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Ashokkumar P, Sathish Aravindh M, Venkatesan A, Lakshmanan M. Realization of all logic gates and memory latch in the SC-CNN cell of the simple nonlinear MLC circuit. CHAOS (WOODBURY, N.Y.) 2021; 31:063119. [PMID: 34241282 DOI: 10.1063/5.0046968] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
We investigate the State-Controlled Cellular Neural Network framework of Murali-Lakshmanan-Chua circuit system subjected to two logical signals. By exploiting the attractors generated by this circuit in different regions of phase space, we show that the nonlinear circuit is capable of producing all the logic gates, namely, or, and, nor, nand, Ex-or, and Ex-nor gates, available in digital systems. Further, the circuit system emulates three-input gates and Set-Reset flip-flop logic as well. Moreover, all these logical elements and flip-flop are found to be tolerant to noise. These phenomena are also experimentally demonstrated. Thus, our investigation to realize all logic gates and memory latch in a nonlinear circuit system paves the way to replace or complement the existing technology with a limited number of hardware.
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Affiliation(s)
- P Ashokkumar
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Sathish Aravindh
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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Arcadia CE, Dombroski A, Oakley K, Chen SL, Tann H, Rose C, Kim E, Reda S, Rubenstein BM, Rosenstein JK. Leveraging autocatalytic reactions for chemical domain image classification. Chem Sci 2021; 12:5464-5472. [PMID: 34163768 PMCID: PMC8179570 DOI: 10.1039/d0sc05860b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2020] [Accepted: 03/02/2021] [Indexed: 01/04/2023] Open
Abstract
Autocatalysis is fundamental to many biological processes, and kinetic models of autocatalytic reactions have mathematical forms similar to activation functions used in artificial neural networks. Inspired by these similarities, we use an autocatalytic reaction, the copper-catalyzed azide-alkyne cycloaddition, to perform digital image recognition tasks. Images are encoded in the concentration of a catalyst across an array of liquid samples, and the classification is performed with a sequence of automated fluid transfers. The outputs of the operations are monitored using UV-vis spectroscopy. The growing interest in molecular information storage suggests that methods for computing in chemistry will become increasingly important for querying and manipulating molecular memory.
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Affiliation(s)
| | | | - Kady Oakley
- Department of Chemistry, Brown University Providence RI USA
| | - Shui Ling Chen
- Department of Chemistry, Brown University Providence RI USA
| | - Hokchhay Tann
- School of Engineering, Brown University Providence RI USA
| | | | - Eunsuk Kim
- Department of Chemistry, Brown University Providence RI USA
| | - Sherief Reda
- School of Engineering, Brown University Providence RI USA
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Stoof R, Goñi-Moreno Á. Modelling co-translational dimerization for programmable nonlinearity in synthetic biology. J R Soc Interface 2020; 17:20200561. [PMID: 33143595 DOI: 10.1098/rsif.2020.0561] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity remains an unmet challenge. This is largely due to a lack of mathematical modelling that accounts for the mechanistic basis of nonlinearity. We introduce a model for gene regulatory circuits that explicitly simulates protein dimerization-a well-known source of nonlinear dynamics. Specifically, our approach focuses on modelling co-translational dimerization: the formation of protein dimers during-and not after-translation. This is in contrast to the prevailing assumption that dimer generation is only viable between freely diffusing monomers (i.e. post-translational dimerization). We provide a method for fine-tuning nonlinearity on demand by balancing the impact of co- versus post-translational dimerization. Furthermore, we suggest design rules, such as protein length or physical separation between genes, that may be used to adjust dimerization dynamics in vivo. The design, build and test of genetic circuits with on-demand nonlinear dynamics will greatly improve the programmability of synthetic biological systems.
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Affiliation(s)
- Ruud Stoof
- School of Computing, Newcastle University, Urban Sciences Building, Science Square, Newcastle upon Tyne NE4 5TG, UK
| | - Ángel Goñi-Moreno
- School of Computing, Newcastle University, Urban Sciences Building, Science Square, Newcastle upon Tyne NE4 5TG, UK.,Centro de Biotecnología y Genómica de Plantas (CBGP, UPM-INIA), Universidad Politénica de Madrid (UPM), Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Campus de Montegancedo-UPM, 28223 Pozuelo de Alarcón, Madrid, Spain
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Sathish Aravindh M, Venkatesan A, Lakshmanan M. Route to logical strange nonchaotic attractors with single periodic force and noise. CHAOS (WOODBURY, N.Y.) 2020; 30:093137. [PMID: 33003915 DOI: 10.1063/5.0017725] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Accepted: 09/04/2020] [Indexed: 06/11/2023]
Abstract
Strange nonchaotic attractors (SNAs) have been identified and studied in the literature exclusively in quasiperiodically driven nonlinear dynamical systems. It is an interesting question to ask whether they can be identified with other types of forcings as well, which still remains an open problem. Here, we show that robust SNAs can be created by a small amount of noise in periodically driven nonlinear dynamical systems by a single force. The robustness of these attractors is tested by perturbing the system with logical signals, leading to the emulation of different logical elements in the SNA regions.
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Affiliation(s)
- M Sathish Aravindh
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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Kia B, Mendes A, Parnami A, George R, Mobley K, Ditto WL. Nonlinear dynamics based machine learning: Utilizing dynamics-based flexibility of nonlinear circuits to implement different functions. PLoS One 2020; 15:e0228534. [PMID: 32126089 PMCID: PMC7053732 DOI: 10.1371/journal.pone.0228534] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Accepted: 01/17/2020] [Indexed: 11/25/2022] Open
Abstract
The core element of machine learning is a flexible, universal function approximator that can be trained and fit into the data. One of the main challenges in modern machine learning is to understand the role of nonlinearity and complexity in these universal function approximators. In this research, we focus on nonlinear complex systems, and show their capability in representation and learning of different functions. Complex nonlinear dynamics and chaos naturally yield an almost infinite diversity of dynamical behaviors and functions. Physical, biological and engineered systems can utilize this diversity to implement adaptive, robust behaviors and operations. A nonlinear dynamical system can be considered as an embodiment of a collection of different possible behaviors or functions, from which different behaviors or functions can be chosen as a response to different conditions or problems. This process of selection can be manual in the sense that one can manually pick and choose the right function through directly setting parameters. Alternatively, we can automate the process and allow the system itself learn how to do it. This creates an approach to machine learning, wherein the nonlinear dynamics represents and embodies different possible functions, and it learns through training how to pick the right function from this function space. We report on how we utilized nonlinear dynamics and chaos to design and fabricate nonlinear dynamics based, morphable hardware in silicon as a physical embodiment for different possible functions. We demonstrate how this flexible, morphable hardware learns through learning and searching algorithms such as genetic algorithm to implement different desired functions. In this approach, we combine two powerful natural and biological phenomenon, Darwinian evolution and nonlinear dynamics and chaos, as a dynamics-oriented approach to designing intelligent, adaptive systems with applications. Nonlinear dynamics embodies different functions at the hardware level, while an evolutionary method is utilized in order to find the parameters to implement the right function.
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Affiliation(s)
- Behnam Kia
- Nonlinear Artificial Intelligence Laboratory, Department of Physics, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Allen Mendes
- Nonlinear Artificial Intelligence Laboratory, Department of Physics, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Akshay Parnami
- Nonlinear Artificial Intelligence Laboratory, Department of Physics, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Robin George
- Nonlinear Artificial Intelligence Laboratory, Department of Physics, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Kenneth Mobley
- First Pass Engineering, Castle Rock, Colorado, United States of America
| | - William L. Ditto
- Nonlinear Artificial Intelligence Laboratory, Department of Physics, North Carolina State University, Raleigh, North Carolina, United States of America
- * E-mail:
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Sathish Aravindh M, Venkatesan A, Lakshmanan M. Strange nonchaotic attractors for computation. Phys Rev E 2018; 97:052212. [PMID: 29906833 DOI: 10.1103/physreve.97.052212] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Indexed: 06/08/2023]
Abstract
We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange nonchaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in an aperiodic manner as input to a quasiperiodically driven double-well Duffing oscillator system, the response of the system can produce logical output controlled by such a forcing. Changing the threshold or biasing of the system changes the output to another logic operation and memory latch. The interplay of nonlinearity and quasiperiodic forcing yields logical behavior, and the emergent outcome of such a system is a logic gate. It is further shown that the logical behaviors persist even for an experimental noise floor. Thus the SNA turns out to be an efficient tool for computation.
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Affiliation(s)
- M Sathish Aravindh
- PG and Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirappalli 621 007, India
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
| | - A Venkatesan
- PG and Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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Fradkov AL. Horizons of cybernetical physics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160223. [PMID: 28115620 PMCID: PMC5311442 DOI: 10.1098/rsta.2016.0223] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/02/2016] [Indexed: 05/30/2023]
Abstract
The subject and main areas of a new research field-cybernetical physics-are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control.This article is part of the themed issue 'Horizons of cybernetical physics'.
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Affiliation(s)
- Alexander L Fradkov
- Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia
- Department of Control of Complex Systems, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, 197101 Saint Petersburg, Russia
- Department of Theoretical Cybernetics, Saint Petersburg State University, 199034 Saint Petersburg, Russia
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