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Applied behavior analysis ABA , also called behavioral engineering , [1] [2] is a scientific technique concerned with applying empirical approaches based upon the principles of respondent and operant conditioning to change behavior of social significance. The name "applied behavior analysis" has replaced behavior modification because the latter approach suggested attempting to change behavior without clarifying the relevant behavior-environment interactions. In contrast, ABA changes behavior by first assessing the functional relationship between a targeted behavior and the environment. ABA has been utilized in a range of areas, [8] including applied animal behavior, schoolwide positive behavior support , classroom instruction , structured and naturalistic early behavioral interventions for autism , pediatric feeding therapy, rehabilitation of brain injury, [9] dementia , fitness training , substance abuse , phobias , tics , and organizational behavior management. ABA is considered to be controversial by some within the autism rights movement due to a perception that it emphasizes indistinguishability instead of acceptance and a history of, in some embodiments of ABA and its predecessors, the use of aversives such as electric shocks. ABA is an applied science devoted to developing procedures which will produce observable changes in behavior. In The Experiment Students Conditioned Planaria To

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Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions.

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Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. The theory was summarized by Edward Lorenz as: [11].

Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaotic behavior exists in many natural systems, including fluid flow, heartbeat irregularities, weather and climate. Chaos theory has applications in a variety of disciplines, including meteorology[7] anthropology[15] sociologyphysics[16] environmental Studebtscomputer scienceengineeringeconomicsbiologyecologypandemic crisis management[17] [18] and philosophy. The theory formed the basis for such fields of study as complex dynamical systemsIn The Experiment Students Conditioned Planaria To of chaos theory, and self-assembly processes. Chaos theory concerns deterministic systems whose behavior can in principle be predicted.

Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how Planarria its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time.

Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days unproven ; the inner solar system, 4 to 5 million years. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast.

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This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random.

In common usage, "chaos" means "a state of disorder". Although no universally accepted mathematical definition of chaos exists, a commonly used definition, originally formulated by Robert L.

Devaneysays that to classify a dynamical system as chaotic, it must have these properties: [23]. In some cases, the last two properties above have been shown to actually imply sensitivity to initial conditions. If attention is restricted to intervalsthe second property implies the other two. In continuous time dynamical systems, chaos is the phenomenon of the spontaneous breakdown of topological supersymmetry, which is an intrinsic property of evolution operators of all stochastic and deterministic partial differential equations. Within this picture, the long-range dynamical behavior associated with chaotic dynamics e. Sensitivity to initial conditions means that each point in a chaotic system is arbitrarily closely approximated by other points that have significantly different In The Experiment Students Conditioned Planaria To paths or trajectories.

Thus, an arbitrarily small change or perturbation of the current trajectory may lead to significantly different future behavior. Sensitivity to initial conditions is popularly known as the " butterfly effect ", so-called because of the title of a paper given by Edward Lorenz in to the American Association for the Advancement of Science in Washington, D.

Had the butterfly not flapped its wings, the trajectory of the overall system could have been In The Experiment Students Conditioned Planaria To different. A consequence of sensitivity to initial conditions is that if we start with a limited amount of information about the system as is usually the case in practicethen beyond a certain time, the system would no longer be predictable.

This is most prevalent in the case of weather, which is generally predictable only about a week ahead. In more mathematical terms, the Lyapunov exponent measures the sensitivity to initial conditions, in the form of rate of exponential divergence from the perturbed initial conditions.

The rate of separation depends on the orientation of the initial separation vector, so a whole spectrum of Lyapunov exponents can exist.

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The number of Lyapunov exponents is equal to the number of dimensions of the phase space, though it is common to just refer to the largest one. For example, the maximal Lyapunov exponent MLE is most often used, because it determines the overall predictability of the system. Conitioned positive MLE is usually taken as an indication that the system is chaotic.]