Pub Date : 2023-06-15DOI: 10.25088/complexsystems.32.1.19
Maurice Margenstern
The present paper revisits the proof given in a paper of the author published in 2008 proving that the general tiling problem of the hyperbolic plane is algorithmically unsolvable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is algorithmically unsolvable for the Euclidean plane, initially proved by Robert Berger in 1966. The present construction improves that of the 2008 paper. It also very strongly reduces the number of prototiles.
{"title":"The Domino Problem of the Hyperbolic Plane Is Undecidable: New Proof","authors":"Maurice Margenstern","doi":"10.25088/complexsystems.32.1.19","DOIUrl":"https://doi.org/10.25088/complexsystems.32.1.19","url":null,"abstract":"The present paper revisits the proof given in a paper of the author published in 2008 proving that the general tiling problem of the hyperbolic plane is algorithmically unsolvable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is algorithmically unsolvable for the Euclidean plane, initially proved by Robert Berger in 1966. The present construction improves that of the 2008 paper. It also very strongly reduces the number of prototiles.","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134981974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-18DOI: 10.25088/complexsystems.29.4.759
A. Adamatzky, E. Goles, G. J. Martínez, Michail-Antisthenis I. Tsompanas, M. Tegelaar, H. Wosten
We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their pores allow for the flow of cytoplasm between compartments and hyphae. The septal pores of the fungal phylum of the Ascomycota can be closed by organelles called Woronin bodies. Septal closure is increased when the septa become older and when exposed to stress conditions. Thus, Woronin bodies act as informational flow valves. The one-dimensional fungal automaton is a binary-state ternary neighborhood CA, where every compartment follows one of the elementary cellular automaton (ECA) rules if its pores are open and either remains in state 0 (first species of fungal automata) or its previous state (second species of fungal automata) if its pores are closed. The Woronin bodies closing the pores are also governed by ECA rules. We analyze a structure of the composition space of cell-state transition and pore-state transition rules and the complexity of fungal automata with just a few Woronin bodies, and exemplify several important local events in the automaton dynamics.
{"title":"Fungal Automata","authors":"A. Adamatzky, E. Goles, G. J. Martínez, Michail-Antisthenis I. Tsompanas, M. Tegelaar, H. Wosten","doi":"10.25088/complexsystems.29.4.759","DOIUrl":"https://doi.org/10.25088/complexsystems.29.4.759","url":null,"abstract":"We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their pores allow for the flow of cytoplasm between compartments and hyphae. The septal pores of the fungal phylum of the Ascomycota can be closed by organelles called Woronin bodies. Septal closure is increased when the septa become older and when exposed to stress conditions. Thus, Woronin bodies act as informational flow valves. The one-dimensional fungal automaton is a binary-state ternary neighborhood CA, where every compartment follows one of the elementary cellular automaton (ECA) rules if its pores are open and either remains in state 0 (first species of fungal automata) or its previous state (second species of fungal automata) if its pores are closed. The Woronin bodies closing the pores are also governed by ECA rules. We analyze a structure of the composition space of cell-state transition and pore-state transition rules and the complexity of fungal automata with just a few Woronin bodies, and exemplify several important local events in the automaton dynamics.","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43862746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-15DOI: 10.25088/complexsystems.27.4.355
Vinícius Barros da Silva
Universality classes are defined for an idealized nonlinear system that governs the competition between biological species. The decay to asymptotic steady state is examined for supercritical Hopf bifurcation by considering a phenomenological approach supported by numerical simulations and confirmed by an analytical description. The formalism is general and it is expected to be universal for systems exhibiting Hopf bifurcations.
{"title":"Statistical Scaling Laws for Competing Biological Species","authors":"Vinícius Barros da Silva","doi":"10.25088/complexsystems.27.4.355","DOIUrl":"https://doi.org/10.25088/complexsystems.27.4.355","url":null,"abstract":"Universality classes are defined for an idealized nonlinear system that governs the competition between biological species. The decay to asymptotic steady state is examined for supercritical Hopf bifurcation by considering a phenomenological approach supported by numerical simulations and confirmed by an analytical description. The formalism is general and it is expected to be universal for systems exhibiting Hopf bifurcations.","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47047264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-15DOI: 10.25088/complexsystems.27.4.415
U. Srinivasa Rao, J. L
A two-state, one-dimensional cellular automaton (1D CA) with uniform linear rules on an r + 1-neighborhood replicates any arbitrary binary image given as an initial configuration. By these linear rules, any cell gets updated by an EX-OR operation of the states of extreme (first and last) cells of its r + 1-neighborhood. These linear rules replicate the binary image in two ways on the 1D CA: one is without changing the position of the original binary image at time step t 0 and the other is by changing the position of the original binary image at time step t 0. Based on the two ways of replication, we have classified the linear rules into three types. In this paper, we have proven that the binary image of size m gets replicated exactly at time step 2k of the uniform linear rules on the r + 1-neighborhood 1D CA, where k is the least positive integer satisfying the inequality m r ≤ 2k. We have also proved that there are exactly r * 2k -m cells between the last cell of
{"title":"Replication of a Binary Image on a One-Dimensional Cellular Automaton with Linear Rules","authors":"U. Srinivasa Rao, J. L","doi":"10.25088/complexsystems.27.4.415","DOIUrl":"https://doi.org/10.25088/complexsystems.27.4.415","url":null,"abstract":"A two-state, one-dimensional cellular automaton (1D CA) with uniform linear rules on an r + 1-neighborhood replicates any arbitrary binary image given as an initial configuration. By these linear rules, any cell gets updated by an EX-OR operation of the states of extreme (first and last) cells of its r + 1-neighborhood. These linear rules replicate the binary image in two ways on the 1D CA: one is without changing the position of the original binary image at time step t 0 and the other is by changing the position of the original binary image at time step t 0. Based on the two ways of replication, we have classified the linear rules into three types. In this paper, we have proven that the binary image of size m gets replicated exactly at time step 2k of the uniform linear rules on the r + 1-neighborhood 1D CA, where k is the least positive integer satisfying the inequality m r ≤ 2k. We have also proved that there are exactly r * 2k -m cells between the last cell of","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72849809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-03-15DOI: 10.25088/COMPLEXSYSTEMS.22.1.75
Luan Carlos de S. M. Ozelim, André Luís Brasil Cavalcante, L. P. D. F. Borges
{"title":"10.25088/ComplexSystems.22.1.61","authors":"Luan Carlos de S. M. Ozelim, André Luís Brasil Cavalcante, L. P. D. F. Borges","doi":"10.25088/COMPLEXSYSTEMS.22.1.75","DOIUrl":"https://doi.org/10.25088/COMPLEXSYSTEMS.22.1.75","url":null,"abstract":"","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2013-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69221109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-01-01DOI: 10.25088/complexsystems.22.3.247
R. Anderson
{"title":"High-Probability Trajectories in the Phase Space and the System Complexity","authors":"R. Anderson","doi":"10.25088/complexsystems.22.3.247","DOIUrl":"https://doi.org/10.25088/complexsystems.22.3.247","url":null,"abstract":"","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69221112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of “complex systems”. After a brief review of the systems themselves, I will discuss how spin glass concepts have found use in and, in some cases, further advanced areas such as computer science, biology, and other fields: what one might term “old complexity”. I will then turn to a discussion of more recent concepts and ideas that have flowed from studies of spin glasses, and using these introduce a proposal for a kind of “new complexity”.
{"title":"Spin Glasses: Old and New Complexity","authors":"Daniel L. Stein","doi":"10.1063/1.3637770","DOIUrl":"https://doi.org/10.1063/1.3637770","url":null,"abstract":"Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of “complex systems”. After a brief review of the systems themselves, I will discuss how spin glass concepts have found use in and, in some cases, further advanced areas such as computer science, biology, and other fields: what one might term “old complexity”. I will then turn to a discussion of more recent concepts and ideas that have flowed from studies of spin glasses, and using these introduce a proposal for a kind of “new complexity”.","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2011-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84111872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop two novel non‐equilibrium simulation methods which are suitable for calculation of thermal conductivity with good accuracy. These methods are based on simple algorithms, and it will be very easy to extend their range of application. In particular, there are no restrictions (from e.g. the force‐field) to apply them to a variety of systems. Here, they are applied to the calculation of the thermal conductivity of amorphous polyamide‐6,6. We treat two models of the polymer with different degrees of freedoms constrained. The results suggest that the methods are quite efficient, and that thermal conductivity strongly depends on the number of degrees of freedom in the model.
{"title":"The Thermal Conductivity of Amorphous Polymers Calculated by Non‐Equilibrium Molecular Dynamics Simulation","authors":"T. Terao, E. Lussetti, F. Müller-Plathe","doi":"10.1063/1.2897842","DOIUrl":"https://doi.org/10.1063/1.2897842","url":null,"abstract":"We develop two novel non‐equilibrium simulation methods which are suitable for calculation of thermal conductivity with good accuracy. These methods are based on simple algorithms, and it will be very easy to extend their range of application. In particular, there are no restrictions (from e.g. the force‐field) to apply them to a variety of systems. Here, they are applied to the calculation of the thermal conductivity of amorphous polyamide‐6,6. We treat two models of the polymer with different degrees of freedoms constrained. The results suggest that the methods are quite efficient, and that thermal conductivity strongly depends on the number of degrees of freedom in the model.","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2008-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.2897842","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58348162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper reviews the recent activities on radio‐frequency (rf) electromagnetic‐field‐assisted magnetohydrodynamic (MHD) power generation experiments at the Tokyo Institute of Technology. An inductively coupled rf field (13.56 MHz) is continuously supplied to the disk‐shaped Hall‐type MHD generator. The first part of this paper describes a method of obtaining increased power output from a pure Argon plasma MHD power generator by incorporating an rf power source to preionize and heat the plasma. The rf heating enhances ionization of the Argon and raises the temperature of the free electron population above the nominally low 4500 K temperatures obtained without rf heating. This in turn enhances the plasma conductivity making MHD power generation feasible. We demonstrate an enhanced power output when rf heating is on approximately 5 times larger than the input power of the rf generator. The second part of this paper is a demonstration of a physical phenomenon of the rf‐stabilization of the ionization instability, that had been conjectured for some time, but had not been seen experimentally. The rf heating suppresses the ionization instability in the plasma behavior and homogenizes the nonuniformity of the plasma structures. The power‐generating performance is significantly improved with the aid of the rf power under wide seeding conditions. The increment of the enthalpy extraction ratio of around 2% is significantly greater than the fraction of the net rf power, that is, 0.16%, to the thermal input.
{"title":"Non‐Equilibrium Plasma MHD Electrical Power Generation at Tokyo Tech","authors":"T. Murakami, Y. Okuno, H. Yamasaki","doi":"10.1063/1.2897867","DOIUrl":"https://doi.org/10.1063/1.2897867","url":null,"abstract":"This paper reviews the recent activities on radio‐frequency (rf) electromagnetic‐field‐assisted magnetohydrodynamic (MHD) power generation experiments at the Tokyo Institute of Technology. An inductively coupled rf field (13.56 MHz) is continuously supplied to the disk‐shaped Hall‐type MHD generator. The first part of this paper describes a method of obtaining increased power output from a pure Argon plasma MHD power generator by incorporating an rf power source to preionize and heat the plasma. The rf heating enhances ionization of the Argon and raises the temperature of the free electron population above the nominally low 4500 K temperatures obtained without rf heating. This in turn enhances the plasma conductivity making MHD power generation feasible. We demonstrate an enhanced power output when rf heating is on approximately 5 times larger than the input power of the rf generator. The second part of this paper is a demonstration of a physical phenomenon of the rf‐stabilization of the ionization instability, that had been conjectured for some time, but had not been seen experimentally. The rf heating suppresses the ionization instability in the plasma behavior and homogenizes the nonuniformity of the plasma structures. The power‐generating performance is significantly improved with the aid of the rf power under wide seeding conditions. The increment of the enthalpy extraction ratio of around 2% is significantly greater than the fraction of the net rf power, that is, 0.16%, to the thermal input.","PeriodicalId":46935,"journal":{"name":"Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2008-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.2897867","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58348244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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