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 biological organisms, minerals and chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space.
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). The latter was 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.
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.
Structural biology is concerned with the biomolecular structure of macromolecules, particularly proteins and nucleic acids. 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 helix and the 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.
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. By Neumann's law, the symmetry of a crystal determines what physical properties, including piezoelectricity and ferromagnetism, the crystal can have.
In analogy to linguistic terminology, motifs and phrases can be combined to make complete musical ideas such as sentences and phrases. 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. 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.
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 has an index that can be used for immediate access to any data item, but depending on the programming language used, its size must be specified when it is 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. Out of these any number of other data structures can be created such as stacks, queues, trees and hash tables.
As a branch of philosophy, logic 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 premises from which a conclusion is inferred. 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.