Random walkIn mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.
Statistical mechanicsIn physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience.
Random number generationRandom number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can be hardware random-number generators (HRNGs), wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model.
Algorithmically random sequenceIntuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free or not) universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet (e.g. decimal digits). Random sequences are key objects of study in algorithmic information theory. As different types of algorithms are sometimes considered, ranging from algorithms with specific bounds on their running time to algorithms which may ask questions of an oracle machine, there are different notions of randomness.
Joint probability distributionGiven two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).
Population geneticsPopulation genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure. Population genetics was a vital ingredient in the emergence of the modern evolutionary synthesis. Its primary founders were Sewall Wright, J. B. S. Haldane and Ronald Fisher, who also laid the foundations for the related discipline of quantitative genetics.
Population declinePopulation decline, also known as depopulation, is a reduction in a human population size. Over the long term, stretching from prehistory to the present, Earth's total human population has continued to grow; however, current projections suggest that this long-term trend of steady population growth may be coming to an end. Until the beginning of the Industrial Revolution, the global population grew very slowly, at about 0.04% per year. After about 1800, the growth rate accelerated to a peak of 2.
Zero population growthZero population growth, sometimes abbreviated ZPG, is a condition of demographic balance where the number of people in a specified population neither grows nor declines; that is, the number of births plus in-migrants equals the number of deaths plus out-migrants. ZPG has been a prominent political movement since the 1960s. As part of the concept of optimum population, the movement considers zero population growth to be an objective towards which countries and the whole world should strive in the interests of accomplishing long-term optimal standards and conditions of living.
Population ageingPopulation ageing is an increasing median age in a population because of declining fertility rates and rising life expectancy. Most countries have rising life expectancy and an ageing population, trends that emerged first in developed countries but are now seen in virtually all developing countries. That is the case for every country in the world except the 18 countries designated as "demographic outliers" by the United Nations. The aged population is currently at its highest level in human history.
Wiener processIn mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the physical process of the same name originally observed by Scottish botanist Robert Brown.
Population growthPopulation growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to 7.9 billion in 2020. The UN projected population to keep growing, and estimates have put the total population at 8.6 billion by mid-2030, 9.8 billion by mid-2050 and 11.2 billion by 2100.
Factor analysisFactor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables.
