# Transients as the Basis for Information Flow in Complex Adaptive Systems

## Abstract

**:**

## 1. Introduction

_{i}} and that they are transmitted by an ergodic Markov process, so that the statistical properties of almost all generated sequences are identical. If p

_{i}is the probability of occurrence of the i-th symbol, then the average amount of information carried by the channel is defined as

- Self-Organization.
- Stochastic determinism.
- Interactive determinism.
- Nonrepresentational contextual dependence: knowledge within a collective intelligence is nonrepresentational. The environment carries the information that a collective intelligence requires.
- Phase transitions, critical, and control parameters.
- Broken ergodicity.
- Broken symmetry.
- Pattern isolation and reconfiguration refers to the appearance of dynamical regularities amongst the dynamical transients exhibited by a system, such that these transients can be identified as entities or as states of entities in their own right, having their own temporal evolution, and patterns of action and interaction.
- Salience refers to the identification of dynamical stimuli that are capable of influencing the dynamical behavior of a system in a meaningful and consistent manner. Salient stimuli produce dynamically robust and stable effects. Conversely;
- Irrelevance refers to the situation in which specific features of the dynamical behavior of a system at one level, say for example the functional form of a phase transition curve, do not depend in any meaningful manner upon knowledge of the dynamical behavior at lower levels, such as the specific nature of microscopic interactions. Saliency and irrelevance play opposite roles in understanding the relationships between the dynamics of individuals and the dynamics of the collective.
- Compatibility and the mutual agreement principle [9] refers to the notion that interactions between the individuals of a collective are not always random, but they frequently involve a choice to interact or not which depends upon extrinsic factors that are salient to the individuals, and an interaction does not occur unless both parties agree.

## 2. The Role of Transients in NOCS

_{T}consisting of all intervals of the form [0,q), where $0\le q\in T$. The semigroup operation is given by concatenation, [0,q)[0,p)=[0,p+q),and the identity is the empty interval [0,0). We form two new monoids, Y(I

_{T}) and Ω(I

_{T}), consisting of all maps from the elements of I

_{T}to Yand Ω, respectively. That is, an element of Y(I

_{T}) consists of a map from some interval [0,t) in I

_{T}toY. The monoid operation is given by concatenation. For example, given maps $[0,p)\stackrel{\psi}{\mapsto}\mathsf{{\rm Y}}$ and $[0,q)\stackrel{\rho}{\mapsto}\mathsf{{\rm Y}}$, we can define a map ψρ from [0,p+q) to Y by $\psi \rho (y)=\psi (y)$ if $y\in [0,p)$, and $\rho (y-p)$ if $y\in [p,p+q)$.

_{T}) (likewise Ω(I

_{T})), we may assign a value μ(ψ) in T given by $\mu (\psi )=t$ if $[0,t)\stackrel{\psi}{\mapsto}\mathsf{{\rm Y}}$.

_{T}), Ω(I

_{T}), Δ), where the transition function Δ from Y(I

_{T}) × Ω(I

_{T}) to Y(I

_{T}) satisfies the following:

- (1)
- $\Delta (0,\rho )=0$
- (2)
- $\Delta (\psi ,\rho )=\psi {\psi}^{\prime}$
- (3)
- $\mu {\psi}^{\prime}=\mu \rho $
- (4)
- $\Delta (\psi ,0)=\psi $
- (5)
- $\Delta (\psi ,\rho {\rho}^{\prime})=\Delta (\Delta (\psi ,\rho ),{\rho}^{\prime})$

_{T}), Ω(I

_{T}), Δ), be a dynamical automata. An instance of an information process is a pair P = (W

_{Q}, W

_{R}), where W

_{Q}is an open, bounded subset of termed the question, and W

_{R}is an open, bounded subset of Y(I

_{T}), termed the response. The automaton A processes P weakly if there exists states ψ $\in $ Y(I

_{T}), ρ ∈ W

_{Q}, and ϕ ∈ W

_{R}, such that $\Delta (\psi ,\rho )=\varphi $. The automaton A processes P effectively if there exists an open, bounded subset ${W}_{E}\subset \mathsf{{\rm Y}}({I}_{T})$, and a subset ${{W}^{\prime}}_{Q}\subset {W}_{Q}$, such that $\Delta ({W}_{E},{{W}^{\prime}}_{Q})\subset {W}_{R}$. The automaton A processes P strongly if there exists a subset ${{W}^{\prime}}_{Q}\subset {W}_{Q}$, such that $\Delta (\mathsf{{\rm Y}}({I}_{T}),{{W}^{\prime}}_{Q})\subset {W}_{R}$. The automaton A processes P error free if ${{W}^{\prime}}_{Q}={W}_{Q}$.

## 3. Information in Formal Complex Adaptive Systems

## 4. Discussion

^{100})

^{450}possible patterns. There were 256

^{100}possible rule configurations per time step, and so (256

^{100})

^{450}rule trajectories. Simulations clearly cannot explore the totality of such a space, but theory guided explorations can shed considerable light on the mechanisms that are involved in TIGoRS. Meanwhile, the naturalistic observation of NOCS, especially collective intelligence and neural systems, might demonstrate whether or not TIGoRS like phenomena occur in these systems, as well as their prevalence.

## Funding

## Conflicts of Interest

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**Figure 1.**The pictures illustrate transient induced global response synchronization (TIGoRS) in a cocktail party automaton. The first two pictures show individual runs under different initial conditions and different low frequency samples of the same stimulus pattern. The third picture shows discordance between the first two runs. The fourth picture shows discordance between the first run and the stimulus. The final two pictures show the distributions of the rules at the end of each run.

**Figure 2.**The graphs depict the Hamming distance between the stimulus and response and efficacy as a function of the stimulus sampling rate in the absence of TIGoRS.

**Figure 3.**The graphs depict the Hamming distance between the stimulus and response and efficacy as a function of the stimulus sampling rate in the presence of TIGoRS.

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Sulis, W. Transients as the Basis for Information Flow in Complex Adaptive Systems. *Entropy* **2019**, *21*, 94.
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Sulis W. Transients as the Basis for Information Flow in Complex Adaptive Systems. *Entropy*. 2019; 21(1):94.
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https://doi.org/10.3390/e21010094