A structure is an arrangement and organization of interrelated elements in a material object or

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...

, or the object or system so organized. Material structures include man-made objects such as buildings and

machine A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules ...

s and natural objects such as biological organisms,

mineral In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...

s and

chemicals A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., with ...

. Abstract structures include

data structure In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, a ...

s in computer science and

musical form In music, ''form'' refers to the structure of a musical composition or performance. In his book, ''Worlds of Music'', Jeff Todd Titon suggests that a number of organizational elements may determine the formal structure of a piece of music, such ...

. Types of structure include a

hierarchy A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important ...

(a cascade of one-to-many relationships), a

network Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics ...

featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space.

Load-bearing

Buildings,

aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. ...

skeleton A skeleton is the structural frame that supports the body of an animal. There are several types of skeletons, including the exoskeleton, which is the stable outer shell of an organism, the endoskeleton, which forms the support structure inside ...

s, anthills,

beaver dam A beaver dam or beaver impoundment is a dam built by beavers to create a pond which protects against predators such as coyotes, wolves and bears, and holds their food during winter. These structures modify the natural environment in such a way th ...

s, bridges and salt domes are all examples of

load Load or LOAD may refer to: Aeronautics and transportation *Load factor (aeronautics), the ratio of the lift of an aircraft to its weight *Passenger load factor, the ratio of revenue passenger miles to available seat miles of a particular transpo ...

-bearing structures. The results of construction are divided into buildings and non-building structures, and make up the

infrastructure Infrastructure is the set of facilities and systems that serve a country, city, or other area, and encompasses the services and facilities necessary for its economy, households and firms to function. Infrastructure is composed of public and priv ...

of a human society. Built structures are broadly divided by their varying design approaches and standards, into

categories Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally *Category of being * ''Categories'' (Aristotle) * Category (Kant) *Categories (Peirce) * ...

including building structures,

architectural structure Architectural engineers apply and theoretical knowledge to the engineering design of buildings and building systems. The goal is to engineer high performance buildings that are sustainable, economically viable and ensure the safety health. Archi ...

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 Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and cal ...

. The structural elements can be classified as one-dimensional (

rope A rope is a group of yarns, plies, fibres, or strands that are twisted or braided together into a larger and stronger form. Ropes have tensile strength and so can be used for dragging and lifting. Rope is thicker and stronger than similarly ...

strut A strut is a structural component commonly found in engineering, aeronautics, architecture and anatomy. Struts generally work by resisting longitudinal compression, but they may also serve in tension. Human anatomy Part of the functionality o ...

s, beams,

arch An arch is a vertical curved structure that spans an elevated space and may or may not support the weight above it, or in case of a horizontal arch like an arch dam, the hydrostatic pressure against it. Arches may be synonymous with vault ...

es), two-dimensional ( membranes, plates,

slab Slab or SLAB may refer to: Physical materials * Concrete slab, a flat concrete plate used in construction * Stone slab, a flat stone used in construction * Slab (casting), a length of metal * Slab (geology), that portion of a tectonic plate that i ...

, shells, vaults), or three-dimensional (solid masses). Three-dimensional elements were the main option available to early structures such as

Chichen Itza Chichen Itza , es, Chichén Itzá , often with the emphasis reversed in English to ; from yua, Chiʼchʼèen Ìitshaʼ () "at the mouth of the well of the Itza people" was a large pre-Columbian city built by the Maya people of the Termin ...

. 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 In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elong ...

stiffness of the element. Two-dimensional elements with a thin third dimension have little of either but can resist biaxial traction. 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 A truss is an assembly of ''members'' such as beams, connected by ''nodes'', that creates a rigid structure. In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assembla ...

es, ''surface-active'' structures such as shells and folded plates, ''form-active'' structures such as cable or membrane structures, and hybrid structures. 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.

Biological

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

, one of the properties of

life Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energy trans ...

is its highly ''ordered'' structure, which can be observed at multiple levels such as in

cell Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...

s, tissues, organs, and

organism In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells ( cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fung ...

s. In another context, structure can also observed in

macromolecule A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...

s, particularly proteins and

nucleic acid Nucleic acids are biopolymers, macromolecules, essential to all known forms of life. They are composed of nucleotides, which are the monomers made of three components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main clas ...

s. The function of these molecules is determined by their shape as well as their composition, and their structure has multiple levels.

Protein structure Protein structure is the three-dimensional arrangement of atoms in an amino acid-chain molecule. Proteins are polymers specifically polypeptides formed from sequences of amino acids, the monomers of the polymer. A single amino acid monomer ma ...

has a four-level hierarchy. The ''

primary structure Protein primary structure is the linear sequence of amino acids in a peptide or protein. By convention, the primary structure of a protein is reported starting from the amino-terminal (N) end to the carboxyl-terminal (C) end. Protein biosynthes ...

'' is the sequence of

amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...

s that make it up. It has a

peptide Peptides (, ) are short chains of amino acids linked by peptide bonds. Long chains of amino acids are called proteins. Chains of fewer than twenty amino acids are called oligopeptides, and include dipeptides, tripeptides, and tetrapeptides. A p ...

backbone made up of a repeated sequence of a nitrogen and two carbon atoms. The ''

secondary structure Protein secondary structure is the three dimensional form of ''local segments'' of proteins. The two most common secondary structural elements are alpha helices and beta sheets, though beta turns and omega loops occur as well. Secondary struct ...

'' consists of repeated patterns determined by

hydrogen bonding In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a ...

. The two basic types are the

α-helix The alpha helix (α-helix) is a common motif in the secondary structure of proteins and is a right hand-helix conformation in which every backbone N−H group hydrogen bonds to the backbone C=O group of the amino acid located four residues ear ...

and the β-pleated sheet. The ''

tertiary structure Protein tertiary structure is the three dimensional shape of a protein. The tertiary structure will have a single polypeptide chain "backbone" with one or more protein secondary structures, the protein domains. Amino acid side chains may inte ...

'' is a back and forth bending of the polypeptide chain, and the ''

quaternary structure Protein quaternary structure is the fourth (and highest) classification level of protein structure. Protein quaternary structure refers to the structure of proteins which are themselves composed of two or more smaller protein chains (also refe ...

'' is the way that tertiary units come together and interact.

Structural biology Structural biology is a field that is many centuries old which, and as defined by the Journal of Structural Biology, deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every le ...

is concerned with

biomolecular structure Biomolecular structure is the intricate folded, three-dimensional shape that is formed by a molecule of protein, DNA, or RNA, and that is important to its function. The structure of these molecules may be considered at any of several length s ...

of macromolecules.

Chemical

Chemical structure refers to both molecular geometry and electronic structure. The structure can be represented by a variety of diagrams called

structural formula The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bond ...

Lewis structure Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons tha ...

s use a dot notation to represent the

valence electron In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair form ...

s for an atom; these are the electrons that determine the role of the atom in chemical reactions. 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 The skeletal formula, or line-angle formula or shorthand formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of a molecule's bonding and some details of its molecular geometry. A ...

, only carbon-carbon bonds and functional groups are shown. Atoms in a crystal have a

structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...

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 Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...

operations that include rotations about a point, reflections about a symmetry planes, and ''

translations Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...

'' (movements of all the points by the same amount). Each crystal has a finite group, called the

space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unch ...

, of such operations that map it onto itself; there are 230 possible space groups. By

Neumann's law Neumann's law states that the molecular heat in compounds of analogous constitution is always the same. It is named after German mineralogist and physicist Franz Ernst Neumann Franz Ernst Neumann (11 September 1798 – 23 May 1895) was a German m ...

, the symmetry of a crystal determines what physical properties, including

piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ' ...

and

ferromagnetism Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...

, the crystal can have.

Mathematical

Musical

A large part of

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods t ...

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. Elements of music such as pitch, duration and

timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...

combine into small elements like motifs and

phrases In syntax and grammar, a phrase is a group of words or singular word acting as a grammatical unit. For instance, the English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy". Phrases can cons ...

, and these in turn combine in larger structures. Not all music (for example, that of

John Cage John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading fig ...

) has a

hierarchical organization A hierarchical organization or hierarchical organisation (see spelling differences) is an organizational structure where every entity in the organization, except one, is subordinate to a single other entity. This arrangement is a form of a hierar ...

, but hierarchy makes it easier for a listener to understand and remember the music. In analogy to

linguistic Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...

terminology, motifs and phrases can be combined to make complete musical ideas such as

sentences ''The Four Books of Sentences'' (''Libri Quattuor Sententiarum'') is a book of theology written by Peter Lombard in the 12th century. It is a systematic compilation of theology, written around 1150; it derives its name from the ''sententiae'' o ...

and

. A larger form is known as the

period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...

. One such form that was widely used between 1600 and 1900 has two phrases, an ''antecedent'' and a ''consequent'', with a half

cadence In Western musical theory, a cadence (Latin ''cadentia'', "a falling") is the end of a phrase in which the melody or harmony creates a sense of full or partial resolution, especially in music of the 16th century onwards.Don Michael Randel (1999) ...

in the middle and a full cadence at the end providing punctuation. On a larger scale are single-movement forms such as the

sonata form Sonata form (also ''sonata-allegro form'' or ''first movement form'') is a musical structure generally consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle of the 18th c ...

and the contrapuntal form, and multi-movement forms such as the

symphony A symphony is an extended musical composition in Western classical music, most often for orchestra. Although the term has had many meanings from its origins in the ancient Greek era, by the late 18th century the word had taken on the meaning ...

Social

A social structure is a pattern of relationships. They are social

organization An organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived from ...

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. Sociologists have studied the changing structure of these groups.

Structure and agency In the social sciences there is a standing debate over the primacy of structure or agency in shaping human behaviour. ''Structure'' is the recurrent patterned arrangements which influence or limit the choices and opportunities available. '' 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 A social class is a grouping of people into a set of hierarchical social categories, the most common being the upper, middle and lower classes. Membership in a social class can for example be dependent on education, wealth, occupation, incom ...

religion Religion is usually defined as a social-cultural system of designated behaviors and practices, morals, beliefs, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that generally relates humanity to supernatural, tran ...

gender Gender is the range of characteristics pertaining to femininity and masculinity and differentiating between them. Depending on the context, this may include sex-based social structures (i.e. gender roles) and gender identity. Most cultures us ...

ethnicity An ethnic group or an ethnicity is a grouping of people who identify with each other on the basis of shared attributes that distinguish them from other groups. Those attributes can include common sets of traditions, ancestry, language, history, ...

, customs, etc. that seem to limit or influence individual opportunities.

Data

In computer science, a data structure is a way of organizing information in a computer so that it can be used efficiently. Data structures are built out of two basic types: An

array An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...

has an index that can be used for immediate access to any data item (some

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

s require array size to be initialized). A

linked list In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes whi ...

can be reorganized, grown or shrunk, but its elements must be accessed with a pointer that links them together in a particular order. Out of these any number of other data structures can be created such as stacks, queues,

trees In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are u ...

and

hash table In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', ...

s. In solving a problem, a data structure is generally an integral part of the

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

. In modern programming style, algorithms and data structures are encapsulated together in an

abstract data type In computer science, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior (semantics) from the point of view of a '' user'', of the data, specifically in terms of possible values, po ...

Software

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

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. The purpose of structure is to optimise for (brevity, readability, traceability, isolation and encapsulation, maintainability, extensibility, performance and efficiency), examples being: language choice,

code In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...

, functions,

libraries A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

, builds, system evolution, or diagrams for flow logic and

design A design is a plan or specification for the construction of an object or system or for the implementation of an activity or process or the result of that plan or specification in the form of a prototype, product, or process. The verb ''to design'' ...

. 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. A high redundancy is an essential part of the design of several systems in the

Space Shuttle The Space Shuttle is a retired, partially reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. Its official program nam ...

Logical

As a branch of philosophy,

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

is concerned with distinguishing good arguments from poor ones. A chief concern is with the structure of arguments. An argument consists of one or more

premise A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agre ...

s from which a conclusion is

inferred Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

. 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.

References

External links

* (syllabus and reading list) {{Authority control Systems