{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T10:25:39Z","timestamp":1776680739653,"version":"3.51.2"},"reference-count":114,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,1,27]],"date-time":"2014-01-27T00:00:00Z","timestamp":1390780800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. G\u00f6del\u2019s incompleteness argument is explored here to devise an engine where an astronomically large number of \u201cif-then\u201d arguments are allowed to grow by self-assembly, based on the basic set of arguments written in the system, thus, we explore the beyond Turing path of computing but following a fundamentally different route adopted in the last half-a-century old non-Turing adventures. Our hardware is a multilayered seed structure. If we open the largest seed, which is the final hardware, we find several computing seed structures inside, if we take any of them and open, there are several computing seeds inside. We design and synthesize the smallest seed, the entire multilayered architecture grows by itself. The electromagnetic resonance band of each seed looks similar, but the seeds of any layer shares a common region in its resonance band with inner and upper layer, hence a chain of resonance bands is formed (frequency fractal) connecting the smallest to the largest seed (hence the name invincible rhythm or Ajeya Chhandam in Sanskrit). The computer solves intractable pattern search (Clique) problem without searching, since the right pattern written in it spontaneously replies back to the questioner. To learn, the hardware filters any kind of sensory input image into several layers of images, each containing basic geometric polygons (fractal decomposition), and builds a network among all layers, multi-sensory images are connected in all possible ways to generate \u201cif\u201d and \u201cthen\u201d argument. Several such arguments and decisions (phase transition from \u201cif\u201d to \u201cthen\u201d) self-assemble and form the two giant columns of arguments and rules of phase transition. Any input question is converted into a pattern as noted above, and these two astronomically large columns project a solution. The driving principle of computing is synchronization and de-synchronization of network paths, the system drives towards highest density of coupled arguments for maximum matching. Memory is located at all layers of the hardware. Learning, computing occurs everywhere simultaneously. Since resonance chain connects all computing seeds, wireless processing is feasible without a screening effect. The computing power is increased by maximizing the density of resonance states and bandwidth of the resonance chain together. We discovered this remarkable computing while studying the human brain, so we present a new model of the human brain in terms of an experimentally determined resonance chain with bandwidth 10\u221215 Hz (complete brain with all sensors) to 10+15 Hz (DNA) along with its implementation using a pure organic synthesis of entire computer (brain jelly) in our lab, software prototype as proof of concept and finally a new fourth circuit element (Hinductor) based beyond Complementary metal-oxide semiconductor (CMOS) hardware is also presented.<\/jats:p>","DOI":"10.3390\/info5010028","type":"journal-article","created":{"date-parts":[[2014,1,28]],"date-time":"2014-01-28T03:27:01Z","timestamp":1390879621000},"page":"28-100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Design and Construction of a Brain-Like Computer:  A New Class of Frequency-Fractal Computing Using Wireless Communication in a Supramolecular Organic, Inorganic System"],"prefix":"10.3390","volume":"5","author":[{"given":"Subrata","family":"Ghosh","sequence":"first","affiliation":[{"name":"Advanced Nano Characterization Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan"}]},{"given":"Krishna","family":"Aswani","sequence":"additional","affiliation":[{"name":"Advanced Nano Characterization Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan"}]},{"given":"Surabhi","family":"Singh","sequence":"additional","affiliation":[{"name":"Advanced Nano Characterization Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan"}]},{"given":"Satyajit","family":"Sahu","sequence":"additional","affiliation":[{"name":"Advanced Nano Characterization Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan"}]},{"given":"Daisuke","family":"Fujita","sequence":"additional","affiliation":[{"name":"Advanced Nano Characterization Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan"}]},{"given":"Anirban","family":"Bandyopadhyay","sequence":"additional","affiliation":[{"name":"Advanced Nano Characterization Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2014,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1112\/plms\/s2-42.1.230","article-title":"On computable numbers, with an Application to the Entscheidungs problem","volume":"42","author":"Turing","year":"1937","journal-title":"Proc. Lond. Math. Soc. Ser. 2"},{"key":"ref_2","unstructured":"Martin, D., Sigal, R., and Weyuker, E.J. (1994). Computability, Complexity, and Languages and Logic: Fundamentals of Theoretical Computer Science, Academic Press, Harcourt, Brace & Company. [2nd ed.]."},{"key":"ref_3","unstructured":"Minsky, M. (1967). Computation: Finite and Infinite Machines, Prentice-Hall, Inc.. Chapter 8, Section 8.2 \u201cUnsolvability of the Halting Problem\u201d."},{"key":"ref_4","unstructured":"Hubert, D. (1972). What Computers Can\u2019t Do, MIT Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1162\/1064546054407185","article-title":"A topographical method for the development of neural networks for artificial brain evolution","volume":"11","author":"Jung","year":"2005","journal-title":"Artif. Life"},{"key":"ref_6","unstructured":"Kurzweil, R. (2005). The Singularity is Near, Viking Press."},{"key":"ref_7","unstructured":"A List of Some artificial brain building projects around the globe. Available online:\t\t  http:\/\/www.artificialbrains.com\/."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2983","DOI":"10.1103\/PhysRevLett.82.2983","article-title":"Oscillatory neurocomputers with dynamic connectivity","volume":"82","author":"Hoppensteadt","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","unstructured":"Holographic Neural Net Project. Available online:\t\t  http:\/\/www.andcorporation.com\/."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1126\/science.7973651","article-title":"Molecular computation of solutions to combinatorial problems","volume":"266","author":"Adleman","year":"1994","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1038\/337244a0","article-title":"Image processing using light-sensitive chemical waves","volume":"337","author":"Kuhnert","year":"1989","journal-title":"Nature"},{"key":"ref_12","unstructured":"Ellenbogen, J. A Brief Overview of Nanoelectronic Devices, 1998. Available online:\t\t  http:\/\/www2.mitre.org\/tech\/nanotech\/ourwork\/nano_papers.html#nanoelectronics."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Waldner, J.-B. (2007). Nanocomputers and Swarm Intelligence, ISTE.","DOI":"10.1002\/9780470610978"},{"key":"ref_14","unstructured":"Domino Computer from Wikipedia. Available online:\t\t  http:\/\/en.wikipedia.org\/wiki\/Domino_computer."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Drechsler, R., and Wille, R. (2012, January 23\u201325). Reversible Circuits: Recent Accomplishments and Future Challenges for an Emerging Technology. Proceedings of the International Symposium on VLSI Design, Automation and Test, Hsinchu, Taiwan.","DOI":"10.1007\/978-3-642-31494-0_53"},{"key":"ref_16","unstructured":"Czap, H., Unland, R., Brank, C., and Tianfield, H. (2005). Self-Organization and Autonomic Informatics (I), IOS press."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Quantum computing is getting matured as one does not require now to know solution beforehand (\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              Zhou\n\t\t\t\t\t\t\t              X.-Q.\n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              Kalasuwan\n\t\t\t\t\t\t\t              P.\n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              Ralph\n\t\t\t\t\t\t\t              T.C.\n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              O\u2019Brien\n\t\t\t\t\t\t\t              J.L.\n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t          Calculating unknown eigen values with a quantum algorithm\n\t\t\t\t\t\t\t          Nat. Photonics\n\t\t\t\t\t\t\t          2013\n\t\t\t\t\t\t\t          7\n\t\t\t\t\t\t\t          223\n\t\t\t\t\t\t\t          228\n\t\t\t\t\t\t\t          10.1038\/nphoton.2012.360\n\t\t\t\t\t\t\t        \n\t\t\t\t\t\t\t\t\t), still logical steps in the form of arguments need to be constructed.","DOI":"10.1038\/nphoton.2012.360"},{"key":"ref_18","unstructured":"Jeffress, L.A. (1951). Cerebral Mechanisms in Behavior\u2014The Hixon Symposium, Wiley."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1103\/RevModPhys.55.601","article-title":"Statistical mechanics of cellular automata","volume":"55","author":"Wolfram","year":"1983","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1126\/science.1091277","article-title":"Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication","volume":"304","author":"Jaeger","year":"2004","journal-title":"Science"},{"key":"ref_21","unstructured":"Home page of Reservoir Computing. Available online:\t\t  http:\/\/www.reservoir-computing.org\/."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e52946","DOI":"10.1371\/journal.pone.0052946","article-title":"Real-time parallel processing of grammatical structure in the fronto-striatal system: A recurrent network simulation study using reservoir computing","volume":"8","author":"Hinaut","year":"2013","journal-title":"PLoS One"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1038\/scientificamerican0499-98","article-title":"Alan Turing\u2019s forgotten ideas in computer science","volume":"280","author":"Copeland","year":"1999","journal-title":"Sci. Am."},{"key":"ref_24","unstructured":"Brun, T.A. Computers with Closed Timelike Curves Can Solve Hard Problems, 2008. Available online:\t\t  http:\/\/arxiv.org\/pdf\/gr-qc\/0209061v1.pdf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1103\/RevModPhys.21.447","article-title":"An example of a new type of cosmological solution of Einstein\u2019s field equations of gravitation","volume":"21","year":"1949","journal-title":"Rev. Mod. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.compedu.2010.03.009","article-title":"Learning computer programming: Implementing a fractal in a Turing Machine","volume":"55","author":"Zebende","year":"2010","journal-title":"Comput. Educ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1126\/science.1200970","article-title":"The world\u2019s technological capacity to store, communicate, and compute information","volume":"332","author":"Hilbert","year":"2011","journal-title":"Science"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1126\/science.268.5210.545","article-title":"Computation beyond the Turing limit","volume":"268","author":"Siegelmann","year":"1995","journal-title":"Science"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1145\/253769.253801","article-title":"Why interaction is more powerful than algorithms","volume":"40","author":"Wegner","year":"1997","journal-title":"Commun. ACM"},{"key":"ref_30","unstructured":"The Translation from the German Paper of G\u00f6del\n\t\t\t\t\t\t\t\t\t\tAvailable online:\n\t\t\t\t\t\t\t\t\t\t  http:\/\/www.research.ibm.com\/people\/h\/hirzel\/papers\/canon00-goedel.pdf\n\t\t\t\t\t\t\t\t\t\t(accessed on 15 January 2014)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tThe second order logic is relevant of this paper, we provide the Wiki link \n\t\t\t\t\t\t\t\t\t\tAvailable online:\n\t\t\t\t\t\t\t\t\t\t  http:\/\/en.wikipedia.org\/wiki\/Second-order_logic\n\t\t\t\t\t\t\t\t\t\t(accessed on 15 January 2014)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tAnd several classes of incompleteness theorem\n\t\t\t\t\t\t\t\t          Available online:\n\t\t\t\t\t\t\t\t\t\t  http:\/\/en.wikipedia.org\/wiki\/G%C3%B6del\u2019s_incompleteness_theorems\n\t\t\t\t\t\t\t\t\t\t  (accessed on 15 January 2014)"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1002\/adfm.200700937","article-title":"Fabrication of a memory chip by a complete self-assembly process using state-of-the-art Multilevel Cell (MLC) Technology","volume":"18","author":"Bandyopadhyay","year":"2008","journal-title":"Adv. Funct. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"10301","DOI":"10.1103\/PhysRevA.61.010301","article-title":"Quantum search without entanglement","volume":"61","author":"Lloyd","year":"1999","journal-title":"Phys. Rev. A."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2011","DOI":"10.1098\/rspa.2002.1097","article-title":"On the role of entanglement in quantum computational speed up","volume":"459","author":"Jozsa","year":"2003","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"243506","DOI":"10.1063\/1.2402895","article-title":"Writing and erasing information in multilevel logic systems of a single molecule using scanning tunneling microscope","volume":"89","author":"Bandyopadhyay","year":"2006","journal-title":"Appl. Phys. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"023512","DOI":"10.1063\/1.2430767","article-title":"Origin of negative differential resistance in molecular Junctions of Rose Bengal","volume":"90","author":"Bandyopadhyay","year":"2007","journal-title":"Appl. Phys. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3668","DOI":"10.1073\/pnas.0703105105","article-title":"A 16 bit parallel processing in a molecular assembly","volume":"105","author":"Bandyopadhyay","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1126\/science.1143254","article-title":"Wireless power transfer via strongly coupled magnetic resonances","volume":"317","author":"Kurs","year":"2007","journal-title":"Science"},{"key":"ref_38","unstructured":"Nakamura, S., Ajisaka, S., Koma, R., Hashimoto, H., and Lee, B.H. (2011, January 15\u201318). Electro-Magnetic Resonance Coupling Sensing for Secure, Comfortable and Energy-Saving Space. Proceedings of the 2011 8th Asian Control Conference (ASCC), Kaohsiung, Taiwan."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1137\/0150098","article-title":"Synchronization of pulse coupled biological oscillators","volume":"50","author":"Mirollo","year":"1990","journal-title":"SIAM J. Appl. Math."},{"key":"ref_40","unstructured":"Feige, U., Goldwasser, S., Lov\u00e1sz, L., Safra, S., and Szegedy, M. (1991, January 1\u20134). Approximating Clique is almost NP-Complete. Proceedings of the 32nd IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2198","DOI":"10.1039\/B913691F","article-title":"A new approach to extract multiple distinct conformers and co-existing distinct electronic properties of a single molecule by point-contact method","volume":"12","author":"Bandyopadhyay","year":"2010","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ghosh, S., Dutta, M., Sahu, S., Fujita, D., and Bandyopadhyay, A. (2013). Nano molecular-platform: A protocol to write energy transmission program inside a molecule for bio-inspired supramolecular engineering. Adv. Func. Mater.","DOI":"10.1002\/adfm.201302111"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Hohlfeld, R.G., and Cohen, N. (1999). Self-similarity and the geometric requirements for frequency independence in antenna. Fractals, 7.","DOI":"10.1142\/S0218348X99000098"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1162\/089976606775093882","article-title":"Polychronization: Computation with spikes","volume":"18","author":"Izhikevich","year":"2006","journal-title":"Neural Comput."},{"key":"ref_45","unstructured":"Vitiello, G. (2012). Quantum Interaction, Springer. Lecture Notes in Computer Science."},{"key":"ref_46","unstructured":"Lie Alzebra from Wikipedia. Available online:\t\t  http:\/\/en.wikipedia.org\/wiki\/Lie_algebra."},{"key":"ref_47","unstructured":"Carbone, L., Freyn, W., and Lee, K.-H. Dimensions of imaginary root spaces of hyperbolic Kac-Moody Algebras. Available online:\t\t  http:\/\/www.math.uconn.edu\/~khlee\/Papers\/ImagRootMult.pdf."},{"key":"ref_48","unstructured":"Anderson, C.C. Defining physics at imaginary time: Reflection positivity for certain Riemannian manifolds. Available online:\t\t  http:\/\/www.math.harvard.edu\/theses\/senior\/anderson\/anderson.pdf."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1109\/72.761708","article-title":"Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory","volume":"10","author":"Izhikevich","year":"1999","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1142\/S0218348X05002799","article-title":"A fractal valued random iteration algorithm and fractal hierarchy","volume":"13","author":"Barnsley","year":"2005","journal-title":"Fractals"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Oraizi, H., and Hedayati, S. (2011, January 12\u201316). Combined Fractal Geometries for the Design of Wideband Microstrip Antennas with Circular Polarization. Proceedings of Progress In Electromagnetics Research Symposium (PIERS), Suzhou, China.","DOI":"10.1109\/MMW.2010.5605210"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1016\/j.aim.2008.04.011","article-title":"V-variable fractals: Fractals with partial self similarity","volume":"218","author":"Barnsley","year":"2008","journal-title":"Adv. Math."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1126\/science.1193125","article-title":"Greater neural pattern similarity across repetitions is associated with better memory","volume":"330","author":"Xue","year":"2010","journal-title":"Science"},{"key":"ref_54","unstructured":"World of Fractal. Available online:\t\t  http:\/\/www.math.nus.edu.sg\/aslaksen\/gem-projects\/maa\/World_of_Fractal.pdf."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1038\/81460","article-title":"Neurocomputational models of working memory","volume":"3","author":"Durstewitz","year":"2000","journal-title":"Nat. Neurosci."},{"key":"ref_56","first-page":"347","article-title":"Fractint formula for overlaying fractals","volume":"3","author":"Pandey","year":"2012","journal-title":"J. Inf. Syst. Commun."},{"key":"ref_57","first-page":"423","article-title":"Undecidable problems in Fractal geometry","volume":"7","author":"Dubey","year":"1993","journal-title":"Complex Syst."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1098\/rspa.1985.0070","article-title":"Quantum theory, the Church-Turing principle and the universal quantum computer","volume":"400","author":"Deutsch","year":"1985","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_59","unstructured":"MIT Physics Demo\u2014Tuning Forks: Resonance & Beat Frequency. Available online:\t\t  http:\/\/video.mit.edu\/watch\/tuning-forks-resonance-a-beat-frequency-11447\/."},{"key":"ref_60","unstructured":"Beats. Available online:http:\/\/www-math.mit.edu\/daimp\/Beats.html."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1126\/science.1225266","article-title":"A large scale model of the functioning brain","volume":"338","author":"Eliasmith","year":"2012","journal-title":"Science"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2193","DOI":"10.1137\/S0036139997330623","article-title":"Weakly connected quasiperiodic oscillators, FM interactions, and multiplexing in the brain","volume":"59","author":"Izhikevich","year":"1999","journal-title":"SIAM J. Appl. Math."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"018102","DOI":"10.1103\/PhysRevLett.94.018102","article-title":"Scale free brain functional networks","volume":"94","author":"Eguiluz","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_64","unstructured":"Cohen, N. Fractals new era in millitary antenna design. Available online:\t\t  http:\/\/rfdesign.com\/mag\/508RFDSF1.pdf."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1029\/96RS02126","article-title":"Frequency-independent features of self-similar fractal antennas","volume":"31","author":"Werner","year":"1996","journal-title":"Radio Sci."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.biosystems.2004.05.032","article-title":"Bio-steps beyond Turing","volume":"77","author":"Caludea","year":"2004","journal-title":"BioSystems"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1126\/science.1167782","article-title":"Explosive percolation in random networks","volume":"323","author":"Achlioptas","year":"2009","journal-title":"Science"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1142\/S0218127492000446","article-title":"Riddled basins","volume":"2","author":"Alexander","year":"1992","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/0167-2789(94)90047-7","article-title":"The transition to chaotic attractors with riddled basins","volume":"76","author":"Ott","year":"1994","journal-title":"Physica D"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/S0166-2236(03)00034-1","article-title":"Bursts as a unit of neural information: Selective communication via resonance","volume":"26","author":"Izhikevich","year":"2003","journal-title":"Trends Neurosci."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S0303-2647(02)00067-9","article-title":"Resonance and selective communication via bursts in neurons having subthreshold oscillations","volume":"67","author":"Izhikevich","year":"2002","journal-title":"BioSystems"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/S0893-6080(01)00078-8","article-title":"Resonate-and-fire neurons","volume":"14","author":"Izhikevich","year":"2001","journal-title":"Neural Netw."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"123701","DOI":"10.1063\/1.4793995","article-title":"Multi-level memory-switching properties of a single brain microtubule","volume":"102","author":"Sahu","year":"2013","journal-title":"Appl. Phys. Lett."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.bios.2013.02.050","article-title":"Atomic water channel controlling remarkable properties of a single brain microtubule: Correlating single protein to its supramolecular assembly","volume":"47","author":"Sahu","year":"2013","journal-title":"Biosens. Bioelectron."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1038\/nature11129","article-title":"Neural population dynamics during reaching","volume":"487","author":"Churchland","year":"2012","journal-title":"Nature"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"50","DOI":"10.4018\/jnmc.2009010104","article-title":"Architecture of a massive parallel processing nano brain operating 100 billion molecular neurons simultaneously","volume":"1","author":"Bandyopadhyay","year":"2009","journal-title":"Int. J. Nanotech. Mol. Comp."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"113702","DOI":"10.1063\/1.3227887","article-title":"Smallest artificial molecular neural-net for collective and emergent information processing","volume":"95","author":"Bandyopadhyay","year":"2009","journal-title":"Appl. Phys. Lett."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1038\/nphys1636","article-title":"Massively parallel computing on an organic molecular layer","volume":"6","author":"Bandyopadhyay","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1038\/nphys1663","article-title":"Molecular computing: Aromatic arithmetic","volume":"6","author":"Adamatzky","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1038\/nn826","article-title":"The information efficacy of a synapse","volume":"5","author":"London","year":"2002","journal-title":"Nat. Neurosci."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/S0166-2236(96)10038-2","article-title":"Long-range interactions in visual perception","volume":"19","author":"Spillmann","year":"1996","journal-title":"Trends Neurosci."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1097\/00000542-200611000-00013","article-title":"Non-linear changes in brain dynamics during emergence from sevoflurane anesthesia","volume":"105","author":"Walling","year":"2006","journal-title":"Anesthesiology"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1143\/PTPS.173.99","article-title":"A mathematical model for the hippocampus: Towards the understanding of episodic memory and imagination","volume":"173","author":"Tsuda","year":"2008","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"e1002918","DOI":"10.1371\/journal.pcbi.1002918","article-title":"Evidence for model-based computations in the human amygdala during pavlovian conditioning","volume":"9","author":"McNamee","year":"2013","journal-title":"PLoS Comput. Biol."},{"key":"ref_85","unstructured":"Tian, X., and Xiao, Z.G. (2005, January 13\u201315). Functional Model of Brainstem-Cortex-Thalamus Circuit. Proceedings of the 2005 Neural International Conference on Networks and Brain, ICNN&B \u201905, Beijing, China."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10015-007-0472-6","article-title":"A mathematical model of planning in the prefrontal cortex","volume":"12","author":"Oku","year":"2008","journal-title":"Artif. Life Robot."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1093\/brain\/awh729","article-title":"Cognition, emotion and the cerebellum","volume":"129","author":"Schmahmann","year":"2006","journal-title":"Brain"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/S0959-4388(97)80006-2","article-title":"Network models of the basal ganglia","volume":"7","author":"Beiser","year":"1997","journal-title":"Curr. Opin. Neurobiol."},{"key":"ref_89","unstructured":"Ritch, S. Mathematical Model of Basal Ganglia and Oscillatory Neuron Clusters in Relation to Parkingsonian Tremors. Available online:\t\t  http:\/\/www.math.duke.edu\/mathbio\/documents\/reu-posters\/rich_poster.pdf."},{"key":"ref_90","unstructured":"Nugent, A. (2009). Fractal Memory and Computational Methods and Systems Based on Nanotechnology. (7502769 B2), U.S. Patent."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1002\/chem.200701080","article-title":"Supramolecular helical columns from the self-assembly of chiral rods","volume":"14","author":"Ryu","year":"2008","journal-title":"Chemistry"},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Friston, K. (2010). The free energy principle: A unified brain theory?. Nat. Rev. Neurosci., 11.","DOI":"10.1038\/nrn2787"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1137\/070704873","article-title":"Bifurcations from synchrony in a homogeneous networks","volume":"8","author":"Golubitsky","year":"2009","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1007\/978-3-642-15979-4_73","article-title":"Molecular Implementations of Cellular Automata","volume":"Volume 6350","author":"Sahu","year":"2010","journal-title":"Cellular Automata"},{"key":"ref_95","unstructured":"Sahu, S., Bandyopadhyay, A., and Fujita, D. (2009, January 7\u20139). Remarkable Potential of Pattern Based Computing on an Organic Molecular Layer Using the Concept of Cellular Automata. Proceedings of International Symposium on Intelligent Signal Processing and Communication Systems, 2009, ISPACS 2009, Kanazawa, Japan."},{"key":"ref_96","unstructured":"Bandyopadhyay, A., Bhartiya, R., Sahu, S., and Fujita, D. (2010). Natural Computing, Springer."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s11047-012-9314-0","article-title":"On Cellular Automata rules of molecular arrays","volume":"11","author":"Sahu","year":"2012","journal-title":"Nat. Comput."},{"key":"ref_98","doi-asserted-by":"crossref","unstructured":"Anderson, J.A. (2005, January 8\u201310). A Brain-like Computer for Cognitive Software Applications: The Ersatz Brain Project. Proceedings of the 4th IEEE International Conference on Cognitive Informatics, ICCI 2005, Irvine, CA, USA.","DOI":"10.1109\/COGINF.2005.1532612"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"e1000211","DOI":"10.1371\/journal.pcbi.1000211","article-title":"Hierarchical models in the brain","volume":"4","author":"Friston","year":"2008","journal-title":"PLoS Comput. Biol."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0303-2647(98)00053-7","article-title":"Thalamo-cortical interactions modeled by weakly connected oscillators: Could brain use FM radio principles?","volume":"48","author":"Hoppensteadt","year":"1998","journal-title":"BioSystems"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0031-3203(99)00041-2","article-title":"Comparison of algorithms that select features for pattern classifiers","volume":"33","author":"Kudo","year":"2000","journal-title":"Pattern Recognit."},{"key":"ref_102","unstructured":"Sternberg, R.J. (2006). Cognitive Psychology, Thomson Wadsworth. [4th ed.]."},{"key":"ref_103","unstructured":"Eyseneck, M.W., and Keane, M.T. (2010). Cognitive Psychology: A Students Handbook, Psychology Press. [6th ed.]."},{"key":"ref_104","unstructured":"Hung, N.V. (2007). Polygon Fractal. [Ph.D. Thesis, Ernst-Moritz-Arndt-Universit\u00e4t]."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1016\/j.patcog.2007.08.018","article-title":"Binarization and cleanup of handwritten text from carbon copy medical form images","volume":"41","author":"Milewski","year":"2008","journal-title":"Pattern Recognit."},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Wolpert, D.H. (2001). The Supervised Learning No Free Lunch Theorems, NASA Ames Research Center. Available online:\t\t  http:\/\/www.no-free-lunch.org\/Wolp01a.pdf.","DOI":"10.1007\/978-1-4471-0123-9_3"},{"key":"ref_107","unstructured":"Andrew, N., and Dean, J. Building high-level features using large scale unsupervised learning, 2012. Available online:\t\t  http:\/\/arxiv.org\/pdf\/1112.6209.pdf."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"2497","DOI":"10.1162\/08997660260293319","article-title":"Many-layered learning","volume":"14","author":"Utgoff","year":"2002","journal-title":"Neural Comput."},{"key":"ref_109","first-page":"194","article-title":"Information Processing in Dynamical Systems: Foundations of Harmony Theory","volume":"Volume 1","author":"Rumelhart","year":"1986","journal-title":"Parallel Distributed Processing: Explorations in the Microstructure of Cognition"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1109\/TCT.1971.1083337","article-title":"Memristor\u2014The missing circuit element","volume":"18","author":"Chua","year":"1971","journal-title":"IEEE Trans. Circuits Theory"},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"Di Ventra, M., Pershin, Y.V., and Chua, L. (2009). Circuit elements with memory: Memristors, memcapacitors and meminductors. IEEE Proc., 97.","DOI":"10.1109\/JPROC.2009.2021077"},{"key":"ref_112","unstructured":"Sahu, S., Fujita, D., and Bandyopadhyay, A. (2010). An inductor made of arrayed capacitors. (JP-096217), (world patent filed)."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/TNN.2004.832808","article-title":"Synchronization of non-linear electronic oscillators for neural computation","volume":"15","author":"Cosp","year":"2004","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_114","unstructured":"Bandyopadhyay, A., and Miki, K. (2013). A vertical parallel processor. (JP-5187804)."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/5\/1\/28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:07:47Z","timestamp":1760216867000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/5\/1\/28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,27]]},"references-count":114,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,3]]}},"alternative-id":["info5010028"],"URL":"https:\/\/doi.org\/10.3390\/info5010028","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,27]]}}}