@article{murali_sinha_kohar_kia_ditto_2018, title={Chaotic attractor hopping yields logic operations}, volume={13}, ISSN={["1932-6203"]}, url={https://doi.org/10.1371/journal.pone.0209037}, DOI={10.1371/journal.pone.0209037}, abstractNote={Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With logic output 0/1 mapped to dynamical attractors bounded in distinct regions of phase space, and logic inputs encoded by a very small bias parameter, we explicitly demonstrate that the system hops consistently in response to an external input stream, operating effectively as a reliable logic gate. This system offers the advantage that very low-amplitude inputs yield highly amplified outputs. Additionally, different dynamical variables in the system yield complementary logic operations in parallel. Further, we show that in certain parameter regions noise aids the reliability of logic operations, and is actually necessary for obtaining consistent outputs. This leads us to a generalization of the concept of Logical Stochastic Resonance to attractors more complex than fixed point states, such as periodic or chaotic attractors. Lastly, the results are verified in electronic circuit experiments, demonstrating the robustness of the phenomena. So we have combined the research directions of Chaos Computing and Logical Stochastic Resonance here, and this approach has potential to be realized in wide-ranging systems.}, number={12}, journal={PLOS ONE}, author={Murali, K. and Sinha, Sudeshna and Kohar, Vivek and Kia, Behnam and Ditto, William L.}, editor={Adamatzky, AndrewEditor}, year={2018}, month={Dec} }
 @article{kia_mobley_ditto_2017, title={An Integrated Circuit Design for a Dynamics-Based Reconfigurable Logic Block}, volume={64}, ISSN={["1558-3791"]}, DOI={10.1109/tcsii.2016.2611442}, abstractNote={In this brief, a nonlinear integrated circuit to harvest different types of digital computation from complex dynamics is designed and fabricated. This circuit can be dynamically reconfigured to implement different two-input, one-output digital functions. The main advantage of the circuit is the ability to implement different digital functions in each clock cycle without halting for reconfiguration.}, number={6}, journal={IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS}, author={Kia, Behnam and Mobley, Kenneth and Ditto, William L.}, year={2017}, month={Jun}, pages={715–719} }
 @article{kia_lindner_ditto_2017, title={Dynamical coupling outperforms "majority wins" in organizing redundancy to mitigate noise}, volume={87}, ISSN={["1573-269X"]}, DOI={10.1007/s11071-016-3063-z}, number={1}, journal={NONLINEAR DYNAMICS}, author={Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2017}, month={Jan}, pages={605–615} }
 @article{kohar_kia_lindner_ditto_2017, title={Implementing Boolean Functions in Hybrid Digital-Analog Systems}, volume={7}, ISSN={["2331-7019"]}, DOI={10.1103/physrevapplied.7.044006}, abstractNote={We propose an architecture to implement multi − input one − output Boolean functions using chaos computing in hybrid digital-analog systems consisting of a digital block of conventional AND gates and a nonlinear circuit. This architecture efficiently utilizes the super-stable initial conditions of a nonlinear circuit and enables us to implement all possible 2 2 m Boolean functions of m data inputs in just m iterations of the nonlinear circuit resulting in better operating speed and noise tolerance. In an ideal nonlinear map, this architecture eliminates the need for a decoder as the outputs are mapped to maxima and minima of the map and can be fed directly to the next stage enabling multilayer concatenation. We demonstrate the utility of this architecture in a 3 − transistor circuit.}, number={4}, journal={PHYSICAL REVIEW APPLIED}, author={Kohar, Vivek and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2017}, month={Apr} }
 @inproceedings{kia_ditto_2017, title={Nonlinear dynamics and chaos for fleixble, reconfigurable computing}, DOI={10.1109/icrc.2017.8123679}, abstractNote={Nonlinear dynamics and chaos contribute flexibility and rich, complex behavior to nonlinear systems. Transistors and transistor circuits are inherently nonlinear. It was demonstrated that this nonlinearity and the flexibility that comes with it can be utilized to implement flexible, reconfigurable computing, and such approaches are called Nonlinear Dynamics-Based Computing. In nonlinear dynamics-based computing, a very same circuit can be reprogrammed to implement and perform many different types of computations, thereby increasing the amount of computing that can be obtained per transistor. For example, at the gate level, the same transistor circuit can implement all different logical gates, such as AND gate or XOR gate. Or at the system level, the same transistor circuit can implement a variety of different higher-level functions, such as addition or subtraction. Another remarkable feature of nonlinear dynamics-based computing is that because different types of functions or operations coexist within the dynamics of the circuit, reprograming and reconfiguring is nearly instant. A recently fabricated VLSI chip for nonlinear dynamics-based computing was shown to be capable of implementing a new function in each clock cycle, with no need for separate reprograming time in between clock cycles. In this paper we briefly review this new approach to computing, present some of our latest results, discuss the implications and possible advantages of nonlinear dynamics-based computing, and plot potential horizons for this exciting new approach to computing.}, booktitle={2017 IEEE International Conference on Rebooting Computing (ICRC)}, author={Kia, B. and Ditto, William}, year={2017}, pages={282–289} }
 @article{kia_lindner_ditto_2017, title={Nonlinear dynamics as an engine of computation}, volume={375}, ISSN={1364-503X 1471-2962}, url={http://dx.doi.org/10.1098/rsta.2016.0222}, DOI={10.1098/rsta.2016.0222}, abstractNote={Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.}, number={2088}, journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, publisher={The Royal Society}, author={Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2017}, month={Mar}, pages={20160222} }
 @inproceedings{kia_parnami_mendes_ditto_2017, title={Nonlinear dynamics-based adaptive hardware}, DOI={10.1109/ahs.2017.8046379}, abstractNote={In this paper we briefly review some recent results in the field of nonlinear dynamics-based computing and how it can be utilized to implement flexible, reprogrammable hardware. Then we propose that such internal flexibility can be utilized to compensate for the negative effects of both internal and external changes. More specifically, we report results of an experimental study that we performed on an integrated circuit fabricated for nonlinear dynamics-based computing, where we overheated the circuit to a point that its operation and performance changed, but then we reprogramed the circuit so that the overheated circuit could again perform the same operations reliably. This inherent flexibility and reprogrammability opens the door to implementing adaptive circuits and systems that can withstand both variable environments and adverse conditions.}, booktitle={2017 nasa/esa conference on adaptive hardware and systems (ahs)}, author={Kia, B. and Parnami, A. and Mendes, A. and Ditto, William}, year={2017}, pages={200–205} }
 @inbook{kia_kohar_ditto_2017, title={Present and the Future of Chaos Computing}, ISBN={9783319526201 9783319526218}, ISSN={2367-3370 2367-3389}, url={http://dx.doi.org/10.1007/978-3-319-52621-8_9}, DOI={10.1007/978-3-319-52621-8_9}, abstractNote={We study chaos computing as a new approach for reconfigurable computing and present some of our latest results and discuss what this new direction to computing means and implies. We discuss the advantages and challenges that come with this new paradigm of computing and envision its future.}, booktitle={Lecture Notes in Networks and Systems}, publisher={Springer International Publishing}, author={Kia, Behnam and Kohar, Vivek and Ditto, William}, year={2017}, pages={101–109} }
 @inproceedings{kia_kohar_ditto_2017, title={Present and the future of chaos computing}, volume={6}, booktitle={Proceedings of the 4th international conference on applications in nonlinear dynamics (icand 2016)}, author={Kia, B. and Kohar, V. and Ditto, W.}, year={2017}, pages={101–109} }
 @inbook{kohar_lindner_kia_ditto_2017, title={Spectral Scaling Analysis of RR Lyrae Stars in OGLE-IV Galactic Bulge Fields}, ISBN={9783319526201 9783319526218}, ISSN={2367-3370 2367-3389}, url={http://dx.doi.org/10.1007/978-3-319-52621-8_6}, DOI={10.1007/978-3-319-52621-8_6}, abstractNote={Recent studies of variable stars have uncovered characteristic nonlinear features in flux of these stars and indicate the presence of quasiperiodicity. A common technique to study quasiperiodic systems is spectral scaling analysis which relies on the fact that different dynamical behaviors can be identified on the basis of distribution of peaks in the periodogram. Here we apply the spectral scaling technique to the OGLE-IV photometry of the RR Lyrae stars in the Galactic bulge. We find that spectra of the fundamental mode (RRab) and first overtone RR Lyrae stars (RRc) scales differently and thus the spectral scaling can be used to distinguish between different RR Lyrae sub classes. Furthermore, goodness of fit for RRc stars with multiple modes is better than other stars. The scaling exponent for stars observed in high cadence is close to the values reported using Kepler photometry. This analysis can help us to reclassify the stars based on their dynamical characteristics.}, booktitle={Lecture Notes in Networks and Systems}, publisher={Springer International Publishing}, author={Kohar, Vivek and Lindner, John F. and Kia, Behnam and Ditto, William L.}, year={2017}, pages={65–76} }
 @inproceedings{kohar_lindner_kia_ditto_2017, title={Spectral scaling analysis of RR Lyrae stars in OGLE-IV Galactic Bulge Fields}, volume={6}, booktitle={Proceedings of the 4th international conference on applications in nonlinear dynamics (icand 2016)}, author={Kohar, V. and Lindner, J. F. and Kia, B. and Ditto, W. L.}, year={2017}, pages={65–76} }
 @article{kia_lindner_ditto_2016, title={A Simple Nonlinear Circuit Contains an Infinite Number of Functions}, volume={63}, ISSN={["1558-3791"]}, DOI={10.1109/tcsii.2016.2538358}, abstractNote={The complex dynamics of a simple nonlinear circuit contains an infinite number of functions. Specifically, this brief shows that the number of different functions that a nonlinear or chaotic circuit can implement exponentially increases as the circuit evolves in time, and this exponential increase is quantified with an exponent that is named the computing exponent. This brief argues that a simple nonlinear circuit that illustrates rich complex dynamics can embody infinitely many different functions, each of which can be dynamically selected. In practice, not all of these functions may be accessible due to factors such as noise or instability of the functions. However, these infinitely many functions do exist within the dynamics of the nonlinear circuit regardless of accessibility or inaccessibility of the functions in practice. This nonlinear-dynamics-based approach to computation opens the door for implementing extremely slim low-power circuits that are capable of performing many different types of functions.}, number={10}, journal={IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS}, author={Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={Oct}, pages={944–948} }
 @article{kohar_kia_kia_lindner_ditto_2016, title={Role of network topology in noise reduction using coupled dynamics}, volume={84}, ISSN={["1573-269X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84954519290&partnerID=MN8TOARS}, DOI={10.1007/s11071-016-2607-6}, number={3}, journal={NONLINEAR DYNAMICS}, author={Kohar, Vivek and Kia, Sarvenaz and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={May}, pages={1805–1812} }
 @article{lindner_kohar_kia_hippke_learned_ditto_2016, title={Simple nonlinear models suggest variable star universality}, volume={316}, ISSN={0167-2789}, url={http://dx.doi.org/10.1016/J.PHYSD.2015.10.006}, DOI={10.1016/J.PHYSD.2015.10.006}, abstractNote={Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near −1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier BV}, author={Lindner, John F. and Kohar, Vivek and Kia, Behnam and Hippke, Michael and Learned, John G. and Ditto, William L.}, year={2016}, month={Feb}, pages={16–22} }
 @article{kohar_kia_lindner_ditto_2016, title={Superlinearly scalable noise robustness of redundant coupled dynamical systems}, volume={93}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.93.032213}, abstractNote={We illustrate through theory and numerical simulations that redundant coupled dynamical systems can be extremely robust against local noise in comparison to uncoupled dynamical systems evolving in the same noisy environment. Previous studies have shown that the noise robustness of redundant coupled dynamical systems is linearly scalable and deviations due to noise can be minimized by increasing the number of coupled units. Here, we demonstrate that the noise robustness can actually be scaled superlinearly if some conditions are met and very high noise robustness can be realized with very few coupled units. We discuss these conditions and show that this superlinear scalability depends on the nonlinearity of the individual dynamical units. The phenomenon is demonstrated in discrete as well as continuous dynamical systems. This superlinear scalability not only provides us an opportunity to exploit the nonlinearity of physical systems without being bogged down by noise but may also help us in understanding the functional role of coupled redundancy found in many biological systems. Moreover, engineers can exploit superlinear noise suppression by starting a coupled system near (not necessarily at) the appropriate initial condition.}, number={3}, journal={PHYSICAL REVIEW E}, author={Kohar, Vivek and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={Mar} }
 @article{kia_kia_lindner_sinha_ditto_2014, title={Noise tolerant spatiotemporal chaos computing}, volume={24}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.4897168}, DOI={10.1063/1.4897168}, abstractNote={We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Kia, Behnam and Kia, Sarvenaz and Lindner, John F. and Sinha, Sudeshna and Ditto, William L.}, year={2014}, month={Dec}, pages={043110} }
 @article{hippke_learned_zee_edmondson_lindner_kia_ditto_stevens_2014, title={PULSATION PERIOD VARIATIONS IN THE RRc LYRAE STAR KIC 5520878}, volume={798}, ISSN={1538-4357}, url={http://dx.doi.org/10.1088/0004-637X/798/1/42}, DOI={10.1088/0004-637X/798/1/42}, abstractNote={Learned et al. proposed that a sufficiently advanced extra-terrestrial civilization may tickle Cepheid and RR Lyrae variable stars with a neutrino beam at the right time, thus causing them to trigger early and jogging the otherwise very regular phase of their expansion and contraction. This would turn these stars into beacons to transmit information throughout the galaxy and beyond. The idea is to search for signs of phase modulation (in the regime of short pulse duration) and patterns, which could be indicative of intentional, omnidirectional signaling. We have performed such a search among variable stars using photometric data from the Kepler space telescope. In the RRc Lyrae star KIC 5520878, we have found two such regimes of long and short pulse durations. The sequence of period lengths, expressed as time series data, is strongly autocorrelated, with correlation coefficients of prime numbers being significantly higher (p = 99.8%). Our analysis of this candidate star shows that the prime number oddity originates from two simultaneous pulsation periods and is likely of natural origin. Simple physical models elucidate the frequency content and asymmetries of the KIC 5520878 light curve. Despite this SETI null result, we encourage testing of other archival and future time-series photometry for signs of modulated stars. This can be done as a by-product to the standard analysis, and can even be partly automated.}, number={1}, journal={The Astrophysical Journal}, publisher={IOP Publishing}, author={Hippke, Michael and Learned, John G. and Zee, A. and Edmondson, William H. and Lindner, John F. and Kia, Behnam and Ditto, William L. and Stevens, Ian R.}, year={2014}, month={Dec}, pages={42} }
 @inbook{kia_murali_jahed motlagh_sinha_ditto_2014, place={Cham, Switzerland}, title={Synthetic Computation: Chaos Computing, Logical Stochastic Resonance, and Adaptive Computing}, ISBN={9783319029245 9783319029252}, ISSN={1860-0832 1860-0840}, url={http://dx.doi.org/10.1007/978-3-319-02925-2_5}, DOI={10.1007/978-3-319-02925-2_5}, abstractNote={Nonlinearity and chaos can illustrate numerous behaviors and patterns, and one can select different patterns from this rich library of patterns. In this paper we focus on synthetic computing, a field that engineers and synthesizes nonlinear systems to obtain computation. We explain the importance of nonlinearity, and describe how nonlinear systems can be engineered to perform computation. More specifically, we provide an overview of chaos computing, a field that manually programs chaotic systems to build different types of digital functions. Also we briefly describe logical stochastic resonance (LSR), and then extend the approach of LSR to realize combinational digital logic systems via suitable concatenation of existing logical stochastic resonance blocks. Finally we demonstrate how a chaotic system can be engineered and mated with different machine learning techniques, such as artificial neural networks, random searching, and genetic algorithm, to design different autonomous systems that can adapt and respond to environmental conditions.}, booktitle={International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012)}, publisher={Springer International Publishing}, author={Kia, Behnam and Murali, K. and Jahed Motlagh, Mohammad-Reza and Sinha, Sudeshna and Ditto, William L.}, editor={Palacios, V. A. and Longhini, P.Editors}, year={2014}, month={Dec}, pages={51–65} }
 @inbook{kia_ditto_spano_2011, title={Chaos for Speech Coding and Production}, volume={7015 LNAI}, ISBN={9783642250194 9783642250200}, ISSN={0302-9743 1611-3349}, url={http://dx.doi.org/10.1007/978-3-642-25020-0_35}, DOI={10.1007/978-3-642-25020-0_35}, abstractNote={The presence of nonlinearity and chaotic behavior in the human speech production system has been reported previously; however to date chaotic dynamics has not been widely exploited in speech coding and artificial speech production algorithms. In this paper we illustrate how we can utilize chaotic dynamics in speech coding and synthesis and discuss how it can improve the performance of these processes. As an example we choose code-excited linear predictive coding and, instead of an excitation codebook consisting of Gaussian random waveforms, we use chaotic systems to produce chaotic excitations. This simple technique has the potential to greatly improve the efficiency of modern communication devices such as cell phones. We call the resulting scheme chaos-excited linear predictive coding.}, booktitle={Advances in Nonlinear Speech Processing}, publisher={Springer Berlin Heidelberg}, author={Kia, Behnam and Ditto, William L. and Spano, Mark L.}, year={2011}, pages={270–278} }
 @article{dari_kia_bulsara_ditto_2011, title={Logical stochastic resonance with correlated internal and external noises in a synthetic biological logic block}, volume={21}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.3660159}, DOI={10.1063/1.3660159}, abstractNote={Following the advent of synthetic biology, several gene networks have been engineered to emulate digital devices, with the ability to program cells for different applications. In this work, we adapt the concept of logical stochastic resonance to a synthetic gene network derived from a bacteriophage λ. The intriguing results of this study show that it is possible to build a biological logic block that can emulate or switch from the AND to the OR gate functionalities through externally tuning the system parameters. Moreover, this behavior and the robustness of the logic gate are underpinned by the presence of an optimal amount of random fluctuations. We extend our earlier work in this field, by taking into account the effects of correlated external (additive) and internal (multiplicative or state-dependent) noise. Results obtained through analytical calculations as well as numerical simulations are presented.}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Dari, Anna and Kia, Behnam and Bulsara, Adi R. and Ditto, William L.}, year={2011}, month={Dec}, pages={047521} }
 @article{kia_dari_ditto_spano_2011, title={Unstable periodic orbits and noise in chaos computing}, volume={21}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.3664349}, DOI={10.1063/1.3664349}, abstractNote={Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance.}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Kia, Behnam and Dari, Anna and Ditto, William L. and Spano, Mark L.}, year={2011}, month={Dec}, pages={047520} }
 @article{pourshaghaghi_kia_ditto_jahed-motlagh_2009, title={Reconfigurable logic blocks based on a chaotic Chua circuit}, volume={41}, ISSN={0960-0779}, url={http://dx.doi.org/10.1016/j.chaos.2007.11.030}, DOI={10.1016/j.chaos.2007.11.030}, abstractNote={To investigate morphable chaotic logic we have constructed, out of discrete circuitry, a chaotic logic block that can morph between all two input, one output logic gates. Additionally, we investigate the sensitivity of such a block to noise and have been able to formulate a method that demonstrates that the chaotic saddles of the inherent chaotic dynamics can be exploited to enhance the robustness of the logic functions with respect to noise.}, number={1}, journal={Chaos, Solitons & Fractals}, publisher={Elsevier BV}, author={Pourshaghaghi, Hamid Reza and Kia, Behnam and Ditto, William and Jahed-Motlagh, Mohammad Reza}, year={2009}, month={Jul}, pages={233–244} }
 @article{kia_jahed-motiagh_2006, title={A Novel dynamically reconfigurable logic block based on CHAOS}, volume={39}, ISSN={1474-6670}, url={http://dx.doi.org/10.1016/S1474-6670(17)30214-8}, DOI={10.1016/S1474-6670(17)30214-8}, abstractNote={The new idea of chaos based computation is studied and improved to obtain a novel logic block. In new presented scheme rcconfigurability is produced through intrinsic flexibility of chaotic systems. Handle for directing the logic block to simulate different kinds of digital functions is the offsets that one gives to the data inputs. A new form of dynamic reconfiguration that is beyond the conventional meaning of dynamic reconfiguration in FPGAs is introduced. Introduced scheme could reconfigure itself by the arrival of new set of data and control inputs and no suspension in the operation of the system is needed.}, number={21}, journal={IFAC Proceedings Volumes}, publisher={Elsevier BV}, author={Kia, Behnam and Jahed-Motiagh, Mohammad Reza}, year={2006}, month={Feb}, pages={372–377} }