Complex - Mathematics. A complex number is a number in that field of numbers which includes the real numbers and the imaginary numbers, of the form a + ib, where a and b are real numbers and i is the imaginary number equal to the square root of -1. A complex is an element of a complex algebra or field of sets. A simplicial complex is a space that can be divided into fully adjacent triangles (more generally, simpl

Read more here: » Complex: Encyclopedia - Complex

Including:

Complexity - Study of complexity
Complexity - Complex systems Complexity - Complexity in data Complexity - Complexity of problems
Complexity - Specific meanings Complexity - Quotes about complexity Complexity - Reference

Read more here: » Complexity: Encyclopedia - Complexity

Complexity has always been a part of our environment, and therefore many scientific fields have dealt with complex systems and phenomena. Indeed, some would say that only what is somehow complex - what displays variation without being purely random - is worthy of interest. While this has led some fields to come up with specific definitions of complexity, there is a more recent movement to regroup observations from different fields in order to study complexity in itself, whether it appears in anthills, human brains, or stock markets. Complexity - Complex systems. See also:

Complexity, Complexity - Study of complexity, Complexity - Complex systems, Complexity - Complexity in data, Complexity - Complexity of problems, Complexity - Specific meanings, Complexity - Quotes about complexity, Complexity - Reference

Read more here: » Complexity: Encyclopedia II - Complexity - Study of complexity

Complexity theory can refer to more than one thing: Computational complexity theory: a field in theoretical computer science and mathematics dealing with the resources required during computation to solve a given problem The theoretical treatment of descriptive complexity (or Kolmogorov complexity) of a string is studied in algorithmic information theory by identifying the length of the shortest binary program which can output that string. Systems theory (or systemics o

Read more here: » Complexity theory: Encyclopedia - Complexity theory

A complex in chemistry is a reversible association of molecules, atoms, or ions through weak non-covalent chemical bonds. Simple salts are usually not considered complexes. Complex chemistry - Metal complexes. A metal complex, also known as coordination compound, is a structure composed of a central metal atom or ion, generally a cation, surrounded by a number of negatively charged ions or neutral molecules possessing lone pairs. Counter ions often surround the metal complex ion, causing the compound to hav ...

Including:

Complex chemistry - Metal complexes
Complex chemistry - Naming complexes
Complex chemistry - Receptor-ligand complexes

Read more here: » Complex chemistry: Encyclopedia - Complex chemistry

Advice is a concept in complexity theory. An advice string is an extra input to a Turing machine which is allowed to depend on the length n of the input, but not on input itself. A decision problem is in the complexity class P/f(n) if there is a polynomial time Turing machine M with the following property: for any n, there is an advice string A of length f(n) such that, for any input x of length n, the machine M correctly decides the p ...

Read more here: » Advice complexity: Encyclopedia - Advice complexity

Complex analysis is the branch of mathematics investigating functions of complex numbers. It is of enormous practical use in applied mathematics and in many other branches of mathematics. Complex analysis is particularly concerned with analytic functions of complex variables, known as holomorphic functions. Complex analysis - Complex functions. A complex function, , is a function in which the independent variable, , and the dependent variable, , are both complex numbers: ...

Including:

Complex analysis - Complex functions Complex analysis - Holomorphic functions Complex analysis - Major results Complex analysis - History

Read more here: » Complex analysis: Encyclopedia - Complex analysis

Complex Family is a generic term for any family structure involving more than two adults. The term can refer to any extended family or to a polygamy of any type. It is often used to refer to the group marriage form of polygamy. A joint family is also known as a complex family, parents and their children's families often live under a single roof. This type of family often includes multiple generations in the family. In India, the family is a patriarchal society, wit ...

Read more here: » Complex family: Encyclopedia - Complex family

Many natural phenomena may be called complex systems, and complexity science is highly interdisciplinary. Examples of complex systems include ant-hills, ants themselves, human economies, nervous systems, cells and so forth, as well as human beings and their psychology, emotions, bodies and interactions. Beyond the fact that these things are all networks of some kind, and that they are complex, it may appear that they have little in common, and hence that the term "complex system" is vacuous. However, all complex systems ...

Including:

Complex system - Overview Complex system - Formal Definition Complex system - Behavior of Complex Systems Complex system - Applications of Complex Systems Theory Complex system - Informal Descriptions of Complex Systems Complex system - Features of natural complex systems
Complex system - Relationships are non-linear Complex system - Relationships contain feedback loops Complex system - Complex systems are open Complex system - Complex systems have a history Complex system - Complex systems may be nested Complex system - Boundaries are difficult to determine Complex system - Dynamic Network of Multiplicity
Complex system - Quotes

Read more here: » Complex system: Encyclopedia - Complex system

In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently, if we define decision problems as sets of finite strings, then the complement of this set over some fixed domain is its complement problem. For example, one important problem is whether a number is a prime number. Its complement is to determine whether a number is a composite number (a number which is not prime). Here the doma ...

Read more here: » Complement complexity: Encyclopedia - Complement complexity

In psychology a complex is generally an important group of unconscious associations, or a strong unconscious impulse lying behind an individual's otherwise mysterious condition: the detail varies widely from theory to theory. However their existence is quite widely agreed upon in the area of depth psychology at least, being instrumental in the systems of both Freud and Jung. They are generally a way of mapping the psyche, and are crucial th ...

Read more here: » Complex psychology: Encyclopedia - Complex psychology

In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. Thus, the conjugate of the complex number z = a + ib (where a and b are real numbers) is defined to be z * = a − ib. The complex conjugate of a number z can be denoted by: or The symbol can also denote the conjugate transpose of a matrix A so care must be taken not to confuse notations. If a complex number i ...

Including:

Complex conjugate - Properties Complex conjugate - Generalizations

Read more here: » Complex conjugate: Encyclopedia - Complex conjugate

In mathematics, a complex number is an expression of the form a + bi, where a and b are real numbers, and i stands for the square root of minus one (−1), which cannot be represented by any real number. For example, 3 + 2i is a complex number, where 3 is called the real part and 2 the imaginary part. Since a complex number a + bi is uniquely specified by an ordered pair (a, b) of real numbers, the complex numbers are in one-to-one corresponde ...

Including:

Complex number - Definition
Complex number - The complex number field Complex number - The complex plane Complex number - Absolute value conjugation and distance Complex number - Complex number division Complex number - Matrix representation of complex numbers
Complex number - Geometric interpretation of the operations on complex numbers Complex number - Some properties
Complex number - Real vector space Complex number - Solutions of polynomial equations Complex number - Algebraic characterization Complex number - Characterization as a topological field
Complex number - Complex analysis Complex number - Applications
Complex number - Control theory Complex number - Signal analysis Complex number - Improper integrals Complex number - Quantum mechanics Complex number - Relativity Complex number - Applied mathematics Complex number - Fluid dynamics Complex number - Fractals
Complex number - History

Read more here: » Complex number: Encyclopedia - Complex number

In computational complexity theory, a complexity class is a set of problems of related complexity. A typical complexity class has a definition of the form: the set of problems that can be solved by abstract machine M using O(f(n)) of resource R (n is the size of the input) For example, the class NP is the set of decision problems that can be solved by a non-deterministic Turing machine in polynomial time, while the class PSPACE is the set of decision problems that can be solved by a deterministic Turing machine in polynomial space. Some comple ...

Including:

Complexity class - Relationships Between Complexity Classes

Read more here: » Complexity class: Encyclopedia - Complexity class

In differential geometry, a complex manifold is a manifold such that every neighborhood looks like the complex n-space in a coherent way. More precisely, a complex manifold has an atlas of charts to Cn, such that the change of coordinates between charts are holomorphic. Complex manifolds can be regarded as a special case of differentiable manifolds. For example, a 1-dimensional complex manifold is geometrically a surface, known as a Riemann surface. The requirement that the transition functions b ...

Including:

Complex manifold - Examples of complex manifolds Complex manifold - Integrable almost-complex structures Complex manifold - Kähler and Calabi-Yau manifolds

Read more here: » Complex manifold: Encyclopedia - Complex manifold

In biology, a cryptic species complex is a group of species that satisfy the scientific definition of species — that is, they are reproductively isolated from each other — but which are anatomically indistinguishable. The individual species within the complex can only be separated using methods from molecular genetics such as DNA barcoding. Other related archivesDNA barcoding, biology, molecular genetics, species

Read more here: » Cryptic species complex: Encyclopedia - Cryptic species complex

In computer science, computational complexity theory is the branch of the theory of computation that studies the resources required during computation to solve a given problem. The most common resources are time (how many steps it takes to solve a problem) and space (how much memory it takes). Other resources can also be considered, such as how many parallel processors are needed to solve a problem in parallel. Complexity theory differs from the computability theory, which deals with whether a problem can be solved at al ...

Including:

Computational complexity theory - Overview Computational complexity theory - Decision problems Computational complexity theory - Complexity classes Computational complexity theory - The P = NP question Computational complexity theory - Intractability Computational complexity theory - Notable researchers

Read more here: » Computational complexity theory: Encyclopedia - Computational complexity theory

In topology, a CW complex is a type of topological space introduced by J.H.C. Whitehead to meet the needs of homotopy theory. The idea was to have a class of spaces that was broader than simplicial complexes (we could say now, had better categorical properties); but still retained a combinatorial nature, so that computational considerations were not ignored. The name itself is unrevealing: C ...

Including:

CW complex - Attaching cells CW complex - CW complexes are defined inductively CW complex - 'The' homotopy category CW complex - Properties

Read more here: » CW complex: Encyclopedia - CW complex

In network science, which touches scientific disciplines as varied as computer science, mathematics, physics, biology and sociology, the term "complex network" refers to a network (graph) that has non-trivial topological structure. Most real world networks can be considered complex on account of their having several topological features that do not exist in simple networks, e.g., a heavy-tail in the degree distribution, a high clustering coefficient, assortativity or disassortativty among vertices, community structure at many scales and evid ...

Including:

Complex network - Scale-free networks Complex network - Small-world networks Complex network - Researchers and scientists Complex network - Links Complex network - Books

Read more here: » Complex network: Encyclopedia - Complex network

Complex adaptive systems, are a special case of complex systems. They are complex in that they are diverse and made up of multiple interconnected elements and adaptive in that they have the capacity to change and learn from experience. The term complex adaptive systems was coined at the interdisciplinary Santa Fe Institute (SFI), by John H. Holland, Murray Gell-Mann and others. John H. Holland is one of the inventors of evolutionary computation and genetic algor ...

Including:

Complex adaptive systems - Definitions Complex adaptive systems - Properties of CAS Complex adaptive systems - Graphic Complex adaptive systems - Researchers and scientists

Read more here: » Complex adaptive systems: Encyclopedia - Complex adaptive systems