Human controllers as pilots or drivers can be described by linear time invariant systems cascaded with time delay. Inspired by this, we ‘generalize’ the definition of passivity index to irrational transfer functions and use the passivity index to examine passivity of some existing human models. The results show that the human model is non-passive due to the time delay which represents inherent ...

For simplicity, we follow the rules: k, n, p, K, N are natural numbers, x, y, e1 are real numbers, s1, s2, s3 are sequences of real numbers, and s4 is a finite sequence of elements of R. Let us consider x. We introduce x is irrational as an antonym of x is rational. Let us consider x, y. We introduce x as a synonym of x. One can prove the following two propositions: (1) If p is prime, then √ p ...

Fractional differential systems are infinite-dimensional systems which are difficult to study and simulate: they can be represented with poles and cuts. This representation applies to a wider class of irrational transfer functions, and is most useful for signal processing purposes, such as frequency-domain and time-domain simulations: the approximations in low dimension which give the most stri...

Background and aims The addictive nature of compulsive buying implies that mood disturbances, stress, and cognitive biases that underlie compulsive buying might operate in ways similar in both genders. In the current study, we aimed to test hypothetical pathways of mood compensation and irrational cognitions, which may explain compulsive buying tendencies. We also examined potential gender diff...

Irrational beliefs play a central role in cognitive theory and therapy; they have been shown to be related to a variety of disorders such as depression and anxiety. Irrational beliefs, which can be assessed via clinical interviewing techniques, are frequently assessed by self-report measures, both clinically and for research purposes. Much of the research demonstrating the effect of irrational ...

Previous studies have shown right parietal activation in response to observing irrational actions. Behavioral studies show that people sometimes imitate irrational actions, a phenomenon called overimitation. However, limitations on movement in functional magnetic resonance imaging (fMRI) mean that the neural basis of overimitation has not been studied. To address this, our study employed a less...