Matrix is a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules.

Formulating the logical constructs of human thinking. Mind Maps - Neural Networks - Lattice - Array - Structure.

Matrix in mathematics is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Row is an arrangement of objects or people side by side in a line horizontally. A linear array of numbers, letters, or symbols side by side.

Column is a vertical array of numbers or other information. Database.

Tabular is information arranged in a table, with rows and columns. Flat like a table in form. Periodic Table.

Array is an orderly arrangement. Organized logically in a line or as if in a line.

Grid is a pattern of regularly spaced horizontal and vertical lines. Smart Grid.

Matrix Multiplication is a binary operation that produces a matrix from two matrices and produces another matrix. Numbers such as the real or complex numbers can be multiplied according to elementary arithmetic. On the other hand, matrices are arrays of numbers, so there is no unique way to define "the" multiplication of matrices. As such, in general the term "matrix multiplication" refers to a number of different ways to multiply matrices. The key features of any matrix multiplication include: the number of rows and columns the original matrices have (called the "size", "order" or "dimension"), and specifying how the entries of the matrices generate the new matrix. The definition is motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering The matrix product is not commutative in general, although it is associative and is distributive over matrix addition. The identity element of the matrix product is the identity matrix (analogous to multiplying numbers by 1), and a square matrix may have an inverse matrix (analogous to the multiplicative inverse of a number). Determinant multiplicativity applies to the matrix product. The matrix product is also important for matrix groups, and the theory of group representations and irreps. Computing matrix products is both a central operation in many numerical algorithms and potentially time consuming, making it one of the most well-studied problems in numerical computing. Various algorithms have been devised for computing C = AB, especially for large matrices.

Matrix Number is an alphanumeric code (and on occasion, other symbols) stamped or handwritten (or a combination of the two) into the run-out groove area of a gramophone record. This is the non-grooved area between the end of the final band on a record's side and the label, also known as the run-off groove area, end-groove area, matrix area, or "dead wax".

Logical Matrix or binary matrix, relation matrix, Boolean matrix, or (0,1) matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can be used to represent a binary relation between a pair of finite sets.

Matrix Similarity matrices represent the same linear operator under two different bases.

Traceability Matrix is a document, usually in the form of a table, used to assist in determining the completeness of a relationship by correlating any two baselined documents using a many-to-many relationship comparison.

Visual Maps - Linking Data

Cellular Automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton.

Extracellular Matrix (cells)

Matrix Attachment Region are sequences in the DNA of eukaryotic chromosomes where the nuclear matrix attaches.

Matrix in music is an element of variations which does not change.

Similarity Matrix is a real-valued function that quantifies the similarity between two objects.

Position-Specific Scoring Matrix is a commonly used representation of motifs (patterns) in biological sequences. Also known as a position-specific weight matrix (PSWM) or position-specific scoring matrix (PSSM).

Brain Matrix - Matrix the Movie

Matrix Mechanics is a formulation of quantum mechanics interpreting the physical properties of particles as matrices that evolve in time.

Matrix in biology is the material or tissue in animal or plant cells, in which more specialized structures are embedded, and a specific part of the mitochondrion that is the site of oxidation of organic molecules. The internal structure of connective tissues is an extracellular matrix. Finger nails and toenails grow from matrices. It is found in various connective tissue. It is generally used as a jelly like structure instead of cytoplasm in connective tissue.

Substitution Matrix describes the rate at which one character in a sequence changes to other character states over time.

Distance Matrix is a matrix or two-dimensional array containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved, the distance being used to define this matrix may or may not be a metric.

Formulation Logic are simple, first-order logic knowledge representations of natural language sentences formed by the conjunction of concept predicates related through shared arguments.

First-Order Logic is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic. First-order logic uses quantified variables over (non-logical) objects. It allows the use of sentences that contain variables, so that rather than propositions such as Socrates is a man one can have expressions in the form X is a man where X is a variable. This distinguishes it from propositional logic, which does not use quantifiers.

Transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).

Spatial Intelligence - Language of Thought Hypothesis

Human Operating System - Thinking Levels

Invertible Matrix in linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate).

Covariance Matrix in probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i th and j th elements of a random vector. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable. Each element has either a finite number of observed empirical values or a finite or infinite number of potential values. The potential values are specified by a theoretical joint probability distribution.

Jacobian Matrix and Determinant is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square matrix, both the matrix and its determinant are referred to as the Jacobian in literature.

Matrix Ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication (Lam 1999). Angles.

Square Matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied.

Invertible Matrix (wiki) - Invertible is having an additive or multiplicative inverse. Multiplicative Inverse is one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7.

Dot Matrix is a 2-dimensional patterned array, used to represent characters, symbols and images. Every type of modern technology uses dot matrices for display of information, including cell phones, televisions, and printers. They are also used in textiles with sewing, knitting, and weaving. An alternate form of information display using lines and curves is known as a vector display, was used with early computing devices such as air traffic control radar displays and pen-based plotters but is no longer used. Electronic vector displays were typically monochrome only, and either don't fill in the interiors of closed vector shapes, or shape-filling is slow, time-consuming, and often non-uniform, as on pen-based plotters. In printers, the dots are usually the darkened areas of the paper. In displays, the dots may light up, as in an LED, CRT, or plasma display, or darken, as in an LCD.

Quantum Matrix is a term referring to a natural component of the structure of matter, as well as an engineering component capable of generating a quantum field. The quantum matrix of Meridian fluctuated, causing it to shift into our dimension for a brief period every sixty years.

First: Read the words in each Row from Left to Right - Connotation.

Second: Read the words in each Column from Top to Bottom - Association.

Third: Read the words in each Group and as a Whole - Construct.

First Layer Word Matrix

Second Layer Word Matrix - Below is the second level word matrix that goes behind the single words above in the top level word matrix. Two similar words with similar meanings for each single word above in the top level word matrix. Understand the Progressions and Connections in each Row from Left to Right and each Column from Top to Bottom. Subset - Dimensions.

Community Structure is when the nodes of the network can be easily grouped into potentially overlapping sets of nodes, such that each set of nodes is densely connected internally. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, here the goal is to find a community that a certain vertex belongs to. Louvain Modularity is the Louvain Method for community detection is a method to extract communities from large networks.

Latticework - Neural Networks - Deep Learning - (Word2vec - Word Embedding)

Cellular Automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. Mathematical Function.

Coupled Map Lattice is a dynamical system that models the behavior of non-linear systems (especially partial differential equations). They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems. This includes the dynamics of spatiotemporal chaos where the number of effective degrees of freedom diverges as the size of the system increases. Features of the CML are discrete time dynamics, discrete underlying spaces (lattices or networks), and real (number or vector), local, continuous state variables. Studied systems include populations, chemical reactions, convection, fluid flow and biological networks. More recently, CMLs have been applied to computational networks identifying detrimental attack methods and cascading failures. CMLs are comparable to cellular automata models in terms of their discrete features. However, the value of each site in a cellular automata network is strictly dependent on its neighbor (s) from the previous time step. Each site of the CML is only dependent upon its neighbors relative to the coupling term in the recurrence equation. However, the similarities can be compounded when considering multi-component dynamical systems.

Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems.

Majority problem in cellular automaton is the problem of finding one-dimensional cellular automaton rules that accurately perform majority voting.

Majority Function is a function from n inputs to one output. The value of the operation is false when n/2 or more arguments are false, and true otherwise. Alternatively, representing true values as 1 and false values as 0.

Connotation is what you must know in order to determine the reference of an expression. Connotation is a commonly understood cultural or emotional association that some word or phrase carries, in addition to the word's or phrase's explicit or literal meaning, which is its denotation.

Organizing - Cross-Reference - Machine Learning - Index Publishing - Linking - Analogies.

Association is the state of being connected together. A relation resulting from interaction or dependence. Logical connections.

Associations is a process by which representations arise in consciousness, and also for a principle put forward by an important historical school of thinkers to account generally for the succession of mental phenomena. Organize.

Association in psychology refers to a connection between conceptual entities or mental states that results from the similarity between those states or their proximity in space or time.

Association of Ideas is a process by which representations arise in consciousness, and also for a principle put forward by an important historical school of thinkers to account generally for the succession of mental phenomena. It is used mostly in the history of philosophy and of psychology. One idea was thought to follow another in consciousness if it were associated by some principle. The three commonly asserted principles of association were similarity, contiguity, and contrast, numerous others had been added by the nineteenth century. Everyday observation of the association of one idea or memory with another gives a face validity to the notion. In addition, the notion of association between ideas and behavior gave some early impetus to behaviorist thinking. The core ideas of associationist thinking recur in some recent thought on cognition, especially consciousness.

Simultaneous (associations) - Associative Memory (Simultaneous)

Associationism is the idea that mental processes operate by the association of one mental state with its successor states.

Association in object-oriented programming

Word Association Games

Associative Model of Data is a data model for database systems. Other data models, such as the relational model and the object data model, are record-based. These models involve encompassing attributes about a thing, such as a car, in a record structure. Such attributes might be registration, colour, make, model, etc. In the associative model, everything which has “discrete independent existence” is modeled as an entity, and relationships between them are modeled as associations. The granularity at which data is represented is similar to schemes presented by Chen (Entity-relationship model); Bracchi, Paolini and Pelagatti (Binary Relations); and Senko (The Entity Set Model).

Associative Memory Base or Content-addressable memory, is a special type of computer memory used in certain very-high-speed searching applications.

Associative Storage is a special type of computer memory used in certain very-high-speed searching applications. It is also known as associative memory, associative storage, or associative array, although the last term is more often used for a programming data structure. It compares input search data (tag) against a table of stored data, and returns the address of matching data (or in the case of associative memory, the matching data).

Memory - Search Technology

Coupling in computer programming is the degree of interdependence between software modules; a measure of how closely connected two routines or modules are; the strength of the relationships between modules. Coupling is usually contrasted with cohesion. Low coupling often correlates with high cohesion, and vice versa. Low coupling is often a sign of a well-structured computer system and a good design, and when combined with high cohesion, supports the general goals of high readability and maintainability

Brainwave Entrainment

"Neurons that fire together wire together." Plasticity.

Paired Associate Learning is the presentation of one leads to the recall of the other. Learning of Pairs of items. (PAL)

Ontology is a knowledge domain that is usually hierarchical and contains all the relevant entities and their relations.

Ontology in information science are types, properties, and interrelationships of the entities that really or fundamentally exist for a particular domain of discourse.

Relation is an abstraction belonging to or characteristic of two entities or parts together. Thematic Euclid.

Algorithms - Meanings

Relating is to make a logical or causal connection. Be relevant to. Be in a relationship with. Have or establish a relationship to.

Sample is a small part of something intended as representative of the whole. All or part of a natural object that is collected and preserved as an example of its class.

Correlation is a reciprocal relation between two or more things. A statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other. Correlations.

Interconnectivity refers to the state or quality of being connected together.

Interconnectedness is a oneness in all things - Relational Database.

Connection is a relation between things or events (as in the case of one causing the other or sharing features with it) The act of bringing two things into contact (especially for communication).

Set in mathematics is a well-defined collection of distinct objects, considered as an object in its own right.

Comparisons - Connections

Connectedness is the process of bringing ideas or events together in memory or imagination.

Anatomy is the study of the structure of organisms and their parts.

Ethernet Hub is a network hardware device for connecting multiple Ethernet devices together and making them act as a single network segment. It has multiple input/output (I/O) ports, in which a signal introduced at the input of any port appears at the output of every port except the original incoming. A hub works at the physical layer (layer 1) of the OSI model. Repeater hubs also participate in collision detection, forwarding a jam signal to all ports if it detects a collision. In addition to standard 8P8C ("RJ45") ports, some hubs may also come with a BNC or Attachment Unit Interface (AUI) connector to allow connection to legacy 10BASE2 or 10BASE5 network segments.

Parse Tree is an ordered, rooted tree that represents the syntactic structure of a string according to some context-free grammar. The term parse tree itself is used primarily in computational linguistics; in theoretical syntax, the term syntax tree is more common.

Binary Symmetric Channel is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver receives a bit. It is assumed that the bit is usually transmitted correctly, but that it will be "flipped" with a small probability (the "crossover probability"). This channel is used frequently in information theory because it is one of the simplest channels to analyze.

Shannon Weaver Model refers to an integrated model of the concepts of information source, message, transmitter, signal, channel, noise, receiver, information destination, probability of error, encoding, decoding, information rate, channel capacity, etc.

Fourier Analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.

Heaviside Step Function is a discontinuous function whose value is zero for negative argument and one for positive argument. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.

Word Triangles (PDF)

Intersection in set theory is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

Venn Diagram is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set.

BEST Cover the Spot Carnival Game Tutorial (5 silver disks cover a red circle)/

Grey Relational Analysis defines situations with no information as black, and those with perfect information as white. However, neither of these idealized situations ever occurs in real world problems.

Mind Maps

Cognitive Model is an approximation to animal cognitive processes, predominantly human, for the purposes of comprehension and prediction. Cognitive models can be developed within or without a cognitive architecture, though the two are not always easily distinguishable.

Network is an interconnected system of things or people. Reciprocally connected. Operating as a unit.

Network Science - Computer Network

Complex Network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in graphs modelling of real systems.

Biological Network is any network that applies to biological systems. A network is any system with sub-units that are linked into a whole, such as species units linked into a whole food web. Biological networks provide a mathematical representation of connections found in ecological, evolutionary, and physiological studies, such as neural networks. The analysis of biological networks with respect to human diseases has led to the field of network medicine, which is the application of network science towards identifying, preventing, and treating diseases.

Neural Network (Artificial Intelligence)

Narrative Network is a system which represents complex event sequences or characters’ interactions as depicted by a narrative text.

Network Motif: All networks, including biological networks, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as graphs, which include a wide variety of subgraphs. One important local property of networks are so-called network motifs, which are defined as recurrent and statistically significant sub-graphs or patterns.

Hopfield Network is a form of recurrent Artificial Neural Network.

Organizing - Social Network

Relational Frame Theory is a psychological theory of human language that argues that the building block of human language and higher cognition is 'relating', i.e. the human ability to create links between things. It can be contrasted with associative learning, which discusses how animals form links between stimuli in the form of the strength of associations in memory. However, relational frame theory argues that natural human language typically specifies not just the strength of a link between stimuli but also the type of relation as well as the dimension along which they are to be related.

Affinity in immunology is the attraction between an antigen and an antibody. Affinity in anthropology is kinship by marriage or adoption; not a blood relationship. Affinity in biology is the state of relationship between organisms or groups of organisms resulting in resemblance in structure or structural parts. A close connection marked by community of interests or similarity in nature or character. The force attracting atoms to each other and binding them together in a molecule. Inherent resemblance between persons or things. A natural attraction or feeling of kinship.

Integration is the act of combining into an integral whole. The action of incorporating a racial or religious group into a community.

System Integration is the process of bringing together the component sub-systems into one system (an aggregation of subsystems cooperating so that the system is able to deliver the overarching functionality) and ensuring that the subsystems function together as a system, and in information technology as the process of linking together different computing systems and software applications physically or functionally, to act as a coordinated whole.

Affine is pertaining to the Geometry of Affine Transformations, which is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line.

Representational State Transfer are one way of providing interoperability between computer systems on the Internet. Interoperability is the ability to exchange and use information (usually in a large heterogeneous network made up of several local area networks).

Simultaneous Subject Teaching - Logically Ordered Steps - Thinking Layers - Organizing - Knowledge Management.

Data Set corresponds to the contents of a single database table, or a single statistical data matrix, where every column of the table represents a particular variable, and each row corresponds to a given member of the data set in question. The data set lists values for each of the variables, such as height and weight of an object, for each member of the data set. Each value is known as a datum. The data set may comprise data for one or more members, corresponding to the number of rows. The term data set may also be used more loosely, to refer to the data in a collection of closely related tables, corresponding to a particular experiment or event. An example of this type is the data sets collected by space agencies performing experiments with instruments aboard space probes.

Set in mathematics is a well-defined collection of distinct objects, considered as an object in its own right.

Data Model is an abstract model that organizes elements of data and standardizes how they relate to one another and to properties of the real world. For instance, a data model may specify that a data element representing a car comprise a number of other elements which in turn represent the color, size and owner of the car.

Data Matrix is a matrix of data of dimension n-by-p, where n is the number of samples observed, and p is the number of variables (features) measured in all samples.

Table in a database is a collection of related data held in a structured format within a database. It consists of columns, and rows. A table is a set of data elements (values) using a model of vertical columns (identifiable by name) and horizontal rows, the cell being the unit where a row and column intersect. A table has a specified number of columns, but can have any number of rows. Each row is identified by one or more values appearing in a particular column subset. The columns subset which uniquely identifies a row is called the primary key.

Flat File Database is a database which is stored on its host computer system as an ordinary "flat file". To access the structure of the data and manipulate it, the file must be read in its entirety into the computer's memory. Upon completion of the database operations, the file is again written out in its entirety to the host's file system. In this stored mode the database is "flat", which means it has no structure for indexing and there are usually no structural relationships between the records. A flat file can be a plain text file or a binary file.

Relational Database is a digital database whose organization is based on the relational model of data. The various software systems used to maintain relational databases are known as a relational database management system (RDBMS). Virtually all relational database systems use SQL (Structured Query Language) as the language for querying and maintaining the database.

Content-Addressable Memory is a special type of computer memory used in certain very-high-speed searching applications. It is also known as associative memory, associative storage, or associative array, although the last term is more often used for a programming data structure. It compares input search data (tag) against a table of stored data, and returns the address of matching data (or in the case of associative memory, the matching data).

Data Matrix in multivariate statistics is a matrix of data of dimension n-by-p, where n is the number of samples observed, and p is the number of variables (features) measured in all samples. In this representation different rows typically represent different repetitions of an experiment, while columns represent different types of data (say, the results from particular probes). For example, suppose an experiment is run where 10 people are pulled off the street and asked four questions. The data matrix M would be a 10×4 matrix (meaning 10 rows and 4 columns). The datum in row i and column j of this matrix would be the answer of the i th person to the j th question.

Mesh Networking - Internet Web - Internet Collaboration

Grid Computing is the collection of computer resources from multiple locations to reach a common goal.

Schema is an internal representation of the world; an organization of concepts and actions that can be revised by new information about the world. A schematic or preliminary plan.

Schema describes a pattern of thought or behavior that organizes categories of information and the relationships among them. It can also be described as a mental structure of preconceived ideas, a framework representing some aspect of the world, or a system of organizing and perceiving new information. Schemata influence attention and the absorption of new knowledge: people are more likely to notice things that fit into their schema, while re-interpreting contradictions to the schema as exceptions or distorting them to fit. Schemata have a tendency to remain unchanged, even in the face of contradictory information. Schemata can help in understanding the world and the rapidly changing environment. People can organize new perceptions into schemata quickly as most situations do not require complex thought when using schema, since automatic thought is all that is required. People use schemata to organize current knowledge and provide a framework for future understanding. Examples of schemata include academic rubrics, social schemas, stereotypes, social roles, scripts, worldviews, and archetypes. In Piaget's theory of development, children construct a series of schemata, based on the interactions they experience, to help them understand the world.

Construct is the combining of materials and parts. Put together out of artificial or natural components or parts. Draw with suitable instruments and under specified conditions. Create by linking linguistic units. Create by organizing and linking ideas, arguments, or concepts.

Transitive Relation - Associations - Engineering - Operating System - Constitution - Foundation - Seeing the Whole Picture

Framework is a hypothetical description of a complex entity or process. The underlying structure.

Conceptual Framework is an analytical tool with several variations and contexts. It is used to make conceptual distinctions and organize ideas. Strong conceptual frameworks capture something real and do this in a way that is easy to remember and apply.

Computing Platform where any piece of software is executed. It may be the hardware or OS, even a web browser as long as the code is executed in it. The stage on which computer programs can run. The combination of a particular computer and a particular operating system.

Software Framework is an abstraction in which software providing generic functionality can be selectively changed by additional user-written code, thus providing application-specific software. A software framework is a universal, reusable software environment that provides particular functionality as part of a larger software platform to facilitate development of software applications, products and solutions. Software frameworks may include support programs, compilers, code libraries, tool sets, and application programming interfaces (APIs) that bring together all the different components to enable development of a project or system.

Software Feature feature-rich when it has many options and functional capabilities available to the user.

OSI Model is a conceptual model that characterizes and standardizes the communication functions of a telecommunication or computing system without regard to their underlying internal structure and technology. Its goal is the interoperability of diverse communication systems with standard protocols. The model partitions a communication system into abstraction layers. The original version of the model defined seven layers.

Technology Stack is a set of software subsystems or components needed to create a complete platform such that no additional software is needed to support applications. Applications are said to "run on" or "run on top of" the resulting platform. Some definitions of a platform overlap with what is known as system software.

Abstraction Layer is a way of hiding the implementation details of a particular set of functionality, allowing the separation of concerns to facilitate interoperability and platform independence.

Open Systems Interconnection is an effort to standardize computer networking.

Enterprise Architecture Framework defines how to create and use an enterprise architecture. An architecture framework provides principles and practices for creating and using the architecture description of a system. It structures architects' thinking by dividing the architecture description into domains, layers or views, and offers models - typically matrices and diagrams - for documenting each view. This allows for making systemic design decisions on all the components of the system and making long-term decisions around new design, requirements, sustainability and support.

Enterprise Architecture is a defined practice for conducting enterprise analysis, design, planning, and implementation, using a holistic approach at all times, for the successful development and execution of strategy. Enterprise architecture applies architecture principles and practices to guide organizations through the business, information, process, and technology changes necessary to execute their strategies. These practices utilize the various aspects of an enterprise to identify, motivate, and achieve these changes.

Encapsulation Object-Oriented Programming is used to refer to one of two related but distinct notions, and sometimes to the combination thereof: A language mechanism for restricting direct access to some of the object's components. A language construct that facilitates the bundling of data with the methods (or other functions) operating on that data.

"One of the best things about the digital world is that we can see Multiple Layers Deep, without moving."

Concurrence is an agreement of results or opinions. Acting together, as agents or circumstances or events. A state of cooperation. The temporal property of two things happening at the same time.

String in computer science is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally understood as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. A string may also denote more general arrays or other sequence (or list) data types and structures.

Concurrency in computer science is the decomposability property of a program, algorithm, or problem into order-independent or partially-ordered components or units. This means that even if the concurrent units of the program, algorithm, or problem are executed out-of-order or in partial order, the final outcome will remain the same. This allows for parallel execution of the concurrent units, which can significantly improve overall speed of the execution in multi-processor and multi-core systems.

Grouping heuristics for word-level decision diagrams.

Familiarity Heuristic.

Palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward, such as madam or racecar. Sentence-length palindromes may be written when allowances are made for adjustments to capital letters, punctuation, and word dividers, such as "A man, a plan, a canal, Panama!", "Was it a car or a cat I saw?" or "No 'x' in Nixon".

Structure is the complex composition of knowledge as elements and their combinations. Having definite and highly organized structure. A thing constructed; a complex entity constructed of many parts. The manner of construction of something and the arrangement of its parts. 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.

Complexities describes the behavior of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions. Generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. Complex is a complicated in structure consisting of interconnected parts. A conceptual whole made up of complicated and related parts.

Composition is the spatial property resulting from the arrangement of parts in relation to each other and to the whole. A mixture of ingredients. Something that is created by arranging several things to form a unified whole.

Web Application Framework is a software framework that is designed to support the development of web applications including web services, web resources, and web APIs.

Logical Framework Approach is a methodology mainly used for designing, monitoring, and evaluating international development projects. Variations of this tool are known as Goal Oriented Project Planning (GOPP) or Objectives Oriented Project Planning (OOPP).

Networks (computers) - Infrastructure (city management) - Scaffold.

Data Structure is a particular way of organizing data in a computer so that it can be used efficiently.

Crystal Structure (lattice) - Structural Engineering - Foundation - Mindset - Human Operating System

Linked Data Structure is a data structure which consists of a set of data records (nodes) linked together and organized by references (links or pointers). The link between data can also be called a connector. In linked data structures, the links are usually treated as special data types that can only be dereferenced or compared for equality. Linked data structures are thus contrasted with arrays and other data structures that require performing arithmetic operations on pointers. This distinction holds even when the nodes are actually implemented as elements of a single array, and the references are actually array indices: as long as no arithmetic is done on those indices, the data structure is essentially a linked one. Linking can be done in two ways – using dynamic allocation and using array index linking. Linked data structures include linked lists, search trees, expression trees, and many other widely used data structures. They are also key building blocks for many efficient algorithms, such as topological sort and set union-find. List of Data Structures (wiki)

Tree Structure is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree, even though the chart is generally upside down compared to an actual tree, with the "root" at the top and the "leaves" at the bottom. A tree structure is conceptual, and appears in several forms. For a discussion of tree structures in specific fields, see Tree (data structure) for computer science: insofar as it relates to graph theory, see tree (graph theory), or also tree (set theory). Mind Maps.

Structured Programming is a programming paradigm aimed at improving the clarity, quality, and development time of a computer program by making extensive use of subroutines, block structures, for and while loops—in contrast to using simple tests and jumps such as the go to statement which could lead to "spaghetti code" causing difficulty to both follow and maintain.

Routines - Foundation - Default Mode Network (focus)

Structural Rule is an inference rule that does not refer to any logical connective, but instead operates on the judgment or sequents directly. Structural rules often mimic intended meta-theoretic properties of the logic. Logics that deny one or more of the structural rules are classified as substructural logics.

Unstructured Data refers to information that either does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured information is typically text-heavy, but may contain data such as dates, numbers, and facts as well. This results in irregularities and ambiguities that make it difficult to understand using traditional programs as compared to data stored in fielded form in databases or annotated (semantically tagged) in documents. Fragmented.

Structured Analysis are methods for analyzing business requirements and developing specifications for converting practices into computer programs, hardware configurations, and related manual procedures. Structured analysis and design techniques are fundamental tools of systems analysis.

Engineering - Software Architecture

Abstract Structure in mathematics is a formal object that is defined by a set of laws, properties, and relationships in a way that is logically if not always historically independent of the structure of contingent experiences, for example, those involving physical objects. Abstract structures are studied not only in logic and mathematics but in the fields that apply them, as computer science, and in the studies that reflect on them, such as philosophy and especially the philosophy of mathematics.

Interpretation in model theory is a technical notion that approximates the idea of representing a logical structure inside another structure.

Combination - Working Together

Structure Mapping Engine is an implementation in software of an algorithm for analogical matching with the idea being that an analogy is a mapping of knowledge from one domain (the base) into another (the target). The theory is useful because it ignores surface features and finds matches between potentially very different things if they have the same representational structure. For example, SME could determine that a pen is like a sponge because both are involved in dispensing liquid, even though they do this very differently. The structure-mapping engine is a computer simulation of the analogy and similarity comparisons. Connected knowledge is preferred over independent facts. Therefore, the structure mapping engine should ignore isolated source-target mappings unless they are part of a bigger structure. The SME, the theory goes, should map objects that are related to knowledge that has already been mapped.

Structure-Mapping Theory is a theory of analogical reasoning that aims to improve upon previous theories of analogy, by distinguishing analogy from literal similarity.

Algebraic Structure is any set upon which arithmetic-like operations have been defined.

Abstract algebra is the name that is commonly given to the study of algebraic structures.

Mathematical Structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance. A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories. Sometimes, a set is endowed with more than one structure simultaneously; this enables mathematicians to study it more richly. For example, an ordering imposes a rigid form, shape, or topology on the set. As another example, if a set has both a topology and is a group, and these two structures are related in a certain way, the set becomes a topological group. Mappings between sets which preserve structures (so that structures in the source or domain are mapped to equivalent structures in the destination or codomain) are of special interest in many fields of mathematics. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures.

Map in mathematics refers to either a function, often with some sort of special structure, in particular when the relation is taken together with a set that constitutes the codomain, or a morphism in category theory, which generalizes the idea of a function. There are also a few, less common uses in logic and graph theory.

Form is a perceptual structure. Establish or impress firmly in the mind. Create as an entity. To compose or represent. Give shape or form to. Make something, usually for a specific function. The spatial arrangement of something as distinct from its substance. The visual appearance of something or someone. An arrangement of the elements in a composition or discourse. In biology, form is a group of organisms within a species that differ in trivial ways from similar groups. In physical chemistry, form is a distinct state of matter in a system; matter that is identical in chemical composition and physical state and separated from other material by the phase boundary.

The twelve systems are not scientific models but insights into degrees of organization. How Structures Work. The Monad gives totality – without distinction of parts, hence universality as the systemic attribute. The Dyad gives difference without degrees, hence complementarity. The Triad gives relatedness without relativity and hence dynamism as distinct from force. The Tetrad gives structured activity and combines relativity and order, and hence activity as distinct from potential. Why Structures Work (how they enter into the pattern of Reality). The Pentad gives significance both inner and outer: hence also potentiality as distinct from actual occurrences. Here entities make their first appearance in the scheme of understanding. The Hexad gives structure capable of transformation without loss of identity, hence recurrence and the character of events and so the historical character of experience. The systemic attribute is called coalescence. The Heptad gives completeness combined with distinctions of quality: hence transformation. The Octad gives the property whereby a structure can be understood in and for itself without reference to other structures, hence completedness. The Harmony of Structures (the conditions that enable them to fulfill their destined purpose). The Ennead gives harmonization. The Decad gives Integrative Complementarity. The Undecad gives Synergism. The Duodecad gives Perfection.

Latticework is an openwork framework consisting of a criss-crossed pattern of strips of building material, typically wood or metal. The design is created by crossing the strips to form a network. Can be ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material.

Lattice is an arrangement of points or particles or objects in a regular periodic pattern in 2 or 3 dimensions.

Crystal Lattice is the symmetrical three-dimensional arrangement of atoms inside a crystal.

Crystal Structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. Self-Organizing?

E8 Lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system. The norm of the E8 lattice (divided by 2) is a positive definite even unimodular quadratic form in 8 variables, and conversely such a quadratic form can be used to construct a positive-definite, even, unimodular lattice of rank 8. The existence of such a form was first shown by H. J. S. Smith in 1867, and the first explicit construction of this quadratic form was given by A. Korkin and G. Zolotarev in 1873. The E8 lattice is also called the Gosset lattice after Thorold Gosset who was one of the first to study the geometry of the lattice itself around 1900. An 8-Dimensional Crystal is called the E8 Lattice. The E8 lattice is an 8D point set representing the densest packing of spheres in 8D. The basic cell of the E8 lattice, the Gosset polytope, has 240 vertices and accurately corresponds to all particles and forces in our (3D) reality and their interactions, specifically the way they can all transform from one to another through a process called gauge symmetry transformation (you can view a Ted Talk by Garret Lisi on this subject here). The first operation we perform is take the E8 lattice and project a slice of it to 4D, through one of two processes: cut-and-project, or Hopf mapping. Either process gives us the same result: a 4-dimensional quasicrystal called the Elser-Sloane quasicrystal. When the E8's basic cell, the Gosset polytope is projected to 4D, it creates two identical, 4D shapes of different sizes. The ratio of their sizes is the golden ratio. Each of these shapes is constructed of 600 3-dimensional tetrahedra rotated from one another by a golden ratio based angle. We refer to this 4D shape as the “600-Cell.” The 600-cells interact in specific ways (they intersect in 7 golden ratio related ways and “kiss” in one particular way) to form the 4D quasicrystal. This is a representation of the two 600-Cells that make up the 4D quasicrystal. Next we take five 3D subspaces, or tetragrid, of this 4D quasicrystal (one subspace being all tetrahedra that are oriented in the same direction) and then rotate them from one another by 15.522 degrees, we come up with a 3D quasicrystal that can be seen as a representation of the 4D, Elser-Sloane quasicrystal. We call this the “Compound Quasicrystal” (CQC). Here is a representation of five subspaces - the image on the left is one subspace, the second one has a second subspace layered onto it and so on. The fifth image is the CQC. Quasi-Crystalline Spin Network.

Atomic Lattice in mineralogy refers to the arrangement of atoms into a crystal structure. Atomic Lattice in order theory is when the underlying partial order is atomic.

Close-Packing of Equal Spheres (wiki) - Pixels

Unimodular Lattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1. The E8 lattice and the Leech lattice are two famous examples. Fractals

Leech Lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem.

Kissing Number Problem is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere. For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another. Other names for kissing number that have been used are Newton number (after the originator of the problem), and contact number. In general, the kissing number problem seeks the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space. Ordinary spheres correspond to two-dimensional closed surfaces in three-dimensional space. Finding the kissing number when centers of spheres are confined to a line (the one-dimensional case) or a plane (two-dimensional case) is trivial. Proving a solution to the three-dimensional case, despite being easy to conceptualise and model in the physical world, eluded mathematicians until the mid-20th century. Solutions in higher dimensions are considerably more challenging, and only a handful of cases have been solved exactly. For others investigations have determined upper and lower bounds, but not exact solutions.

Lattice in reference to a group is a subgroup of the additive group R which is isomorphic to the additive group Z , and which spans the real vector space R. In other words, for any basis of R, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice. A lattice may be viewed as a regular tiling of a space by a primitive cell.

Lattice in reference to order is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

Lattice Path (wiki)

Optical Lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift.[why?] Atoms are cooled and congregate in the locations of potential minima. The resulting arrangement of trapped atoms resembles a crystal lattice.

Hexagonal Lattice or triangular lattice is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths. Honeycomb Lattice is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb lattice can be seen as the union of two offset triangular lattices.In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb lattice.

Electrical Grid - Scaffolding

Mesh is a barrier made of connected strands of metal, fiber, or other flexible/ductile materials. A mesh is similar to a web or a net in that it has many attached or woven strands.

Mesh Generation is the practice of generating a polygonal or polyhedral mesh that approximates a geometric domain.

Mesh Networking

Spider Web is a device created by a spider out of proteinaceous spider silk extruded from its spinnerets, generally meant to catch its prey.

Net is any textile in which the yarns are fused, looped or knotted at their intersections, resulting in a fabric with open spaces between the yarns. Net has many uses, and come in different varieties. Depending on the type of yarn or filament that is used to make up the textile, its characteristics can vary from durable to not durable.

Internet - Interface - Menu

Activity Relationship Chart is a tabular means of displaying the closeness rating among all pairs of activities or departments. In an ARC there are six closeness ratings which may be assigned to each pair of departments, as well as nine reasons for those ratings (each is assigned by a reason code).

Category Theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups.

Set Theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.

Ring Theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.

Group Theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.

Organize is causing to be structured or ordered or operating according to some principle or idea. Bring order and organization to. Plan and direct (a complex undertaking). Arrange by systematic planning and united effort.

Organize - Human Operating System

Human Search Engine - Code

"I'm temporally assigning connections. Organizing is an on going process. You find new ways that things can be organized. You organize information in several different ways so that the information can be utilized in more then one way, and so that it can also be adjusted for unique applications."

Mental Orientation is a person's awareness of self with regard to position and time and place and personal relationships.

First Observation of a Square Lattice of Merons and Antimerons. Scientists have, for the first time, observed a square lattice of merons and antimerons -- tiny magnetic vortices and antivortices that form in a thin plate of the helical magnet Co8Zn9Mn3. The ability to manipulate nanometer-scale spin textures such as merons and skyrmions is a key to the development of spintronics -- next-generation electronic devices that are very low in power consumption. magnetic skyrmions.

Array is a systematic arrangement of similar objects, usually in rows and columns.

Array Data Structure is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is stored so that the position of each element can be computed from its index tuple by a mathematical formula The simplest type of data structure is a linear array, also called one-dimensional array.

Array Data Type is a data type that represents a collection of elements (values or variables), each selected by one or more indices (identifying keys) that can be computed at run time during program execution. Such a collection is usually called an array variable, array value, or simply array. By analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively. Antenna Array - Microphone Array - Sensors.

Associative Array is an abstract data type composed of a collection of (key, value) pairs, such that each possible key appears at most once in the collection. Operations associated with this data type allow: The addition of a pair to the collection. The removal of a pair from the collection. The modification of an existing pair. The lookup of a value associated with a particular key.

Parallel Array is a form of implicit data structure that uses multiple arrays to represent a singular array of records. It keeps a separate, homogeneous data array for each field of the record, each having the same number of elements. Then, objects located at the same index in each array are implicitly the fields of a single record. Pointers from one object to another are replaced by array indices. This contrasts with the normal approach of storing all fields of each record together in memory (also known as array of structures or AoS). For example, one might declare an array of 100 names, each a string, and 100 ages, each an integer, associating each name with the age that has the same index.

Array Programming generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays. Array programming primitives concisely express broad ideas about data manipulation. The level of concision can be dramatic in certain cases: it is not uncommon to find array programming language one-liners that require more than a couple of pages of Java code.

Programmable Array Logic is a family of programmable logic device semiconductors used to implement logic functions in digital circuits introduced by Monolithic Memories, Inc. (MMI) in March 1978.

Processor Array is like a storage array but contains and manages processing elements instead of storage elements. The processor array should have the following characteristics: Should support forty or more processing elements (blades) per chassis. The chassis should support the use of commodity motherboards. The chassis should only backplane power and management capabilities to extend the life of the chassis and reduce chassis change costs. Will provide end to end redundant power. Each processing element should support two or more redundant virtualized I/O connections.

Array Processing signal processing is a wide area of research that extends from the simplest form of 1-D signal processing to the complex form of M-D and array signal processing.

Asynchronous Array of Simple Processors architecture comprises a 2-D array of reduced complexity programmable processors with small scratchpad memories interconnected by a reconfigurable mesh network.

Gate Array is an approach to the design and manufacture of application-specific integrated circuits (ASICs), using a prefabricated chip with active devices like NAND-gates, that are later interconnected according to a custom order by adding metal layers in the factory.

Transistor Array are used for general purpose applications, function generation and low-level, low-noise amplifiers. They include two or more transistors on a common substrate to ensure close parameter matching and thermal tracking, characteristics that are especially important for 'long tailed pair' differential amplifiers, current mirrors, log amplifiers.

Search Tree is a tree data structure used for locating specific keys from within a set. In order for a tree to function as a search tree, the key for each node must be greater than any keys in subtrees on the left and less than any keys in subtrees on the right.

Get or Gather Together

Collect

Select

Choose

Prepare

Apply

Use

Question

Cause to be structured or ordered or operating according to some principle or idea

Arrange

Sort

List

Set Up

Assemble

Construct

Organize

Compare

Relate

Match

Compose

Identify

Recognize

Classify

Name

Define

Label

Question

Estimate the nature of, quality, ability, extent, or significance of

Evaluate

Formulate

Interpret

Translate

Differentiate

Synthesize

Estimate

Analyze

Examine

Calculate

Rate

Score

Assess

Judge

Value

Appraise

Question

Make or cause to be or to become, Bring into existence.

Create

Design

Illustrate

Sketch

Diagram

Write

Demonstrate

Experiment

Explain

Describe

Discuss

Question

Carry on or function, Handle effectively

Manage

Operate

Practice

Schedule

Employ

Support

Plan

Prepare

Inventory

Report

Review

Question

Transition Words - Linking Words (PDF)

Language of Thought Hypothesis (words shape our thoughts)

Word Embedding is the collective name for a set of language modeling and feature learning techniques in natural language processing (NLP) where words or phrases from the vocabulary are mapped to vectors of real numbers. Conceptually it involves a mathematical embedding from a space with one dimension per word to a continuous vector space with much lower dimension. Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models, and explicit representation in terms of the context in which words appear. Word and phrase embeddings, when used as the underlying input representation, have been shown to boost the performance in NLP tasks such as syntactic parsing and sentiment analysis. Media Literacy - Machine Learning.

Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a vector space, typically of several hundred dimensions, with each unique word in the corpus being assigned a corresponding vector in the space. Word vectors are positioned in the vector space such that words that share common contexts in the corpus are located in close proximity to one another in the space.

Wordnet is a large lexical database of English. Nouns, verbs, adjectives and adverbs are grouped into sets of cognitive synonyms (synsets), each expressing a distinct concept. Synsets are interlinked by means of conceptual-semantic and lexical relations. The resulting network of meaningfully related words and concepts can be navigated with the browser. WordNet is also freely and publicly available for download. WordNet's structure makes it a useful tool for computational linguistics and natural language processing.

WordNet superficially resembles a thesaurus, in that it groups words together based on their meanings. However, there are some important distinctions. First, WordNet interlinks not just word forms—strings of letters—but specific senses of words. As a result, words that are found in close proximity to one another in the network are semantically disambiguated. Second, WordNet labels the semantic relations among words, whereas the groupings of words in a thesaurus does not follow any explicit pattern other than meaning similarity.

Structure

The main relation among words in WordNet is synonymy, as between the words shut and close or car and automobile. Synonyms--words that denote the same concept and are interchangeable in many contexts--are grouped into unordered sets (synsets). Each of WordNet’s 117 000 synsets is linked to other synsets by means of a small number of “conceptual relations.” Additionally, a synset contains a brief definition (“gloss”) and, in most cases, one or more short sentences illustrating the use of the synset members. Word forms with several distinct meanings are represented in as many distinct synsets. Thus, each form-meaning pair in WordNet is unique.

Relations

The most frequently encoded relation among synsets is the super-subordinate relation (also called hyperonymy, hyponymy or ISA relation). It links more general synsets like {furniture, piece_of_furniture} to increasingly specific ones like {bed} and {bunkbed}. Thus, WordNet states that the category furniture includes bed, which in turn includes bunkbed; conversely, concepts like bed and bunkbed make up the category furniture. All noun hierarchies ultimately go up the root node {entity}. Hyponymy relation is transitive: if an armchair is a kind of chair, and if a chair is a kind of furniture, then an armchair is a kind of furniture. WordNet distinguishes among Types (common nouns) and Instances (specific persons, countries and geographic entities). Thus, armchair is a type of chair, Barack Obama is an instance of a president. Instances are always leaf (terminal) nodes in their hierarchies.

Meronymy, the part-whole relation holds between synsets like {chair} and {back, backrest}, {seat} and {leg}. Parts are inherited from their superordinates: if a chair has legs, then an armchair has legs as well. Parts are not inherited “upward” as they may be characteristic only of specific kinds of things rather than the class as a whole: chairs and kinds of chairs have legs, but not all kinds of furniture have legs.

Verb synsets are arranged into hierarchies as well; verbs towards the bottom of the trees (troponyms) express increasingly specific manners characterizing an event, as in {communicate}-{talk}-{whisper}. The specific manner expressed depends on the semantic field; volume (as in the example above) is just one dimension along which verbs can be elaborated. Others are speed (move-jog-run) or intensity of emotion (like-love-idolize). Verbs describing events that necessarily and unidirectionally entail one another are linked: {buy}-{pay}, {succeed}-{try}, {show}-{see}, etc.

Adjectives are organized in terms of antonymy. Pairs of “direct” antonyms like wet-dry and young-old reflect the strong semantic contract of their members. Each of these polar adjectives in turn is linked to a number of “semantically similar” ones: dry is linked to parched, arid, dessicated and bone-dry and wet to soggy, waterlogged, etc. Semantically similar adjectives are “indirect antonyms” of the contral member of the opposite pole. Relational adjectives ("pertainyms") point to the nouns they are derived from (criminal-crime).

There are only few adverbs in WordNet (hardly, mostly, really, etc.) as the majority of English adverbs are straightforwardly derived from adjectives via morphological affixation (surprisingly, strangely, etc.)

Cross-POS relations

The majority of the WordNet’s relations connect words from the same part of speech (POS). Thus, WordNet really consists of four sub-nets, one each for nouns, verbs, adjectives and adverbs, with few cross-POS pointers. Cross-POS relations include the “morphosemantic” links that hold among semantically similar words sharing a stem with the same meaning: observe (verb), observant (adjective) observation, observatory (nouns). In many of the noun-verb pairs the semantic role of the noun with respect to the verb has been specified: {sleeper, sleeping_car} is the LOCATION for {sleep} and {painter}is the AGENT of {paint}, while {painting, picture} is its RESULT.

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