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95 relations: Alfred J. Lotka, An Essay on the Principle of Population, Anderson Gray McKendrick, Antiderivative, Artificial neural network, Artificial neuron, Autocatalysis, Backpropagation, Bernoulli differential equation, Biological life cycle, Biology, Boundary value problem, Car, Carrying capacity, Chemistry, Constant of integration, Continuum (measurement), Cumulative distribution function, Demography, Dependent and independent variables, Derivative, Differential equation, Diffusion of innovations, Dimensional analysis, E (mathematical constant), Earth science, Ecology, Economics, Electrification, Elo rating system, Even and odd functions, Exponential function, Exponential growth, Fermi–Dirac statistics, Gabriel Tarde, Generalised logistic function, Gompertz function, Heaviside step function, Hubbert curve, Hyperbolic function, Integration by substitution, International Institute for Applied Systems Analysis, Item response theory, Johns Hopkins University, Kondratiev wave, Language change, Likelihood-ratio test, Linear combination, Linguistics, Log-linear model, ..., Logistic distribution, Logistic map, Logistic regression, Logit, Lowell Reed, Machine learning, Malthusian growth model, Mathematical and theoretical biology, Mathematical psychology, Maximum likelihood estimation, Multinomial logistic regression, Natural logarithm, Natural selection, Neural network, Nonlinear system, Odds, Ordinary differential equation, Parabola, Perceptron, Phase line (mathematics), Pierre François Verhulst, Political science, Population dynamics, Population growth, Probability, Proceedings of the National Academy of Sciences of the United States of America, R/K selection theory, Ramp function, Range (mathematics), Rasch model, Raymond Pearl, Real number, Rectifier (neural networks), Segmented regression, Shifted Gompertz distribution, Sigmoid function, Sociology, Softmax function, Soil salinity, Species, STAR model, Statistics, Thomas Robert Malthus, Tipping point (sociology), Water table. Expand index (45 more) »
Alfred J. Lotka
Alfred James Lotka (March 2, 1880 – December 5, 1949) was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics.
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An Essay on the Principle of Population
The book An Essay on the Principle of Population was first published anonymously in 1798, but the author was soon identified as Thomas Robert Malthus.
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Anderson Gray McKendrick
Lt Col Anderson Gray McKendrick DSc FRSE (8 September 1876 – 30 May 1943) was a Scottish military physician and epidemiologist pioneered the use of mathematical methods in epidemiology.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Artificial neural network
Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.
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Artificial neuron
An artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network.
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Autocatalysis
A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction.
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Backpropagation
Backpropagation is a method used in artificial neural networks to calculate a gradient that is needed in the calculation of the weights to be used in the network.
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Bernoulli differential equation
In mathematics, an ordinary differential equation of the form: is called a Bernoulli differential equation where n is any real number and n \ne 0 and n \ne 1.
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Biological life cycle
In biology, a biological life cycle (or just life cycle when the biological context is clear) is a series of changes in form that an organism undergoes, returning to the starting state.
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Biology
Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Car
A car (or automobile) is a wheeled motor vehicle used for transportation.
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Carrying capacity
The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment.
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Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
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Constant of integration
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.
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Continuum (measurement)
Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities.
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Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
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Demography
Demography (from prefix demo- from Ancient Greek δῆμος dēmos meaning "the people", and -graphy from γράφω graphō, implies "writing, description or measurement") is the statistical study of populations, especially human beings.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Diffusion of innovations
Diffusion of innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread.
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Dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.
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E (mathematical constant)
The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.
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Earth science
Earth science or geoscience is a widely embraced term for the fields of natural science related to the planet Earth.
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Ecology
Ecology (from οἶκος, "house", or "environment"; -λογία, "study of") is the branch of biology which studies the interactions among organisms and their environment.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Electrification
Electrification is the process of powering by electricity and, in many contexts, the introduction of such power by changing over from an earlier power source.
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Elo rating system
The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess.
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Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
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Fermi–Dirac statistics
In quantum statistics, a branch of physics, Fermi–Dirac statistics describe a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle.
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Gabriel Tarde
Gabriel Tarde (in full Jean-Gabriel De Tarde; 12 March 1843 – 13 May 1904) was a French sociologist, criminologist and social psychologist who conceived sociology as based on small psychological interactions among individuals (much as if it were chemistry), the fundamental forces being imitation and innovation.
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Generalised logistic function
The generalised (generalized) logistic function or curve, also known as Richards' curve, originally developed for growth modelling, is an extension of the logistic or sigmoid functions, allowing for more flexible S-shaped curves: where Y.
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Gompertz function
The Gompertz curve or Gompertz function, is a type of mathematical model for a time series and is named after Benjamin Gompertz (1779-1865).
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Heaviside step function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes, or), is a discontinuous function named after Oliver Heaviside (1850–1925), whose value is zero for negative argument and one for positive argument.
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Hubbert curve
The Hubbert curve is an approximation of the production rate of a resource over time.
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Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
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Integration by substitution
In calculus, integration by substitution, also known as u-substitution, is a method for finding integrals.
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International Institute for Applied Systems Analysis
The International Institute for Applied Systems Analysis (IIASA) is an international research organization located in Laxenburg, near Vienna, in Austria.
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Item response theory
In psychometrics, item response theory (IRT) (also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables.
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Johns Hopkins University
Johns Hopkins University is an American private research university in Baltimore, Maryland.
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Kondratiev wave
In economics, Kondratiev waves (also called supercycles, great surges, long waves, K-waves or the long economic cycle) are hypothesized cycle-like phenomena in the modern world economy.
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Language change
Language change is variation over time in a language's phonological, morphological, semantic, syntactic, and other features.
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Likelihood-ratio test
In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Linguistics
Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context.
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Log-linear model
A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression.
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Logistic distribution
In probability theory and statistics, the logistic distribution is a continuous probability distribution.
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Logistic map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations.
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Logistic regression
In statistics, the logistic model (or logit model) is a statistical model that is usually taken to apply to a binary dependent variable.
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Logit
The logit function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics.
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Lowell Reed
Lowell Jacob Reed (January 8, 1886 – April 29, 1966) was 7th president of the Johns Hopkins University in Baltimore, Maryland.
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Machine learning
Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.
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Malthusian growth model
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on a constant rate.
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Mathematical and theoretical biology
Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories.
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Mathematical psychology
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior.
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Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.
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Multinomial logistic regression
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Natural selection
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype.
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Neural network
The term neural network was traditionally used to refer to a network or circuit of neurons.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Odds
Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
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Perceptron
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers (functions that can decide whether an input, represented by a vector of numbers, belongs to some specific class or not).
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Phase line (mathematics)
In mathematics, a phase line is a diagram that shows the qualitative behaviour of an autonomous ordinary differential equation in a single variable, \tfrac.
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Pierre François Verhulst
Pierre François Verhulst (28 October 1804, Brussels – 15 February 1849, Brussels) was a mathematician and a doctor in number theory from the University of Ghent in 1825.
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Political science
Political science is a social science which deals with systems of governance, and the analysis of political activities, political thoughts, and political behavior.
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Population dynamics
Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration).
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Population growth
In biology or human geography, population growth is the increase in the number of individuals in a population.
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Probability
Probability is the measure of the likelihood that an event will occur.
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Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.
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R/K selection theory
In ecology, r/K selection theory relates to the selection of combinations of traits in an organism that trade off between quantity and quality of offspring.
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Ramp function
The ramp function is a unary real function, whose graph is shaped like a ramp.
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Range (mathematics)
In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.
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Rasch model
The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty.
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Raymond Pearl
Raymond Pearl (3 June 1879 – 17 November 1940) was an American biologist, regarded as one of the founders of biogerontology.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Rectifier (neural networks)
In the context of artificial neural networks, the rectifier is an activation function defined as the positive part of its argument: f(x).
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Segmented regression
Segmented regression, also known as piecewise regression or "broken-stick regression", is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval.
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Shifted Gompertz distribution
No description.
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Sigmoid function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
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Sociology
Sociology is the scientific study of society, patterns of social relationships, social interaction, and culture.
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Softmax function
In mathematics, the softmax function, or normalized exponential function, is a generalization of the logistic function that "squashes" a -dimensional vector \mathbf of arbitrary real values to a -dimensional vector \sigma(\mathbf) of real values, where each entry is in the range (0, 1, and all the entries add up to 1. The function is given by In probability theory, the output of the softmax function can be used to represent a categorical distribution – that is, a probability distribution over different possible outcomes. In fact, it is the gradient-log-normalizer of the categorical probability distribution. The softmax function is also the gradient of the LogSumExp function. The softmax function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression), multiclass linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. Specifically, in multinomial logistic regression and linear discriminant analysis, the input to the function is the result of distinct linear functions, and the predicted probability for the 'th class given a sample vector and a weighting vector is: This can be seen as the composition of linear functions \mathbf \mapsto \mathbf^\mathsf\mathbf_1, \ldots, \mathbf \mapsto \mathbf^\mathsf\mathbf_K and the softmax function (where \mathbf^\mathsf\mathbf denotes the inner product of \mathbf and \mathbf). The operation is equivalent to applying a linear operator defined by \mathbf to vectors \mathbf, thus transforming the original, probably highly-dimensional, input to vectors in a -dimensional space \mathbb^K.
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Soil salinity
Soil salinity is the salt content in the soil; the process of increasing the salt content is known as salinization.
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Species
In biology, a species is the basic unit of classification and a taxonomic rank, as well as a unit of biodiversity, but it has proven difficult to find a satisfactory definition.
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STAR model
In statistics, Smooth Transition Autoregressive (STAR) models are typically applied to time series data as an extension of autoregressive models, in order to allow for higher degree of flexibility in model parameters through a smooth transition.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Thomas Robert Malthus
Thomas Robert Malthus (13 February 1766 – 23 December 1834) was an English cleric and scholar, influential in the fields of political economy and demography.
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Tipping point (sociology)
In sociology, a tipping point is a point in time when a group—or a large number of group members—rapidly and dramatically changes its behavior by widely adopting a previously rare practice.
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Water table
The water table is the upper surface of the zone of saturation.
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Bisigmoid, Expit, Law of population growth, Logistic Equation, Logistic curve, Logistic differential equation, Logistic growth, Logistic growth curve, Logistic growth model, Logistic model of population growth, Logistic sigmoid, Logistic sigmoid function, Logistical growth, Logistics curve, Logistics equation, Logistics function, Verhulst equation, Verhulst-Pearl equation.
References
[1] https://en.wikipedia.org/wiki/Logistic_function
