Connected relationIn mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all pairs of elements of the set in one direction or the other while it is called strongly connected if it relates pairs of elements. As described in the terminology section below, the terminology for these properties is not uniform. This notion of "total" should not be confused with that of a total relation in the sense that for all there is a so that (see serial relation).
Message Passing InterfaceMessage Passing Interface (MPI) is a standardized and portable message-passing standard designed to function on parallel computing architectures. The MPI standard defines the syntax and semantics of library routines that are useful to a wide range of users writing portable message-passing programs in C, C++, and Fortran. There are several open-source MPI implementations, which fostered the development of a parallel software industry, and encouraged development of portable and scalable large-scale parallel applications.
Converse relationIn mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse.
SubsetIn mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements. The subset relation defines a partial order on sets.
Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
Process (computing)In computing, a process is the instance of a computer program that is being executed by one or many threads. There are many different process models, some of which are light weight, but almost all processes (even entire virtual machines) are rooted in an operating system (OS) process which comprises the program code, assigned system resources, physical and logical access permissions, and data structures to initiate, control and coordinate execution activity.
Hardware abstractionHardware abstractions are sets of routines in software that provide programs with access to hardware resources through programming interfaces. The programming interface allows all devices in a particular class C of hardware devices to be accessed through identical interfaces even though C may contain different subclasses of devices that each provide a different hardware interface. Hardware abstractions often allow programmers to write device-independent, high performance applications by providing standard operating system (OS) calls to hardware.
Asynchronous I/OIn computer science, asynchronous I/O (also non-sequential I/O) is a form of input/output processing that permits other processing to continue before the transmission has finished. A name used for asynchronous I/O in the Windows API is overlapped I/O. Input and output (I/O) operations on a computer can be extremely slow compared to the processing of data. An I/O device can incorporate mechanical devices that must physically move, such as a hard drive seeking a track to read or write; this is often orders of magnitude slower than the switching of electric current.
Asymmetric relationIn mathematics, an asymmetric relation is a binary relation on a set where for all if is related to then is not related to A binary relation on is any subset of Given write if and only if which means that is shorthand for The expression is read as " is related to by " The binary relation is called if for all if is true then is false; that is, if then This can be written in the notation of first-order logic as A logically equivalent definition is: for all at least one of and is , which in first-order logic c
Message queueIn computer science, message queues and mailboxes are software-engineering components typically used for inter-process communication (IPC), or for inter-thread communication within the same process. They use a queue for messaging – the passing of control or of content. Group communication systems provide similar kinds of functionality. The message queue paradigm is a sibling of the publisher/subscriber pattern, and is typically one part of a larger message-oriented middleware system.
Memory hierarchyIn computer organisation, the memory hierarchy separates computer storage into a hierarchy based on response time. Since response time, complexity, and capacity are related, the levels may also be distinguished by their performance and controlling technologies. Memory hierarchy affects performance in computer architectural design, algorithm predictions, and lower level programming constructs involving locality of reference. Designing for high performance requires considering the restrictions of the memory hierarchy, i.
Homogeneous relationIn mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. This is commonly phrased as "a relation on X" or "a (binary) relation over X". An example of a homogeneous relation is the relation of kinship, where the relation is between people. Common types of endorelations include orders, graphs, and equivalences. Specialized studies of order theory and graph theory have developed understanding of endorelations.
