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64-649: The International Classification of Headache Disorders ( ICHD ) is a detailed hierarchical classification of all headache -related disorders published by the International Headache Society . It is considered the official classification of headaches by the World Health Organization , and, in 1992, was incorporated into the 10th edition of their International Classification of Diseases ( ICD-10 ). Each class of headache contains explicit diagnostic criteria—meaning that

128-505: A 3D model of a human for example, the chest is a parent of the upper left arm, which is a parent of the lower left arm, which is a parent of the hand . This pattern is used in modeling and animation for almost everything built as a 3D digital model. Many grammatical theories, such as phrase-structure grammar , involve hierarchy. Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via

192-411: A branching hierarchy , one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including organizations and classification schemes . The broad category of branching hierarchies can be further subdivided based on

256-514: A family tree ) and inheritance ( succession and heirship ). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs - according to Maslow's hierarchy of human needs. Learning steps often follow a hierarchical scheme—to master differential equations one must first learn calculus ; to learn calculus one must first learn elementary algebra ; and so on. Nature offers hierarchical structures, as numerous schemes such as Linnaean taxonomy ,

320-475: A reverse hierarchy , the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings. Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in

384-400: A business setting, a superior is a supervisor/boss and a peer is a colleague . Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in

448-501: A company with self-managing teams is Valve , which also has rotating, not permanent, team leaders - which Valve terms "group contributors", in recognition of the fact that contributing individually and leading at Valve form a spectrum, not a binary dichotomy. Generally the term of a group contributor at Valve is at most one project, after which time they (voluntarily) rotate back to being an individual contributor. Valve also allows team members to work on whatever they find interesting. This

512-446: A containment hierarchy is demonstrated in class inheritance in object-oriented programming . Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy " subsumes " its children, and a compositional hierarchy is " composed " of its children. A hierarchy can also be both subsumptive and compositional . A subsumptive containment hierarchy

576-400: A critical size, organizations can retain a streamlined structure but cannot keep a completely flat manager-to-staff relationship without affecting productivity . Certain financial responsibilities may also require a more conventional structure. A company would not have to give a raise or promotion, based on service length but on greater productivity. Also eliminating certain departments from

640-402: A file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located. For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at

704-409: A flat organization rely less on guidance from superiors because the number of superiors above the manager is limited. Empirical evidence from Ghiselli and Johnson suggests that the amount of independence that managers in flat organizations possess as a result of the flat organizational structure satisfies many of their needs in terms of autonomy and self-realization. The idea behind flat organizations

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768-428: A generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example: A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be

832-485: A hierarchy is diagrammed (see below ). In an organizational context, the following terms are often used related to hierarchies: In a mathematical context (in graph theory ), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures , objects are known as nodes , superiors are called parents and subordinates are called children . In

896-511: A hierarchy of persons. In this system, the three (or four with Algonquian languages ) persons occur in a hierarchy of salience . To distinguish which is subject and which object, inverse markers are used if the object outranks the subject. On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways. The structure of

960-455: A hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates , although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path . All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through

1024-406: A higher-level entity can have on x' s properties and interactions. Furthermore, the entities found at each level are autonomous . Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically. Some conventional definitions of the terms "nation" and "government" suggest that every nation has a government and that every government

1088-503: A highly hierarchical organization into a flat organization is known as delayering . In flat organizations, the number of people directly supervised by each manager is large, and the number of people in the chain of command above each person is small. A manager in a flat organization possesses more responsibility than a manager in a tall organization because there is a greater number of individuals immediately below them who are dependent on direction, help, and support. Moreover, managers in

1152-434: A lack of internal controls , due to its lack of managers. Prof. Cliff Oswick from Cass Business School , who has studied Valve and other examples of "non-leadership", believes that Valve works because it hires high-calibre people who are a good fit for the leaderless environment, and because it was founded as a flat organization from the outset, so that new hires always knew what they were getting into. However, he warns that

1216-436: A manager in self-managing teams determines the overall purpose or goal of the team, the team is at liberty to manage the methods by which to achieve that goal. This can cause conflict with people whose career path expectations include a promotion , which may not be available within the organization due to its flat structure. However, alternative "horizontal" career paths may be available, such as developing greater expertise in

1280-529: A musical composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, see Schenkerian analysis ), and in the (1985) Generative Theory of Tonal Music , by composer Fred Lerdahl and linguist Ray Jackendoff ). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are

1344-449: A path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues ; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form. Hierarchies have their own special vocabulary. These terms are easiest to understand when

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1408-410: A problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with

1472-439: A quadrilateral; it can never be a triangle , hexagon , etc. Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae ), a human can be formulated as: Taxonomies may change frequently (as seen in biological taxonomy ), but the underlying concept of nested hierarchies

1536-404: A required general property. These level hierarchies are characterized by bi-directional causation . Upward causation involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. Downward causation refers to the effect that the incorporation of entity x into

1600-514: A role or mastery of a craft , and/or receiving pay raises for loyalty . An absence of middle managers does not preclude the adoption and retention of mandatory work procedures, including quality assurance procedures. However, due to the fact that significant responsibilities are given to the team members themselves, if a team collectively arrives at the view that the procedures it is following are outdated, or could be improved, it may be able to change them. Such changes may, in some cases, require

1664-466: A world in which complexity had to evolve from simplicity. System hierarchies analysis performed in the 1950s, laid the empirical foundations for a field that would become, from the 1980s, hierarchical ecology . The theoretical foundations are summarized by thermodynamics . When biological systems are modeled as physical systems , in the most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and

1728-555: Is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status). Possibly the first use of the English word hierarchy cited by the Oxford English Dictionary

1792-441: Is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and " IS-A hierarchy". The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that

1856-404: Is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be " strict "—no two sets can be identical. The shapes example above can be modified to demonstrate this: The notation x ⊊ y {\displaystyle x\subsetneq y\,} means x is a subset of y but is not equal to  y . A general example of

1920-485: Is a hierarchical ordering of nested sets . The concept of nesting is exemplified in Russian matryoshka dolls . Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll;

1984-508: Is a member of the level Mammalia "is a" member of the level Animalia ; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of " concepts ". For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal. A compositional containment hierarchy

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2048-405: Is always transitive . The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects. Mathematically, in its most general form, a hierarchy is a partially ordered set or poset . The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with

2112-420: Is always the same. In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion . Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. A containment hierarchy

2176-466: Is an organizational structure with few or no levels of middle management between staff and executives. An organizational structure refers to the nature of the distribution of the units and positions within it, and also to the nature of the relationships among those units and positions. Tall and flat organizations differ based on how many levels of management are present in the organization and how much control managers are endowed with. Transforming

2240-507: Is an ordering of the parts that make up a system—the system is "composed" of these parts. Most engineered structures, whether natural or artificial, can be broken down in this manner. The compositional hierarchy that every person encounters at every moment is the hierarchy of life . Every person can be reduced to organ systems , which are composed of organs , which are composed of tissues , which are composed of cells , which are composed of molecules , which are composed of atoms . In fact,

2304-490: Is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy ) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings. A hierarchy

2368-631: Is hierarchical. Sociologists can analyse socioeconomic systems in terms of stratification into a social hierarchy (the social stratification of societies), and all systematic classification schemes ( taxonomies ) are hierarchical. Most organized religions , regardless of their internal governance structures, operate as a hierarchy under deities and priesthoods . Many Christian denominations have an autocephalous ecclesiastical hierarchy of leadership . Families can be viewed as hierarchical structures in terms of cousinship (e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in

2432-598: Is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. Organizations can be structured as a dominance hierarchy . In an organizational hierarchy, there is a single person or group with the most power or authority , and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments , companies , armed forces , militia and organized religions . The units or persons within an organization may be depicted hierarchically in an organizational chart . In

2496-521: Is known as open allocation , and means that employees can switch to another team at any time, no questions asked; all desks are on wheels to make this easy. However, because new ideas may require significant resources, someone with a new idea may need to persuade a number of their coworkers to join them in order to create a new team and reach the necessary "critical mass" for the new idea to come to fruition. Valve's co-founder has admitted that it has issues with failing to catch bad decisions early on due to

2560-555: Is possible to redefine the position of existing staff within the new flatter structure - the two often coincide". Frank Ostroff, in The Horizontal Organisation , argues that the horizontal structure "delivers value to customers". A "strong form" of flat organization is an organization with no middle management at all . Very small businesses may lack middle managers because there are too few staff to justify hiring middle managers; in this type of organization,

2624-514: Is that well-trained workers will be more productive when they are more directly involved in the decision-making process rather than closely supervised by many layers of management. Delayering plans may aim to secure these benefits, although potential risks include undermining employee's confidence in their managers and putting the remaining managers under greater pressure. This structure is generally possible only in smaller organizations or individual units within larger organizations. Having reached

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2688-420: Is typically depicted as a pyramid , where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. For example, the few Directors of a company could be at the apex , and the base could be thousands of people who have no subordinates. These pyramids are often diagrammed with a triangle diagram which serves to emphasize

2752-484: The "postal district" , consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an overlapping hierarchy , because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter positions allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System

2816-477: The organization of life , and biomass pyramids attempt to document. While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal-code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept,

2880-510: The peer-review -based stack ranking system Valve uses for determining employee remuneration, might become problematic if in the future Valve becomes short of cash. Other examples of companies with self-managing teams include the following: In technology, agile development involves teams self-managing to a large extent (though agile development is commonly still practiced within a hierarchical organization, which means that certain types of decisions such as hiring, firing, and pay raises remain

2944-579: The set/subset relations between dissipative structures can be characterized in a hierarchy. Other hierarchical representations related to biology include ecological pyramids which illustrate energy flow or trophic levels in ecosystems , and taxonomic hierarchies, including the Linnean classification scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species. CGI and computer-animation programs mostly use hierarchies for models. On

3008-433: The approval of executive management and/or customers (consider, for example, a digital agency producing bespoke websites for corporate clients). If executive management is not involved in the decision, or merely rubber-stamps it, this might be an example of consensus decision-making or workplace democracy at the level of a team - or group of teams, if multiple teams are involved in the decision. The foremost example of

3072-470: The business owner or the CEO may perform some of the functions performed by middle managers in larger organizations. However, some organizations do not take on middle managers even as they become larger, remaining extremely flat. An organization with self-managing teams who organize their own work without the need for a middle manager or supervisor above the team may meet or closely approximate this model. While

3136-629: The criteria include quantities rather than vague terms like several or usually —that are based on clinical and laboratory observations. The ICHD was first published in 1988 (now known as the ICHD-1). A second version, the ICHD-2, was published in 2004. The most current version, ICHD-3, was published in 2018. teeth, mouth or other facial or cervical structures Hierarchical A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in

3200-515: The degree. A flat hierarchy (also known for companies as flat organization ) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles. An overlapping hierarchy

3264-447: The foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or Ursatz , which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature. Flat organization A flat organization (also known as horizontal organization or flat hierarchy )

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3328-521: The formation of informal cliques, the " soft power " of popular employees, un professional and sexist attitudes, and lack of workplace diversity . Suzanne J. Baker argues that new power dynamics can emerge that undermine the equality afforded by a non-hierarchical context. When an organization decides to no longer place value on a person's position, Baker suggests that new hierarchies based on personality type, skill set, and communication style can emerge. If these hierarchies don't get acknowledged, it

3392-527: The last two levels apply to all matter , at least at the macroscopic scale . Moreover, each of these levels inherit all the properties of their children . In this particular example, there are also emergent properties —functions that are not seen at the lower level (e.g., cognition is not a property of neurons but is of the brain )—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not

3456-429: The left and descending on the right. Child elements are towards the bottom of the stairs and parent elements are at the top. This structure represents hierarchical relationships through the use of visual stacking. In plain English, a hierarchy can be thought of as a set in which: The first requirement is also interpreted to mean that a hierarchy can have no circular relationships ; the association between two objects

3520-579: The payroll means saving money. The flat organization model promotes employee involvement through decentralized decision-making processes. By elevating the level of responsibility of baseline employees and eliminating layers of middle management, comments and feedback reach all personnel involved in decisions more quickly. Expected response to customer feedback becomes more rapid. Australian researchers Dunford, Bramble and Littler note that delayering in an organisation may also lead to down-sizing: "[a]lthough delayering need not involve down-sizing - because it

3584-408: The prerogative of managers). In scrum , an agile framework, team members assign work to be done among themselves, either by free choice or by consensus. The scrum master role in scrum is not a management role as such, but is a role that involves helping remove obstacles to progress and ensuring that the basic scrum framework is adhered to by all parties, inside and outside the team - both aspects of

3648-407: The problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations. A nested hierarchy or inclusion hierarchy

3712-404: The role being more akin to facilitation than to top-down micromanagement . Agile frameworks such as scrum have also begun being used in non-technology companies and organizations. Drawing on Jo Freeman 's famous essay The Tyranny of Structurelessness , Klint Finley has argued that "bossless" companies like Valve might suffer from problems related to the appropriate handling of grievances ,

3776-477: The rules of visual hierarchy . Visual hierarchy is also important for proper organization of files on computers. An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information. The child element is within the parent element, such as in a Venn diagram . This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open

3840-469: The same property value are grouped together, and each of those resulting levels is referred to as a class . "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to

3904-470: The size differences between the levels (but not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid ). An example of a triangle diagram appears to the right. Another common representation of a hierarchical scheme is as a tree diagram . Phylogenetic trees , charts showing the structure of § Organizations , and playoff brackets in sports are often illustrated this way. More recently, as computers have allowed

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3968-399: The storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees . In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on

4032-517: The system as a whole. Categorization in this way yields two broad classes: linear and branching . In a linear hierarchy , the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. This is referring to the objects and not the levels ; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. In

4096-606: Was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, hierarchia ) both in reference to the celestial hierarchy and the ecclesiastical hierarchy . The Greek term hierarchia means 'rule of a high priest', from hierarches (ἱεράρχης, 'president of sacred rites, high-priest') and that from hiereus (ἱερεύς, 'priest') and arche (ἀρχή, 'first place or power, rule'). Dionysius

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