View source for Structure

{{short description|Arrangement of interrelated elements in an object/system, or the object/system itself}}
{{other uses}}
[[File:DNA simple2.svg|thumb|upright|The structure of a [[DNA]] molecule is essential to its function.]]
A '''structure''' is an arrangement and organization of interrelated elements in a material object or [[system]], or the object or system so organized.<ref name=OED>{{cite encyclopedia |title=structure, n. |encyclopedia=Oxford English Dictionary |edition=Online |url=http://www.oed.com/view/Entry/191895?rskey=pTgPk1&amp;result=1|access-date=1 October 2015}}</ref> Material structures include man-made objects such as [[building]]s and [[machine]]s and natural objects such as [[organism|biological organisms]], [[mineral]]s and [[chemical substance|chemicals]]. Abstract structures include [[data structure]]s in [[computer science]] and [[musical form]]. Types of structure include a [[hierarchy]] (a cascade of one-to-many relationships), a [[Complex network|network]] featuring many-to-many [[Link (geometry)|link]]s, or a [[lattice (order)|lattice]] featuring connections between components that are neighbors in space.

== Load-bearing ==
[[File:Sámi storehouse.jpg|thumb|left|A traditional [[Sami people|Sami]] food storage structure]]
[[File:Voûte de l'église Saint-Séverin à Paris.jpg|thumb|upright|Gothic quadripartite cross-ribbed vaults of the [[Saint-Séverin]] church in Paris]]
[[Building]]s, [[aircraft]], [[skeleton]]s, [[Ant colony|anthills]], [[beaver dam]]s, [[bridge]]s and [[salt dome]]s are all examples of [[Structural load|load]]-bearing structures. The results of [[construction]] are divided into [[building]]s and [[nonbuilding structure|non-building structure]]s, and make up the [[infrastructure]] of a human society. Built structures are broadly divided by their varying design approaches and standards, into [[Structural engineering#Specializations|categories]] including building structures, [[architectural structure]]s, civil engineering structures and mechanical structures.

The effects of loads on physical structures are determined through [[structural analysis]], which is one of the tasks of [[structural engineering]]. The [[Structural engineering#Structural elements|structural elements]] can be classified as one-dimensional ([[rope]]s, [[strut]]s, [[Beam (structure)|beams]], [[arch]]es), two-dimensional ([[membrane]]s, plates, [[Concrete slab|slab]], [[Shell (structure)|shells]], [[Vault (architecture)|vaults]]), or three-dimensional (solid masses).<ref name=Carpinter>{{cite book|last1=Carpinteri|first1=Alberto|title=Structural Mechanics: A unified approach|date=2002|publisher=CRC Press|isbn=9780203474952}}</ref>{{rp|2}} Three-dimensional elements were the main option available to early structures such as [[Chichen Itza]]. A one-dimensional element has one dimension much larger than the other two, so the other dimensions can be neglected in calculations; however, the ratio of the smaller dimensions and the composition can determine the [[Flexural rigidity|flexural]] and [[Compressive strength|compressive]] stiffness of the element. Two-dimensional elements with a thin third dimension have little of either but can resist biaxial traction.<ref name=Carpinter/>{{rp|2–3}}

The structure elements are combined in ''structural systems''. The majority of everyday load-bearing structures are ''section-active'' structures like frames, which are primarily composed of one-dimensional (bending) structures. Other types are ''Vector-active'' structures such as [[truss]]es, ''surface-active'' structures such as shells and folded plates, ''form-active'' structures such as cable or membrane structures, and hybrid structures.<ref>{{cite book|last1=Knippers|first1=Jan|last2=Cremers|first2=Jan|last3=Gabler|first3=Markus|last4=Lienhard|first4=Julian|title=Construction manual for polymers + membranes : materials, semi-finished products, form-finding design|date=2011|publisher=Institut für internationale Architektur-Dokumentation|location=München|isbn=9783034614702|edition=Engl. transl. of the 1. German}}</ref>{{rp|134–136}}

Load-bearing biological structures such as bones, teeth, shells, and tendons derive their strength from a multilevel hierarchy of structures employing biominerals and [[protein]]s, at the bottom of which are [[collagen|collagen fibrils]].<ref>{{cite journal|last1=Zhang|first1=Z.|last2=Zhang|first2=Y.-W.|last3=Gao|first3=H.|title=On optimal hierarchy of load-bearing biological materials|journal=Proceedings of the Royal Society B: Biological Sciences|date=1 September 2010|volume=278|issue=1705|pages=519–525|doi=10.1098/rspb.2010.1093|pmid=20810437|pmc=3025673}}</ref>

== Biological ==
[[File:Helianthus_whorl.jpg | thumb | right | The spiral arrangement of small bright yellow [[floret]]s that make up the [[flower head]] of a [[Helianthus annuus |sunflower]] is an example of the highly ordered structure that characterizes all [[living organism |organism]]s.<ref name = "urry2017a"/>]]
In [[biology]], one of the properties of [[life]] is its highly ''ordered'' structure,<ref name = "urry2017a">{{cite book | last1 = Urry | first1 = Lisa | last2 = Cain | first2 = Michael | last3 = Wasserman | first3 = Steven | last4 = Minorsky | first4 = Peter | last5 = Reece | first5 = Jane | chapter = Evolution, the themes of biology, and scientific inquiry | title = Campbell Biology | publisher = Pearson | edition = 11th | date = 2017 | location = New York | pages = 2–26 | isbn = 978-0134093413}}</ref> which can be observed at [[Biological organisation |multiple levels]] such as in [[cell (biology)|cell]]s, [[Tissue (biology)|tissue]]s, [[organ (anatomy)|organ]]s, and [[organism]]s. 

In another context, structure can also observed in [[macromolecule]]s, particularly [[protein]]s and [[nucleic acid]]s.<ref name ="banaszak2000">{{cite book|last1=Banaszak|first1=Leonard J.|title=Foundations of Structural Biology.|date=2000|publisher=Elsevier|location=Burlington|isbn=9780080521848}}</ref> The function of these molecules is determined by their shape as well as their composition, and their structure has multiple levels. [[Protein structure]] has a four-level hierarchy. The ''[[Protein primary structure|primary structure]]'' is the sequence of [[amino acid]]s that make it up. It has a [[peptide]] backbone made up of a repeated sequence of a nitrogen and two carbon atoms. The ''[[Protein secondary structure|secondary structure]]'' consists of repeated patterns determined by [[hydrogen bonding]]. The two basic types are the [[alpha helix|α-helix]] and the [[beta sheet|β-pleated sheet]]. The ''[[Protein tertiary structure|tertiary structure]]'' is a back and forth bending of the polypeptide chain, and the ''[[Protein quaternary structure|quaternary structure]]'' is the way that tertiary units come together and interact.<ref>{{cite book|last1=Purves|first1=William K.|last2=Sadava|first2=David E.|last3=Orians|first3=Gordon H.|last4=H. Craig|first4=Heller|title=Life, the science of biology|url=https://archive.org/details/lifesciencebiolo00purv_787|url-access=limited|date=2003|publisher=Sinauer Associates|location=Sunderland, Mass.|isbn=9780716798569|pages=[https://archive.org/details/lifesciencebiolo00purv_787/page/n43 41]–44|edition=7th}}</ref> [[Structural biology]] is concerned with [[biomolecular structure]] of macromolecules.<ref name ="banaszak2000"/>

== Chemical ==
{{Main|Chemical structure}}
[[File:Dopamin - Dopamine.svg|thumb|right|A skeletal formula for [[dopamine]]]]
Chemical structure refers to both molecular geometry and electronic structure. The structure can be represented by a variety of diagrams called [[structural formula]]s. [[Lewis structure]]s use a dot notation to represent the [[valence electron]]s for an atom; these are the electrons that determine the role of the atom in chemical reactions.<ref>{{cite book|last1=DeKock|first1=Roger L.|last2=Gray|first2=Harry B.|title=Chemical structure and bonding|date=1989|publisher=University Science Books|location=Mill Valley, Calif.|isbn=9780935702613|edition=2nd|url-access=registration|url=https://archive.org/details/isbn_9780935702613}}</ref>{{rp|71–72}} Bonds between atoms can be represented by lines with one line for each pair of electrons that is shared. In a simplified version of such a diagram, called a [[skeletal formula]], only carbon-carbon bonds and functional groups are shown.<ref>{{cite book|last1=Hill|first1=Graham C.|last2=Holman|first2=John S.|title=Chemistry in context|date=2000|publisher=Nelson|location=Walton-on-Thames|isbn=9780174482765|page=391|edition=5th}}</ref>

Atoms in a crystal have a [[crystal structure|structure]] that involves repetition of a basic unit called a ''unit cell''. The atoms can be modeled as points on a [[Bravais lattice|lattice]], and one can explore the effect of [[symmetry]] operations that include rotations about a point, reflections about a symmetry planes, and ''[[translation (geometry)|translations]]'' (movements of all the points by the same amount). Each crystal has a finite group, called the [[space group]], of such operations that map it onto itself; there are 230 possible space groups.<ref name=Ashcroft>{{cite book|last1=Ashcroft|first1=Neil W.|last2=Mermin|first2=N. David|title=Solid state physics|date=1977|publisher=Holt, Rinehart and Winston|location=New York|isbn=9780030839931|edition=27. repr.|url-access=registration|url=https://archive.org/details/solidstatephysic00ashc}}</ref>{{rp|125–126}} By [[Neumann's law]], the symmetry of a crystal determines what physical properties, including [[piezoelectricity]] and [[ferromagnetism]], the crystal can have.<ref>{{cite book|last1=Newnham|first1=Robert E.|title=Properties of materials anisotropy, symmetry, structure|date=2005|publisher=Oxford University Press|location=Oxford|isbn=9780191523403}}</ref>{{rp|34–36,91–92,168–169}}

== Mathematical ==
{{Main|Mathematical structure}}

== Musical ==
{{see also|Musical form}}
[[File:ChopinOp28no6.png|thumb|right|A motif from the [[Preludes (Chopin)|Preludes by Chopin]], Op. 28 no.6, bars 1–3]]
A large part of [[numerical analysis]] involves identifying and interpreting the structure of musical works. Structure can be found at the level of part of a work, the entire work, or a group of works.<ref name=analysis>{{cite encyclopedia|first1=Ian D. |last1=Bent |first2=Anthony |last2=Pople |title=Analysis |encyclopedia=Grove Music Online. Oxford Music Online |publisher=Oxford University Press |access-date=October 5, 2015 |url=https://www.oxfordmusiconline.com/subscriber/article/grove/music/41862}}</ref> Elements of music such as [[Pitch (music)|pitch]], [[Duration (music)|duration]] and [[timbre]] combine into small elements like [[Motif (music)|motifs]] and [[Phrase (music)|phrases]], and these in turn combine in larger structures. Not all music (for example, that of [[John Cage]]) has a [[hierarchical organization]], but hierarchy makes it easier for a listener to understand and remember the music.<ref name=Meyer>{{cite book|last1=Meyer|first1=Leonard B.|title=Explaining music : essays and explorations.|date=1973|publisher=Univ. of California Press|location=Berkeley|isbn=9780520022164}}</ref>{{rp|80}}

In analogy to [[linguistics|linguistic]] terminology, motifs and phrases can be combined to make complete musical ideas such as [[sentence (music)|sentences]] and [[phrase (music)|phrases]].<ref name=sentence>{{cite encyclopedia|title=Sentence |encyclopedia=Grove Music Online. Oxford Music Online |publisher=Oxford University Press |access-date=October 5, 2015 |url=https://www.oxfordmusiconline.com/subscriber/article/grove/music/25423}}</ref><ref name=phrase>{{cite encyclopedia|title=Phrase |encyclopedia=Grove Music Online. Oxford Music Online |publisher=Oxford University Press |access-date=October 5, 2015 |url=https://www.oxfordmusiconline.com/subscriber/article/grove/music/21599}}</ref> A larger form is known as the [[Period (music)|period]]. One such form that was widely used between 1600 and 1900 has two phrases, an ''antecedent'' and a ''consequent'', with a half [[Cadence (music)|cadence]] in the middle and a full cadence at the end providing punctuation.<ref name=Stein>{{cite book|last1=Stein|first1=Leon|title=Anthology of Musical Forms: Structure & Style (Expanded Edition): The Study and Analysis of Musical Forms|date=1979|publisher=Alfred Music|isbn=9781457400940}}</ref>{{rp|38–39}} On a larger scale are single-movement forms such as the [[sonata form]] and the [[Counterpoint|contrapuntal form]], and multi-movement forms such as the [[symphony]].<ref name=Meyer/>

== Social ==
{{Main|Social structure}}

A social structure is a pattern of relationships. They are social [[organization]]s of individuals in various life situations. Structures are applicable to people in how a society is as a system organized by a characteristic pattern of relationships. This is known as the social organization of the group.<ref name="Lopez">{{cite book |last1=Lopez |first1=J. |last2=Scott |first2=J. |title=Social Structure |date=2000 |publisher=Open University Press |location=Buckingham and Philadelphia |isbn=9780335204960 |oclc=43708597}}</ref>{{rp|3}} Sociologists have studied the changing structure of these groups. [[Structure and agency]] are two confronted theories about human behaviour. The debate surrounding the influence of structure and agency on human thought is one of the central issues in sociology. In this context, ''agency'' refers to the individual human capacity to act independently and make free choices. ''Structure'' here refers to factors such as [[social class]], [[religion]], [[gender]], [[ethnic group|ethnicity]], customs, etc. that seem to limit or influence individual opportunities.

== Data ==
{{Main|Data structure}}
[[File:Singly-linked-list.svg|thumb|right|In a singly linked list, each element has a data value and a pointer to the next element.]]
In [[computer science]], a data structure is a way of organizing information in a [[computer]] so that it can be used efficiently.<ref>{{cite encyclopedia|first=Paul E. |last=Black |title=data structure |encyclopedia=[[Dictionary of Algorithms and Data Structures]] |editor-first1=Vreda |editor-last1=Pieterse |editor-first2=Paul E. |editor-last2=Black |publisher=[[National Institute of Standards and Technology]] |date= 15 December 2004 |url=http://xlinux.nist.gov/dads/HTML/datastructur.html |edition=Online |access-date=1 October 2015}}</ref> Data structures are built out of two basic types: An [[Array data structure|array]] has an index that can be used for immediate access to any data item (some [[programming language]]s require array size to be [[Initialization (programming)|initialized]]). A [[linked list]] can be reorganized, grown or shrunk, but its elements must be accessed with a [[Reference (computer science)|pointer]] that links them together in a particular order.<ref>{{cite book|last1=Sedgewick|first1=Robert|last2=Wayne|first2=Kevin|title=Algorithms|date=2011|publisher=Addison-Wesley Professional|isbn=9780132762564|edition=4th}}</ref>{{rp|156}} Out of these any number of other data structures can be created such as [[Stack (abstract data type)|stacks]], [[Queue (abstract data type)|queues]], [[Tree (data structure)|trees]] and [[hash table]]s.<ref>{{cite book|chapter=Data structures|last1=Cormen|first1=Thomas H.|last2=Leiserson|first2=Charles E.|last3=Rivest|first3=Ronald L.|last4=Stein|first4=Clifford|title=Introduction to algorithms|url=https://archive.org/details/introductiontoal00corm_805|url-access=limited|date=2009|publisher=MIT Press|location=Cambridge, Massachusetts|isbn=978-0262033848|pages=[https://archive.org/details/introductiontoal00corm_805/page/n249 229]–339|edition=3rd}}</ref><ref>{{cite book|last1=Mehta|first1=Dinesh P.|chapter=Basic structures|editor-last1=Mehta|editor-first1=Dinesh P.|editor-last2=Sahni|editor-first2=Sartaj|title=Handbook of data structures and applications|date=2005|publisher=Chapman & Hall/CRC Computer and Information Science Series|location=Boca Raton, Fla.|isbn=9781420035179}}</ref>

In solving a problem, a data structure is generally an integral part of the [[algorithm]].<ref name=Skiena>{{cite book|last1=Skiena|first1=Steven S.|chapter=Data structures|title=The algorithm design manual|url=https://archive.org/details/algorithmdesignm00skie_772|url-access=limited|date=2008|publisher=Springer|location=London|isbn=9781848000704|pages=[https://archive.org/details/algorithmdesignm00skie_772/page/n377 366]–392|edition=2nd}}</ref>{{rp|5}} In modern programming style, algorithms and data structures are [[Encapsulation (computer programming)|encapsulated]] together in an [[abstract data type]].<ref name=Skiena/>{{rp|ix}}

== Software ==
{{Main|Software architecture}}

Software architecture is the specific choices made between possible alternatives within a framework. For example, a framework might require a database and the architecture would specify the type and manufacturer of the database. The [[Structure chart|structure]] of software is the way in which it is partitioned into interrelated components. A key structural issue is minimizing dependencies between these components. This makes it possible to change one component without requiring changes in others.<ref>{{cite book|last1=Gorton|first1=Ian|title=Essential software architecture|date=2011|publisher=Springer|location=Berlin|isbn=9783642191763|edition=2nd}}</ref>{{rp|3}} The purpose of structure is to [[Program optimization|optimise]] for (brevity, readability, traceability, isolation and encapsulation, maintainability, extensibility, performance and efficiency), examples being: [[Computer language|language choice]], [[Indentation style|code]], [[API|functions]], [[Class browser|libraries]], [[makefile|builds]], [[Package manager|system evolution]], or diagrams for [[Control Structure Diagram|flow logic]] and [[Nassi–Shneiderman diagram|design]].<ref>{{cite book|last1=Diehl|first1=Stephan|title=Software visualization : visualizing the structure, behaviour, and evolution of software ; with 5 tables|url=https://archive.org/details/softwarevisualiz00dieh_179|url-access=limited|date=2007|publisher=Springer|location=Berlin|isbn=978-3540465041|pages=[https://archive.org/details/softwarevisualiz00dieh_179/page/n45 38]–47}}</ref> Structural elements reflect the requirements of the application: for example, if the system requires a high fault tolerance, then a redundant structure is needed so that if a component fails it has backups.<ref>{{cite book|last1=Bernardi|first1=Simona|last2=Merseguer|first2=José|last3=Petriu|first3=Dorina Corina|title=Model-Driven Dependability Assessment of Software Systems|date=2013|publisher=Springer Berlin Heidelberg|location=Berlin, Heidelberg|isbn=9783642395123|pages=46–47}}</ref> A high redundancy is an essential part of the design of several systems in the [[Space Shuttle]].<ref>{{cite web|title=Computers in the Space Shuttle Avionics System|url=https://history.nasa.gov/computers/Ch4-4.html|website=Computers in Spaceflight: The NASA Experience|access-date=2 October 2015}}</ref>

== Logical ==
As a branch of philosophy, [[logic]] is concerned with distinguishing good arguments from poor ones. A chief concern is with the structure of arguments.<ref>{{cite web|title=The Structure of Arguments|url=http://philosophy.lander.edu/logic/structure.html|website=Philosophy 103: Introduction to Logic|publisher=philosophy.lander.edu|access-date=4 October 2015}}</ref> An argument consists of one or more [[premise]]s from which a conclusion is [[inference|inferred]].<ref name=Kemerling>{{cite web|last1=Kemerling|first1=Garth|title=Arguments and Inference|url=http://www.philosophypages.com/lg/e01.htm|website=The Philosophy Pages|access-date=4 October 2015}}</ref> The steps in this inference can be expressed in a formal way and their structure analyzed. Two basic types of inference are [[deductive reasoning|deduction]] and [[inductive reasoning|induction]]. In a [[Validity (logic)|valid]] deduction, the conclusion necessarily follows from the premises, regardless of whether they are true or not. An invalid deduction contains some error in the analysis. An inductive argument claims that if the premises are true, the conclusion is likely.<ref name=Kemerling/>

== See also ==
* [[Abstract structure]]
* [[Mathematical structure]]
* [[Structural geology]]
* [[Structure (mathematical logic)]]
* [[Structuralism (philosophy of science)]]

== References ==
{{reflist|30em}}

== Further reading ==
{{refbegin}}
*{{cite book|last1=Carpi|first1=A.|last2=Brebbia|first2=C.A.|title=Design & nature V : comparing design in nature with science and engineering|date=2010|publisher=WIT|location=Southampton|isbn=9781845644543}}
*{{cite book | last = Pullan | first = Wendy | author-link=Wendy Pullan (academic)|title = Structure | publisher = Cambridge University Press | location = Cambridge | year = 2000 | isbn = 0-521-78258-9 }}
*{{cite book|last1=Rottenberg|first1=Annette T.|last2=Winchell|first2=Donna Haisty|title=The structure of argument|date=2012|publisher=Bedford/St. Martins|location=Boston|isbn=9780312650698|edition=7th}}
*{{cite book|last1=Schlesinger|first1=Izchak M.|last2=Keren-Portnoy|first2=Tamar|last3=Parush|first3=Tamar|title=The structure of arguments|date=2001|publisher=J. Benjamins|location=Amsterdam|isbn=9789027223593}}
{{refend}}

==External links==
*{{cite web|first=Christian|last=Wüthrich|title=Structure in philosophy, mathematics and physics (Phil 246, Spring 2010) |publisher=University of California San Diego |url=http://philosophyfaculty.ucsd.edu/faculty/wuthrich/teaching/2010_246/246Syllabus_2010.pdf |access-date=1 October 2015 |url-status=dead |archive-url=https://web.archive.org/web/20160304214729/http://philosophyfaculty.ucsd.edu/faculty/wuthrich/teaching/2010_246/246Syllabus_2010.pdf |archive-date=4 March 2016}} (syllabus and reading list)

{{Authority control}}

[[Category:Structure| ]]