On the Emergent "Quantum" Theory in Complex Adaptive Systems

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or "mock") quantum theory in the Lotka-Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton-Jacobi (HJ) equation and reduce it to an effective Schr\"odinger-type equation, with a (mock) Planck constant \mockbar, which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is cancelled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the "environment." We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we reframe the concept of decoherence into the concept of "quantum turbulence," i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.Comment: 20 pages, 2 figure

Performance of the Product of Three Nakagami-m Random Variables

An output signal from a multi-section wireless relay communication system is equal to the product of the signal envelopes from individual sections. In this paper, a three-sections relay system is considered in the presence of Nakagami-m fading at each section. First, random variable (RV) is formed as the product of three Nakagami-m RVs. For such product, the moments are determined in the closed forms. The first moment is the mean of the signal; the second moment is the average power of the signal, and the third moment is skewness. Then, the Amount of Fading (AoF) is calculated. AoF is a measure of the severity effect of fading in a particular channel model. Besides, all system performance are shown graphically and the parameters influence has been analyzed and discussed

On the Emergent "Quantum" Theory in Complex Adaptive Systems

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or "mock") quantum theory in the Lotka-Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton-Jacobi (HJ) equation and reduce it to an effective Schrödinger-type equation, with a (mock) Planck constant \mockbar, which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is cancelled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the "environment." We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we reframe the concept of decoherence into the concept of "quantum turbulence," i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics

Product of Three Random Variables and its Application in Relay Telecommunication Systems in the Presence of Multipath Fading, Journal of Telecommunications and Information Technology, 2019, nr 1

In this paper, the product of three random variables (RVs) will be considered. Distribution of the product of independent random variables is very important in many applied problems, including wireless relay telecommunication systems. A few of such products of three random variables are observed in this work: the level crossing rate (LCR) of the product of a Nakagami-m random variable, a Rician random variable and a Rayleigh random variable, and of the products of two Rician RVs and one Nakagami-m RV is calculated in closed forms and presented graphically. The LCR formula may be later used for derivation of average fade duration (AFD) of a wireless relay communication radio system with three sections, working in the multipath fading channel. The impact of fading parameters and multipath fading power on the LCR is analyzed based on the graphs presented

Wireless Three-hop Relay Environment with Line-of-Sight: Investigation and Performance Analysis

Lately, the investigation of multi-hop relays is increased in both, academia and engineering practice. Multi-hop relay is introduced to enable data transmission between base station and mobile user dividing great distance into two or more segments to improve link quality. This improvement is specially expressed in environments under deep fading and shadow, where coverage is significantly increased using multi-hop relays. Here, wireless three-hop relay environment with line-of-sight was observed. Output signal from such system is defined as a product of three arbitrary, independent, but not necessarily identically distributed Rician random variables (RVs). For such system, some important performance of the first and second order were analyzed and graphically presented. The impact of Rician factor and signal powers on performance quantities was shown. Derived and displayed first order performance are: probability density function (PDF), cumulative distribution function (CDF), outage probability (Pout), moments, amount of fading (AoF) and channel capacity. Then, the following second order characteristics of wireless three-hop relay communication system working in Rician multipath fading environment were covered: level crossing rate (LCR) and average fade duration (AFD). These results have big application in wireless relay communications with a pronounced line-of-sight, where Rician model is used to describe fading

First-Order Statistical Characteristics of Macrodiversity System with Three Microdiversity MRC Receivers in the Presence of k-µ Short-Term Fading and Gamma Long-Term Fading

Macrodiversity system with macrodiversity SC receiver and three microdiversity MRC (maximum ratio combining) receivers is considered. Independent k-μ short-term fading and correlated Gamma long-term fading are present at the inputs of microdiversity MRC receivers. For this model, the probability density function and the cumulative density function of microdiversity MRC receivers and macrodiversity SC receiver output signal envelopes are calculated. Influences of Gamma shadowing severity, k-μ multipath fading severity, Rician factor and correlation coefficient at probability density function, and cumulative density function of macrodiversity SC receiver output signal envelopes are graphically presented

Product of Three Random Variables and its Application in Relay Telecommunication Systems in the Presence of Multipath Fading

In this paper, the product of three random variables (RVs) will be considered. Distribution of the product of independent random variables is very important in many applied problems, including wireless relay telecommunication systems. A few of such products of three random variables are observed in this work: the level crossing rate (LCR) of the product of a Nakagami-m random variable, a Rician random variable and a Rayleigh random variable, and of the products of two Rician RVs and one Nakagami-m RV is calculated in closed forms and presented graphically. The LCR formula may be later used for derivation of average fade duration (AFD) of a wireless relay communication radio system with three sections, working in the multipath fading channel. The impact of fading parameters and multipath fading power on the LCR is analyzed based on the graphs presented