Abstract
The aim of the study is to provide an analytical description of the dynamics of the processes to form images in the cognitive system and their subsequent processing by the consciousness, as well as the study of the simplest characteristics of the quality of the cognitive system functioning in the form of the signal/noise ratio. In accordance with the ideas of the cognitive theory, it is believed that images (schemes, categories, Gestalt, systems, archetypes, etc.) are firstly generated in the human brain and then processed by the consciousness. These images are formed at random in time and are characterized by a random force of effects and subsequently processed by the consciousness. The images are characterized by random numbers, the common interpretation of which is the amount of information corresponding to the appearance of a certain image. The times of appearance are points on the time axis; their number and position are random as well. The work consists of a logically completed model including the following components: • Justification of a statistical model of the appearance of effects during the operation of the cognitive system in the form of the Poisson point process, characterized by the intensity of occurrence of effects and the random values of those effects. • Development of a mathematical model in the consciousness processing of the random effects in the form of reducing response function, which depends on the current time, the time of occurrence of effects and the magnitudes of these effects. To obtain applied results, exponential response function was applied and the analytical results for the mathematical expectations of the processed and not processed information by the consciousness were received. • Introduction for consideration of the signal/noise ratio, characterizing the performance of cognitive systems in the presence of interference and study of its behavior in the situations with the presence of random background noise, regular and single impact of a large information capacity. The use of mathematical apparatus of random point processes allows us to formulate a dynamic model of random effects and use it to investigate the cognitive systems. The results can be used, in particular, for planning a sequence of control actions in cognitive systems as well as for the formation and formalization of requirements for cognitive and intellectual organizational-technical systems.
Highlights
The aim of the study is to provide an analytical description of the dynamics of the processes to form images in the cognitive system and their subsequent processing by the consciousness, as well as the study of the simplest characteristics of the quality of the cognitive system functioning in the form of the signal/noise ratio
The use of mathematical apparatus of random point processes allows us to formulate a dynamic model of random effects and use it to investigate the cognitive systems
Что случайность времени появления Черного лебедя второго типа, может быть учтена путем усреднения отношения сигнал /помеха на интервале ожидания события, например, [0, T)
Summary
Рассмотрим процесс функционирования системы, развивающийся в непрерывном времени, и предположим, что вход системы дискретно (скачкообразно) меняет свое состояние. На входе системы действует случайный процесс появления точек, каждая из которых характеризуется величиной скачков. В связи с этим сделаем ключевое предположение о том, что времена появления точек Wi, а поэтому и межточечные интервалы ti и число точек N(t) являются случайными величинами. Будем теперь полагать, что точечный процесс является пуассоновским случайным точечным процессом или просто пуассоновским точечным процессом, в котором времена появления точек W1, W2, ..., Wi и их число N(t) к моменту времени t являются случайными величинами. Непосредственными вычислениями можно определить, что математическое ожидание числа точек, появившихся на интервале [s, t) равно, M [N Из соотношения (1.4) следует, что при λ = const математическое ожидание числа точек, появившихся на интервале времени Т равно λТ, поэтому параметр λ характеризует интенсивность появления точек пуассоновского процесса, т.е. Если все математические ожидания случайных меток равны n, то в соответствии с (1.4)
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