Rapid eye movement sleepRapid eye movement sleep (REM sleep or REMS) is a unique phase of sleep in humans, mammals and birds, characterized by random rapid movement of the eyes, accompanied by low muscle tone throughout the body, and the propensity of the sleeper to dream vividly. The REM phase is also known as paradoxical sleep (PS) and sometimes desynchronized sleep or dreamy sleep, because of physiological similarities to waking states including rapid, low-voltage desynchronized brain waves.
DerivativeIn mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Partial derivativeIn mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function with respect to the variable is variously denoted by It can be thought of as the rate of change of the function in the -direction.
Rapid eye movement sleep behavior disorderRapid eye movement sleep behavior disorder or REM behavior disorder (RBD) is a sleep disorder in which people act out their dreams. It involves abnormal behavior during the sleep phase with rapid eye movement (REM) sleep. The major feature of RBD is loss of muscle atonia (i.e., the loss of paralysis) during otherwise intact REM sleep (during which paralysis is not only normal but necessary). The loss of motor inhibition leads to sleep behaviors ranging from simple limb twitches to more complex integrated movements that can be violent or result in injury to either the individual or their bedmates.
Logarithmic derivativeIn mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f. When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f.
