Complex Systems
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Volume 28, Number 4 (2019)

Quantum Cellular Automata, Black Hole Thermodynamics and the Laws of Quantum Complexity Download PDF
Ruhi Shah and Jonathan Gorard

This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming from a formal analogy among quantum computational complexity theory and classical thermodynamics, that have arisen recently in the context of black hole physics. In particular, the apparent resonance and thermalization effects present within such QCAs are investigated, and it is demonstrated that the expected exponential relationships among the quantum circuit complexity of the evolution operator, the classical entropy of the equilibrium QCA state and the characteristic equilibration time of the QCA all hold within this new model. Finally, a rigorous explanation for this empirical relationship is provided, as well as for the relationship with black hole thermodynamics, by drawing an explicit mathematical connection with the mean ergodic theorem and the ergodicity of k-local quantum systems.

Keywords: cellular automata; quantum cellular automata; quantum computing; quantum information theory; complexity theory; ergodic theory; black hole thermodynamics

Cite this publication as:
R. Shah and J. Gorard, “Quantum Cellular Automata, Black Hole Thermodynamics and the Laws of Quantum Complexity,” Complex Systems, 28(4), 2019 pp. 393–410.

Methodological Approaches for the Fokker–Planck Equation Associated to Nonlinear Stochastic Differential Systems with Uncertain Parameters Download PDF
Mohamed Ben Said, Ihsane Salleh, and Lahcen Azrar

This paper is an extension of work originally presented at the World Conference on Complex Systems. In this paper, methodological approaches and numerical procedures are elaborated for nonlinear stochastic differential equations with uncertain parameters. The associated Fokker–Planck equation is used to get the distribution function. Mathematical developments based on the meshfree method with radial basis functions and on exponential closure combined with Monte Carlo and conditional expectation methods are elaborated for numerical solutions. The obtained approximate solutions compare well with available solutions and the effectiveness and accuracy of the proposed methods are demonstrated.

Keywords: exponential closure method; meshfree method; radial basis function; Fokker–Planck equation; stochastic differential equation; uncertain parameters; probability density function; Monte Carlo; conditional expectation  

Cite this publication as:
M. B. Said, I. Salleh and L. Azrar, “Methodological Approaches for the Fokker–Planck Equation Associated to Nonlinear Stochastic Differential Systems with Uncertain Parameters,” Complex Systems, 28(4), 2019 pp. 411–431.

Reservoir Computing with Complex Cellular Automata Download PDF
Neil Babson and Christof Teuscher

Reservoir computing (RC) is a computational framework in which a dynamical system, known as the reservoir, casts a temporal input signal to a high-dimensional space, and a trainable readout layer creates the output signal by extracting salient features from the reservoir. Several researchers have experimented with using the dynamical behavior of elementary cellular automaton (CA) rules as reservoirs. CA reservoirs have the potential to reduce the size, weight and power (SWaP) required to perform complex computation by orders of magnitude compared with traditional RC implementations. The research described in this paper expands this approach to CA rules with larger neighborhoods and/or more states, which are termed complex, as opposed to the elementary rules. Results show that some of these non-elementary cellular automaton rules outperform the best elementary rules at the standard benchmark five-bit memory task, requiring half the reservoir size to produce comparable results. This research is relevant to the design of simple, small, and low-power systems capable of performing complex computation.

Keywords: reservoir computing (RC); cellular automata (CAs); cellular automata based reservoirs (ReCAs)

Cite this publication as:
N. Babson and C. Teuscher, “Reservoir Computing with Complex Cellular Automata,” Complex Systems, 28(4), 2019 pp. 433–455.

Secure and Computationally Efficient Cryptographic Primitive Based on Cellular Automaton Download PDF
Rade Vuckovac

The cellular automaton generator (CAG), a random number generator based on the one-dimensional cellular automaton (CA), is presented. Three procedures of secure implementation using the CAG are proposed and discussed. Implementations are very efficient in a wide range of hardware and software scenarios. That includes the advanced application of internet of things (IoT) and cyber-physical systems, which are both needed for computationally efficient cryptographic primitives. Furthermore, the proposed primitive is inherently resistant against the side-channel attack (SCA), where many currently available ciphers, such as the advanced encryption standard (AES), require additional hardware or software effort to prevent the SCA line of attack.

Keywords: cellular automata; cryptographic primitive; side-channel attack; stream cipher performance  

Cite this publication as:
R. Vuckovac, “Secure and Computationally Efficient Cryptographic Primitive Based on Cellular Automaton,” Complex Systems, 28(4), 2019 pp. 457–474.

Modeling the Spread of Suicide in Greece Download PDF
Elena De la Poza, Lucas Jódar, and Georgia Douklia

Suicide can be defined as the act of purposely ending one’s life. The reasons that explain why people commit suicide are complex and encompass multiple and combined factors (demographic, economic, emotional, social). In recent years, deaths by suicide have increased incessantly in Greece, becoming a social problem. The aim of this study is to build a dynamic model through a system of difference equations that quantifies the number of hidden cases of suicide in Greece during the period July 2015 to January 2019. Then, the results obtained from computing the model are compared with the Spanish ones for the same period from previous research.

Keywords: suicide; risk; quantification; mathematical model; Greece; Spain

Cite this publication as:
E. De la Poza, L. Jódar and G. Douklia, “Modeling the Spread of Suicide in Greece,” Complex Systems, 28(4), 2019 pp. 475–489.

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