Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,

The physiology of emotions is a multifaceted process involving the autonomic nervous system, brain structures, hormones, and neurotransmitters. This intricate interplay dictates how emotions manifest in the body and influence behavior.
Autonomic Nervous System
The autonomic nervous system (ANS) plays a critical role in emotional responses by regulating involuntary physiological functions. It consists of two main components: the sympathetic and parasympathetic systems. The sympathetic system...

Emotional labeling is a cognitive process that involves identifying and naming one's emotions, such as anger, fear, happiness, or sadness. It allows individuals to recognize and express their internal emotional states, a critical aspect of emotional regulation and communication. Labeling emotions requires more than mere recognition; it also involves drawing upon memory and contextual cues to understand the current situation and apply a corresponding emotional label. For instance, feeling...

Stanley Schachter and Jerome Singer proposed the two-factor theory of emotion, which emphasizes the interplay between physiological arousal and cognitive labeling in forming emotional experiences. This theory suggests that emotions are not simply a result of physiological responses but rather a combination of these responses and the individual's cognitive interpretation of them.
Physiological Arousal and Cognitive Labeling
According to this theory, when an individual experiences physiological...

Automatic processing refers to the cognitive operations that occur without conscious intent or awareness, playing a fundamental role in shaping social cognition and behavior. These processes enable individuals to navigate complex social environments efficiently by relying on mental shortcuts and pre-existing knowledge structures known as schemas. One of the most influential mechanisms underlying automatic processing is priming, which subtly activates mental representations through exposure to...