Structure

File:Sámi storehouse.jpg food storage structure]]

File:Voûte de l'église Saint-Séverin à Paris.jpg church in Paris]]

Buildings, aircraft, skeletons, anthills, beaver dams, bridges and salt domes are all examples of load-bearing structures. The results of construction are divided into buildings and non-building structures, and make up the infrastructure of a human society. Built structures are broadly divided by their varying design approaches and standards, into categories including building structures, architectural structures, 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 elements can be classified as one-dimensional (ropes, struts, beams, arches), two-dimensional (membranes, plates, slab, shells, vaults), or three-dimensional (solid masses).{{cite book|last1=Carpinteri|first1=Alberto|title=Structural Mechanics: A unified approach|date=2002|publisher=CRC Press|isbn=9780203474952}}{{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 and compressive stiffness of the element. Two-dimensional elements with a thin third dimension have little of either but can resist biaxial traction.{{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 trusses, surface-active structures such as shells and folded plates, form-active structures such as cable or membrane structures, and hybrid structures.{{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}}{{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 proteins, at the bottom of which are collagen fibrils.{{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}}

File:Helianthus_whorl.jpg s that make up the flower head of a sunflower is an example of the highly ordered structure that characterizes all organisms.]]

In biology, one of the properties of life is its highly ordered structure,{{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}} which can be observed at multiple levels such as in cells, tissues, organs, and organisms.

In another context, structure can also observed in macromolecules, particularly proteins and nucleic acids.{{cite book|last1=Banaszak|first1=Leonard J.|title=Foundations of Structural Biology.|date=2000|publisher=Elsevier|location=Burlington|isbn=9780080521848}} 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 primary structure is the sequence of amino acids that make it up. It has a peptide backbone made up of a repeated sequence of a nitrogen and two carbon atoms. The secondary structure consists of repeated patterns determined by hydrogen bonding. The two basic types are the α-helix and the β-pleated sheet. The tertiary structure is a back and forth bending of the polypeptide chain, and the quaternary structure is the way that tertiary units come together and interact.{{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}} Structural biology is concerned with biomolecular structure of macromolecules.

{{Main|Chemical structure}}

File:Dopamin - Dopamine.svg]]

Chemical structure refers to both molecular geometry and electronic structure. The structure can be represented by a variety of diagrams called structural formulas. Lewis structures use a dot notation to represent the valence electrons for an atom; these are the electrons that determine the role of the atom in chemical reactions.{{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}}{{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.{{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}}

Atoms in a crystal have a structure that involves repetition of a basic unit called a unit cell. The atoms can be modeled as points on a lattice, and one can explore the effect of symmetry operations that include rotations about a point, reflections about a symmetry planes, and 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.{{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}}{{rp|125–126}} By Neumann's law, the symmetry of a crystal determines what physical properties, including piezoelectricity and ferromagnetism, the crystal can have.{{cite book|last1=Newnham|first1=Robert E.|title=Properties of materials anisotropy, symmetry, structure|date=2005|publisher=Oxford University Press|location=Oxford|isbn=9780191523403}}{{rp|34–36,91–92,168–169}}

{{Main|Mathematical structure}}

{{see also|Musical form}}

File:ChopinOp28no6.png, 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.{{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 |archive-date=June 14, 2024 |archive-url=https://web.archive.org/web/20240614043727/https://www.oxfordmusiconline.com/grovemusic/display/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000041862 |url-status=live }} Elements of music such as pitch, duration and timbre combine into small elements like motifs and 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.{{cite book|last1=Meyer|first1=Leonard B.|title=Explaining music : essays and explorations.|date=1973|publisher=Univ. of California Press|location=Berkeley|isbn=9780520022164}}{{rp|80}}

In analogy to linguistic terminology, motifs and phrases can be combined to make complete musical ideas such as sentences and phrases.{{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 |archive-date=June 14, 2024 |archive-url=https://web.archive.org/web/20240614043719/https://www.oxfordmusiconline.com/grovemusic/display/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000025423 |url-status=live }}{{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 |archive-date=June 14, 2024 |archive-url=https://web.archive.org/web/20240614043720/https://www.oxfordmusiconline.com/grovemusic/display/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000021599 |url-status=live }} A larger form is known as the period. One such form that was widely used between 1600 and 1900 has two phrases, an antecedent and a consequent, with a half cadence in the middle and a full cadence at the end providing punctuation.{{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}}{{rp|38–39}} On a larger scale are single-movement forms such as the sonata form and the contrapuntal form, and multi-movement forms such as the symphony.

{{Main|Social structure}}

A social structure is a pattern of relationships. They are social organizations 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.{{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}}{{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, ethnicity, customs, etc. that seem to limit or influence individual opportunities.

{{Main|Data structure}}

File:Singly-linked-list.svg

In computer science, a data structure is a way of organizing information in a computer so that it can be used efficiently.{{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 |archive-date=10 August 2017 |archive-url=https://web.archive.org/web/20170810051100/https://xlinux.nist.gov/dads/HTML/datastructur.html |url-status=live }} Data structures are built out of two basic types: An array has an index that can be used for immediate access to any data item (some programming languages require array size to be initialized). A linked list can be reorganized, grown or shrunk, but its elements must be accessed with a pointer that links them together in a particular order.{{cite book|last1=Sedgewick|first1=Robert|last2=Wayne|first2=Kevin|title=Algorithms|date=2011|publisher=Addison-Wesley Professional|isbn=9780132762564|edition=4th}}{{rp|156}} Out of these any number of other data structures can be created such as stacks, queues, trees and hash tables.{{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}}{{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}}

In solving a problem, a data structure is generally an integral part of the algorithm.{{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}}{{rp|5}} In modern programming style, algorithms and data structures are encapsulated together in an abstract data type.{{rp|ix}}

{{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 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.{{cite book|last1=Gorton|first1=Ian|title=Essential software architecture|date=2011|publisher=Springer|location=Berlin|isbn=9783642191763|edition=2nd}}{{rp|3}} The purpose of structure is to optimise for (brevity, readability, traceability, isolation and encapsulation, maintainability, extensibility, performance and efficiency), examples being: language choice, code, functions, libraries, builds, system evolution, or diagrams for flow logic and design.{{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}} 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.{{cite book|last1=Bernardi|first1=Simona|last2=Merseguer|first2=José|last3=Petriu|first3=Dorina Corina|author3-link=Dorina Petriu|title=Model-Driven Dependability Assessment of Software Systems|date=2013|publisher=Springer Berlin Heidelberg|location=Berlin, Heidelberg|isbn=9783642395123|pages=46–47}} A high redundancy is an essential part of the design of several systems in the Space Shuttle.{{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|date=March 1988 |access-date=2 October 2015|archive-date=9 October 2023|archive-url=https://web.archive.org/web/20231009121408/https://history.nasa.gov/computers/Ch4-4.html|url-status=live |last1=Tomayko |first1=James E. }}

As a branch of philosophy, logic is concerned with distinguishing good arguments from poor ones. A chief concern is with the structure of arguments.{{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|archive-date=9 October 2023|archive-url=https://web.archive.org/web/20231009121501/https://philosophy.lander.edu/logic/structure.html|url-status=live}} An argument consists of one or more premises from which a conclusion is inferred.{{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|archive-date=4 June 2023|archive-url=https://web.archive.org/web/20230604225936/http://philosophypages.com/lg/e01.htm|url-status=live}} The steps in this inference can be expressed in a formal way and their structure analyzed. Two basic types of inference are deduction and induction. In a 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.

• Abstract structure
• Mathematical structure
• Structural geology
• Structure (mathematical logic)
• Structuralism (philosophy of science)

{{reflist|30em}}

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• {{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}}

• {{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)

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