Model in the context of Abstract model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations. A model may help to characterize a system by studying the effects of different components, which may be used to make predictions about behavior or solve specific problems.

Models of communication simplify or represent the process of communication. Most communication models try to describe both verbal and non-verbal communication and often understand it as an exchange of messages. Their function is to give a compact overview of the complex process of communication. This helps researchers formulate hypotheses, apply communication-related concepts to real-world cases, and test predictions. Despite their usefulness, many models are criticized based on the claim that they are too simple because they leave out essential aspects. The components and their interactions are usually presented in the form of a diagram. Some basic components and interactions reappear in many of the models. They include the idea that a sender encodes information in the form of a message and sends it to a receiver through a channel. The receiver needs to decode the message to understand the initial idea and provides some form of feedback. In both cases, noise may interfere and distort the message.

Models of communication are classified depending on their intended applications and on how they conceptualize the process. General models apply to all forms of communication while specialized models restrict themselves to specific forms, like mass communication. Linear transmission models understand communication as a one-way process in which a sender transmits an idea to a receiver. Interaction models include a feedback loop through which the receiver responds after getting the message. Transaction models see sending and responding as simultaneous activities. They hold that meaning is created in this process and does not exist prior to it. Constitutive and constructionist models stress that communication is a basic phenomenon responsible for how people understand and experience reality. Interpersonal models describe communicative exchanges with other people. They contrast with intrapersonal models, which discuss communication with oneself. Models of non-human communication describe communication among other species. Further types include encoding-decoding models, hypodermic models, and relational models.

The term conceptual model refers to any model that is the direct output of a conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience.

An astrolabe (Ancient Greek: ἀστρολάβος, romanized: astrolábos, lit. 'star-taker'; Arabic: ٱلأَسْطُرلاب, romanized: al-Asṭurlāb; Persian: ستاره‌یاب, romanized: Setāreyāb) is an astronomical instrument dating to ancient times. It serves as a star chart and physical model of the visible half-dome of the sky. Its various functions also make it an elaborate inclinometer and an analog calculation device capable of working out several kinds of problems in astronomy. In its simplest form it is a metal disc with a pattern of wires, cutouts, and perforations that allows a user to calculate astronomical positions precisely. It is able to measure the altitude above the horizon of a celestial body, day or night; it can be used to identify stars or planets, to determine local latitude given local time (and vice versa), to survey, or to triangulate. It was used in classical antiquity, the Byzantine Empire, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.

The astrolabe, which is a precursor to the sextant,is effective for determining latitude on land or calm seas. Although it is less reliable on the heaving deck of a ship in rough seas, the mariner's astrolabe was developed to solve that problem.

A business model describes how a business organization creates, delivers, and captures value, in economic, social, cultural or other contexts. The model describes the specific way in which the business conducts itself, spends, and earns money in a way that generates profit. The process of business model construction and modification is also called business model innovation and forms a part of business strategy.

In theory and practice, the term business model is used for a broad range of informal and formal descriptions to represent core aspects of an organization or business, including purpose, business process, target customers, offerings, strategies, infrastructure, organizational structures, profit structures, sourcing, trading practices, and operational processes and policies including culture.

A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in which simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Another way to distinguish between the terms is to define simulation as experimentation with the help of a model. This definition includes time-independent simulations. Often, computers are used to execute the simulation.

Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games. Simulation is also used with scientific modelling of natural systems or human systems to gain insight into their functioning, as in economics. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist.

Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject.

Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. The following was said by John von Neumann.

In biological taxonomy, a domain (/dəˈmeɪn/ or /doʊˈmeɪn/) (Latin: regio or dominium), also dominion, superkingdom, realm, or empire, is the highest taxonomic rank of all organisms taken together. It was introduced in the three-domain system of taxonomy devised by Carl Woese, Otto Kandler and Mark Wheelis in 1990.

According to the domain system, the tree of life consists of either three domains, Archaea, Bacteria, and Eukarya, or two domains, Archaea and Bacteria, with Eukarya included in Archaea. In the three-domain model, the first two are prokaryotes, single-celled microorganisms without a membrane-bound nucleus. All organisms that have a cell nucleus and other membrane-bound organelles are included in Eukarya and called eukaryotes.

A globe is a spherical model of Earth, of some other celestial body, or of the celestial sphere. Globes serve purposes similar to maps, but, unlike maps, they do not distort the surface that they portray except to scale it down. A model globe of Earth is called a terrestrial globe. A model globe of the celestial sphere is called a celestial globe.

A globe shows details of its subject. A terrestrial globe shows landmasses and water bodies. It might show nations and major cities and the network of latitude and longitude lines. Some have raised relief to show mountains and other large landforms. A celestial globe shows notable stars, and may also show positions of other prominent astronomical objects. Typically, it will also divide the celestial sphere into constellations.

An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.

Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.

The term is 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. The study of these complex linkages at various scales is the main goal of complex systems theory.

Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.

Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around Kuwait, using multiple supercomputers in the DoD High Performance Computer Modernization Program.Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the ribosome, in 2005;a complete simulation of the life cycle of Mycoplasma genitalium in 2012; and the Blue Brain project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.

A cognitive model is a representation of one or more cognitive processes in humans or other animals for the purposes of comprehension and prediction. There are many types of cognitive models, and they can range from box-and-arrow diagrams to a set of equations to software programs that interact with the same tools that humans use to complete tasks (e.g., computer mouse and keyboard). In terms of information processing, cognitive modeling is modeling of human perception, reasoning, memory and action.

A model organism is a non-human species that is extensively studied to understand particular biological phenomena, with the expectation that discoveries made in the model organism will provide insight into the workings of other organisms. Model organisms are widely used to research human disease when human experimentation would be unfeasible or unethical. This strategy is made possible by the common descent of all living organisms, and the conservation of metabolic and developmental pathways and genetic material over the course of evolution.

Research using animal models has been central to most of the achievements of modern medicine. It has contributed most of the basic knowledge in fields such as human physiology and biochemistry, and has played significant roles in fields such as neuroscience and infectious disease. The results have included the near-eradication of polio and the development of organ transplantation, and have benefited both humans and animals. From 1910 to 1927, Thomas Hunt Morgan's work with the fruit fly Drosophila melanogaster identified chromosomes as the vector of inheritance for genes, and Eric Kandel wrote that Morgan's discoveries "helped transform biology into an experimental science". Research in model organisms led to further medical advances, such as the production of the diphtheria antitoxin and the 1922 discovery of insulin and its use in treating diabetes, which had previously meant death. Modern general anaesthetics such as halothane were also developed through studies on model organisms, and are necessary for modern, complex surgical operations. Other 20th-century medical advances and treatments that relied on research performed in animals include organ transplant techniques, the heart-lung machine, antibiotics, and the whooping cough vaccine.

A language model is a model of the human brain's ability to produce natural language. Language models are useful for a variety of tasks, including speech recognition, machine translation, natural language generation (generating more human-like text), optical character recognition, route optimization, handwriting recognition, grammar induction, and information retrieval.

Large language models (LLMs), currently their most advanced form as of 2019, are predominantly based on transformers trained on larger datasets (frequently using texts scraped from the public internet). They have superseded recurrent neural network-based models, which had previously superseded the purely statistical models, such as the word n-gram language model.