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In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.[1][2][3] This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.

The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot).[1] That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Douglas Woodall called the criterion mono-raise.

In information theory, the limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy. It was formulated by Edwin Thompson Jaynes to address defects in the initial definition of differential entropy.

The brachistochrone problem was one of the earliest problems posed in the calculus of variations. Newton was challenged to solve the problem in 1696, and did so the very next day (Boyer and Merzbach 1991, p. 405). In fact, the solution, which is a segment of a cycloid, was found by Leibniz, L'Hospital, Newton, and the two Bernoullis. Johann Bernoulli solved the problem using the analogous one of considering the path of light refracted by transparent layers of varying density (Mach 1893, Gardner 1984, Courant and Robbins 1996).

In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless. Such a subset that contains all the useful information is called a Markov blanket. If a Markov blanket is minimal, meaning that it cannot drop any variable without losing information, it is called a Markov boundary. Identifying a Markov blanket or a Markov boundary helps to extract useful features. The terms of Markov blanket and Markov boundary were coined by Judea Pearl in 1988.

The free energy principle is a theory in cognitive science that attempts to explain how living and non-living systems remain in non-equilibrium steady-states by restricting themselves to a limited number of states. It establishes that systems minimise a free energy function of their internal states (not to be confused with thermodynamic free energy), which entail beliefs about hidden states in their environment. The implicit minimisation of free energy is formally related to variational Bayesian methods and was originally introduced by Karl Friston as an explanation for embodied perception in neuroscience,[1] where it is also known as active inference.

Venture capital (VC) is a form of private equity financing that is provided by venture capital firms or funds to startups, early-stage, and emerging companies that have been deemed to have high growth potential or which have demonstrated high growth (in terms of number of employees, annual revenue, scale of operations, etc). Venture capital firms or funds invest in these early-stage companies in exchange for equity, or an ownership stake. Venture capitalists take on the risk of financing risky start-ups in the hopes that some of the firms they support will become successful. Because startups face high uncertainty,[1] VC investments have high rates of failure. The start-ups are usually based on an innovative technology or business model and they are usually from high technology industries, such as information technology (IT), clean technology or biotechnology

The term epistemocracy has many conflicting uses, generally designating someone of rank having some epistemic property or other. Nassim Nicholas Taleb used it in 2007 to designate a utopian type of society where the leadership possesses epistemic humility. He claims the French writer Michel de Montaigne was a modern epistemocrat. He points out, however, that it is difficult to assert authority on the basis of one's uncertainty; leaders who are assertive, even if they are incorrect, still gather people together

In particle physics, mesons (/ˈmiːzɒnz/ or /ˈmɛzɒnz/) are hadronic subatomic particles composed of an equal number of quarks and antiquarks, usually one of each, bound together by strong interactions. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly one femtometre (10−15 m),[1] which is about 0.6 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Heavier mesons decay to lighter mesons and ultimately to stable electrons, neutrinos and photons.

In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical" point. Equivalently, a sufficiently large collection of random samples from a process can represent the average statistical properties of the entire process. Ergodicity is a property of the system; it is a statement that the system cannot be reduced or factored into smaller components. Ergodic theory is the study of systems possessing ergodicity.

he limbic system, also known as the paleomammalian cortex, is a set of brain structures located on both sides of the thalamus, immediately beneath the medial temporal lobe of the cerebrum primarily in the forebrain.[1] It supports a variety of functions including emotion, behavior, long-term memory, and olfaction.[2] Emotional life is largely housed in the limbic system, and it critically aids the formation of memories.

Akrasia (/əˈkreɪziə/; Greek ἀκρασία, "lacking command" or "weakness", occasionally transliterated as acrasia or Anglicised as acrasy or acracy) is a lack of self-control, or acting against one's better judgment.[1] The adjectival form is "akratic".[2]