is a rectangular array of
quantities or expressions set out by rows and columns;
treated as a single element and manipulated according to
Mind MapsFormulating the Logical Constructs of Human Thinking
is a rectangular array of numbers, symbols, or expressions, arranged in
rows and columns.
matrices represent the same linear
operator under two different bases.
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
- Linking Data
is a collection of extracellular molecules secreted by cells that provides
structural and biochemical support to the surrounding cells.
Matrix Attachment Region
are sequences in the DNA of eukaryotic chromosomes where the nuclear
is an element of variations which
does not change.
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).
is a formulation of quantum mechanics interpreting the physical properties
of particles as matrices that evolve in time.
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.
consists of a regular grid of cells, each in one of a finite
number of states, such as
on and off
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.
describes the rate at which one character in a sequence changes to other
character states over time
is a matrix (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
are simple, first-order
knowledge representations of natural language sentences formed
by the conjunction of concept predicates related through shared arguments.
is a collection of formal systems
used in mathematics,
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.
is a group
of related models that are used to produce word embedding's. These models
are shallow, two-layer
neural networks that are trained to reconstruct
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 in a
low-dimensional space relative to the vocabulary size ("continuous
space"). translate the relationships between words into numbers so that a
computer can work with them. Bias
First see the words in each Row from Left to Right - Connotation
Then see the words in each Column
from Top to Bottom - Association
Then look at the words in each Group and as a Whole
First Layer Word Matrix
Second Layer Word Matrix
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.
if 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.
is the Louvain Method for community detection is a method
to extract communities from large networks.
what you must know in order to
determine the reference of an expression. Connotation
is a commonly understood cultural or
emotional association that some
carries, in addition to the word's or phrase's explicit or literal
, which is its
is a URL that is intended to remain
unchanged for many years into the future, yielding a hyperlink that is
less susceptible to link rot. Permalinks are often rendered simply, that
is, as friendly URLs, so as to be easy for people to type and remember.
Most modern blogging and content-syndication software systems support such
links. Sometimes URL shortening is used to create them.
is the state of being connected
together. A relation resulting from interaction or dependence. Logical
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.
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 (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
memory, is a special type of computer memory used in certain
very-high-speed searching applications.
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).
Coupling (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
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
Similarity - Contiguity - Contrast
"Neurons that fire
together wire together."
Paired Associate Learning
is the presentation of one
leads to the recall of the other.
items. (PAL) Ontology
Knowledge domain that is usually hierarchical and contains all the
relevant entities and their relations.
Ontology (information science
are types, properties, and
interrelationships of the entities that really or fundamentally exist for
a particular domain of discourse.
is an abstraction belonging to
or characteristic of two entities or parts together.
is to make a logical or causal connection. Be relevant to. Be
in a relationship with. Have or establish a relationship
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.
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
is a well-defined collection of distinct objects,
considered as an object in its own right.
is the process of bringing ideas
or events together in
is the study of the structure of organisms
and their parts.
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.
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
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
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.
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
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.
Intersection 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.
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)/
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
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
is a reciprocal
relation between two
or more things. A
relation between two or
more variables such that
changes in the value of one variable are accompanied by systematic changes
in the other.
refers to the state or quality of
oneness in all
. Reciprocally connected. Operating as a unit.
- Computer 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.
is any network that applies to
. 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.
is a system which represents
complex event sequences or characters’ interactions as depicted by a
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.
is a form of recurrent
Artificial Neural 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.
is the attraction
between an antigen and an antibody. (anthropology)
kinship by marriage or adoption; not a blood
relationship. (biology) state of relationship between
organisms or groups of organisms resulting in
structure or structural parts. A close connection marked
by community of interests or similarity in nature or
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.
is the act of combining into an
The action of incorporating a racial or religious group into a community.
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.
is pertaining to
, 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
Simultaneous Subject Teaching
Logically Ordered Steps
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
. 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.
is a well-defined collection of distinct objects,
considered as an object in its own right.
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
representing a car comprise a number of other elements which in turn
represent the color, size and owner of the car.
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.
is a collection of related data
held in a structured format within a
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
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.
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 (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.
is the collection of computer
resources from multiple locations to reach a common goal.
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
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
Human Operating System
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).
Language of Thought Hypothesis
is the combining materials
and parts. Put together out of artificial or natural components
Draw with suitable instruments and
under specified conditions. Create by linking linguistic units.
Create by organizing and linking
, arguments, or concepts.
is an analytical tool with
several variations and contexts. It is used to make conceptual
distinctions and organize ideas
conceptual frameworks capture something real and do this in a way that is
easy to remember and apply.
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.
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.
feature-rich when it has many
options and functional capabilities available to the user.
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
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.
is a way of hiding the
implementation details of a particular set of functionality, allowing the
separation of concerns to facilitate interoperability and platform
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.
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
"One of the best things
about the digital world is that we can see
Multiple Layers Deep
is an agreement
of results or opinions. Acting together
agents or circumstances or events. A state of
The temporal property of two things happening at the same time.
String (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
Concurrency (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
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".
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
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
. Abstract structures include data structures in computer
science and musical form
. Types of structure include 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.
describes the behaviour of a
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
parts interact with each other
in a higher order of emergence greater than the sum of its parts.
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).
is a particular way of organizing data in a computer so that it can be
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
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
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.
Default Mode Network
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.
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
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.
- Working Together
Structure Mapping Engine
systematicity principle, which
states that 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.
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. Ice
is an arrangement of
or particles or
objects in a regular periodic
in 2 or 3 dimensions
is an abstract structure studied in the mathematical
subdisciplines of order theory and abstract
is formed by the interference of counter-propagating
laser beams, creating a spatially periodic
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
resembles a crystal
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.
is the practice of generating a polygonal
or polyhedral mesh that approximates a geometric domain.
is a device created by a spider out of
proteinaceous spider silk extruded from its spinnerets, generally meant to
catch its prey.
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.
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).
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.
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.
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.
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.
causing to be structured or ordered or operating according
to some principle or idea. Bring order and organization
Plan and direct (a complex undertaking)
Arrange by systematic planning and united effort.
Human Operating System
Human Search Engine
"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
is a person's
of self with regard to position and time and place and
is a binary operation that takes a
pair of matrices
, and produces another
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.
Words that go Together
Get or Gather Together
be structured or ordered or operating according to some principle or idea
Estimate the nature of,
quality, ability, extent, or significance of
QuestionMake or cause to be or to become, Bring
QuestionCarry on or function, Handle
- Linking Words (PDF)
Language of Thought Hypothesis
(words shape our thoughts)
Word Embedding Bias