydrocephalus head trauma brain hemorrhages skull fractures etc spinal cord trauma traumatic injuries peripheral nerves tumors spine spinal cord peripheral nerves intracerebral hemorrhage subarachnoid hemorrhage interdepartmental intracellular hemorrhages forms drug resistant epilepsy forms movement disorders advanced parkinson 's disease chorea involves use specially developed minimally invasive stereotactic techniques functional stereotactic neurosurgery ablative surgery deep brain stimulation surgery intractable pain cancer trauma patients cranial peripheral nerve pain forms intractable psychiatric disorders vascular malformations ie arteriovenous malformations venous angiomas cavernous angiomas capillary telangectasias


quality evidence supports use medications dexmedetomidine pregabalin gabapentin reduce post operative pain ref name low quality evidence also supports scalp blocks scalp infiltration reduce postoperative pain ref name gabapentin pregabalin may also decrease vomiting nausea following surgery low quality medical evidence ref name notable neurosurgeons saleem abdulrauf developed awake craniotomy complex aneurysms vascular malformations b k misra first neurosurgeon world perform image guided surgery aneurysms first south asia perform stereotactic radiosurgery first india perform awake craniotomy laparoscopic spine


given outstanding neurosurgeons every two years ludvig puuseppknown one founding fathers modern neurosurgery world 's first professor neurosurgery walter dandyknown one founding fathers modern neurosurgery hirotaro narabayashia pioneer stereotactic neurosurgery alim louis benabidknown one developers deep brain stimulation surgery movement disorder wilder penfieldknown one founding fathers modern neurosurgery pioneer epilepsy neurosurgery joseph ransohoffknown pioneering use medical imaging catheterization neurosurgery founding first neurosurgery intensive care unit lars leksellswedish neurosurgeon developed


gamma knife ben carsonretired pediatric neurosurgeon johns hopkins hospital pioneer hemispherectomy pioneer separation craniopagus twins joined head former republican party presidential candidate former united states secretary housing urban development trump administration john r adlerstanford university neurosurgeon invented cyberknife wirginia maixnerpediatric neurosurgeon melbourne 's royal children 's hospital primarily known separating conjoined bangladeshi twins trishna krishna frank henderson mayfieldinvented mayfield skull clamp ayub k ommayainvented ommaya reservoir christopher duntsch former neurosurgeon killed maimed nearly every patient operated


learning community medical students surgical specialties


''table geography hydrography navigation'' ''cyclopaedia'' ''universal dictionary arts sciences'' '''navigation''' ref name hofman field study focuses process monitoring controlling movement craft vehicle one place another ref name bow bowditch ref field navigation includes four general categories land navigation marine navigation aeronautic navigation space navigation ref name hofman ref also term art used specialized knowledge used navigators perform navigation tasks navigational techniques involve locating navigator 's position compared known locations

Human physical performance and recreation