\begin{thebibliography}{100} \bibitem{perera_sensing_2013} Charith Perera, Arkady Zaslavsky, Peter Christen, and Dimitrios Georgakopoulos. \newblock Sensing as a {Service} {Model} for {Smart} {Cities} {Supported} by {Internet} of {Things}. \newblock {\em arXiv:1307.8198 [cs]}, July 2013. \newblock arXiv: 1307.8198. \bibitem{strukov_missing_2008} Dmitri~B. Strukov, Gregory~S. Snider, Duncan~R. Stewart, and R.~Stanley Williams. \newblock The missing memristor found. \newblock {\em Nature}, 453(7191):80--83, May 2008. \bibitem{Di-Ventra} Massimiliano~Di Ventra and Yuriy~V. Pershin. \newblock Memcomputing: a computing paradigm to store and process information on the same physical platform. \newblock {\em CoRR}, abs/1211.4487, 2012. \bibitem{indiveri_memory_2015} Giacomo Indiveri and Shih-Chii Liu. \newblock Memory and information processing in neuromorphic systems. \newblock {\em Proceedings of the IEEE}, 103(8):1379--1397, August 2015. \newblock arXiv: 1506.03264. \bibitem{indiveri_neuromorphic_2011} Giacomo Indiveri, Bernabé Linares-Barranco, Tara~Julia Hamilton, André van Schaik, Ralph Etienne-Cummings, Tobi Delbruck, Shih-Chii Liu, Piotr Dudek, Philipp Häfliger, Sylvie Renaud, Johannes Schemmel, Gert Cauwenberghs, John Arthur, Kai Hynna, Fopefolu Folowosele, Sylvain Saighi, Teresa Serrano-Gotarredona, Jayawan Wijekoon, Yingxue Wang, and Kwabena Boahen. \newblock Neuromorphic {Silicon} {Neuron} {Circuits}. \newblock {\em Frontiers in Neuroscience}, 5, May 2011. \bibitem{chua_memristor-missing_1971} L.~Chua. \newblock Memristor-{The} missing circuit element. \newblock {\em IEEE Transactions on Circuit Theory}, 18(5):507--519, September 1971. \bibitem{jo_nanoscale_2010} Sung~Hyun Jo, Ting Chang, Idongesit Ebong, Bhavitavya~B. Bhadviya, Pinaki Mazumder, and Wei Lu. \newblock Nanoscale {Memristor} {Device} as {Synapse} in {Neuromorphic} {Systems}. \newblock {\em Nano Letters}, 10(4):1297--1301, April 2010. \bibitem{Ho:2009} Yenpo Ho, Garng~M. Huang, and Peng Li. \newblock Nonvolatile memristor memory: device characteristics and design implications. \newblock pages 485--490, 2009. \bibitem{Borghetti} Julien Borghetti, Zhiyong Li, Joseph Straznicky, Xuema Li, Douglas A.~A. Ohlberg, Wei Wu, Duncan~R. Stewart, and R.~Stanley Williams. \newblock A hybrid nanomemristor/transistor logic circuit capable of self-programming. \newblock {\em Proceedings of the National Academy of Sciences}, 106(6):1699--1703, 2009. \bibitem{Hamdioui-mem2} G.~Ch Sirakoulis and S.~Hamdioui. \newblock Editorial note on memristor models, circuits and architectures. \newblock {\em International Journal of Unconventional Computing}, 12:247--250, December 2016. \bibitem{rose10} Garrett~S. Rose. \newblock Overview: Memristive devices, circuits and systems. \newblock In {\em ISCAS}, pages 1955--1958. IEEE, 2010. \bibitem{imp-nature} Julien Borghetti, Gregory~S. Snider, Philip~J. Kuekes, Joshua~J. Yang, Duncan~R. Stewart, and R.~Stanley Williams. \newblock {'Memristive' switches enable 'stateful' logic operations via material implication}. \newblock {\em Nature}, 464(7290):873--876, April 2010. \bibitem{shahsavari_unconventional_2015} Mahyar Shahsavari, M.~Faisal~Nadeem, S.~Arash~Ostadzadeh, Philippe Devienne, and Pierre Boulet. \newblock Unconventional digital computing approach: memristive nanodevice platform. \newblock {\em physica status solidi (c)}, 12(1-2):222--228, January 2015. \bibitem{Leveraging} Garrett~S. Rose, Jeyavijayan Rajendran, Harika Manem, Ramesh Karri, and Robinson~E. Pino. \newblock Leveraging memristive systems in the construction of digital logic circuits. \newblock {\em Proceedings of the IEEE}, 100(6):2033--2049, 2012. \bibitem{LehtonenPL12} E.~Lehtonen, J.~Poikonen, and M.~Laiho. \newblock Implication logic synthesis methods for memristors. \newblock pages 2441--2444, May 2012. \bibitem{Crossbar-mem} I.~Vourkas and G.C. Sirakoulis. \newblock A novel design and modeling paradigm for memristor-based crossbar circuits. \newblock {\em Nanotechnology, IEEE Transactions on}, 11(6):1151--1159, 2012. \bibitem{crossbar} Philip~J. Kuekes, Duncan~R. Stewart, and Stanley~R. Williams. \newblock {The crossbar latch: Logic value storage, restoration, and inversion in crossbar circuits}. \newblock {\em Journal of Applied Physics}, 97(3), 2005. \bibitem{merolla_million_2014} Paul~A. Merolla, John~V. Arthur, Rodrigo Alvarez-Icaza, Andrew~S. Cassidy, Jun Sawada, Filipp Akopyan, Bryan~L. Jackson, Nabil Imam, Chen Guo, Yutaka Nakamura, Bernard Brezzo, Ivan Vo, Steven~K. Esser, Rathinakumar Appuswamy, Brian Taba, Arnon Amir, Myron~D. Flickner, William~P. Risk, Rajit Manohar, and Dharmendra~S. Modha. \newblock A million spiking-neuron integrated circuit with a scalable communication network and interface. \newblock {\em Science}, 345(6197):668--673, August 2014. \bibitem{rajendran_neuromorphic_2016} B.~Rajendran and F.~Alibart. \newblock Neuromorphic {Computing} {Based} on {Emerging} {Memory} {Technologies}. \newblock {\em IEEE Journal on Emerging and Selected Topics in Circuits and Systems}, 6(2):198--211, June 2016. \bibitem{lecun_gradient-based_1998} Y.~LeCun, L.~Bottou, Y.~Bengio, and P.~Haffner. \newblock Gradient-based learning applied to document recognition. \newblock {\em Proceedings of the IEEE}, 86(11):2278--2323, 1998. \bibitem{hinton_fast_2006} Geoffrey~E. Hinton, Simon Osindero, and Yee-Whye Teh. \newblock A {Fast} {Learning} {Algorithm} for {Deep} {Belief} {Nets}. \newblock {\em Neural Comput.}, 18(7):1527--1554, July 2006. \bibitem{kempter_hebbian_1999} Richard Kempter, Wulfram Gerstner, and J.~Leo van Hemmen. \newblock Hebbian learning and spiking neurons. \newblock {\em Physical Review E}, 59(4):4498--4514, April 1999. \bibitem{song_competitive_2000} S.~Song, K.~D. Miller, and L.~F. Abbott. \newblock Competitive {Hebbian} learning through spike-timing-dependent synaptic plasticity. \newblock {\em Nature Neuroscience}, 3(9):919--926, September 2000. \bibitem{jin_fast_2002} Dezhe~Z. Jin and H.~Sebastian Seung. \newblock Fast computation with spikes in a recurrent neural network. \newblock {\em Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics}, 65(5 Pt 1):051922, May 2002. \bibitem{oster_winner-take-all_2004} M.~Oster and Shih-Chii Liu. \newblock A winner-take-all spiking network with spiking inputs. \newblock In {\em Proceedings of the 2004 11th {IEEE} {International} {Conference} on {Electronics}, {Circuits} and {Systems}, 2004. {ICECS} 2004}, pages 203--206, December 2004. \bibitem{lecun_convolutional_1995} Yann LeCun and Yoshua Bengio. \newblock Convolutional networks for images, speech, and time series. \newblock {\em The handbook of brain theory and neural networks}, 3361(10):1995, 1995. \bibitem{bichler_extraction_2012} Olivier Bichler, Damien Querlioz, Simon~J. Thorpe, Jean-Philippe Bourgoin, and Christian Gamrat. \newblock Extraction of temporally correlated features from dynamic vision sensors with spike-timing-dependent plasticity. \newblock {\em Neural Networks}, 32:339--348, August 2012. \bibitem{shahsavari_combining_2016} Mahyar Shahsavari, Pierre Falez, and Pierre Boulet. \newblock Combining a {Volatile} and {Nonvolatile} {Memristor} in {Artificial} {Synapse} to {Improve} {Learning} in {Spiking} {Neural} {Networks}. \newblock In {\em 12th {ACM}/{IEEE} {International} {Symposium} on {Nanoscale} {Architectures} ({Nanoarch} 2016)}, Beijing, China, July 2016. \bibitem{furber_spinnaker_2014} S.~B. Furber, F.~Galluppi, S.~Temple, and L.~A. Plana. \newblock The {SpiNNaker} {Project}. \newblock {\em Proceedings of the IEEE}, 102(5):652--665, May 2014. \bibitem{benjamin_neurogrid:_2014} B.~V. Benjamin, P.~Gao, E.~McQuinn, S.~Choudhary, A.~R. Chandrasekaran, J.~M. Bussat, R.~Alvarez-Icaza, J.~V. Arthur, P.~A. Merolla, and K.~Boahen. \newblock Neurogrid: {A} {Mixed}-{Analog}-{Digital} {Multichip} {System} for {Large}-{Scale} {Neural} {Simulations}. \newblock {\em Proceedings of the IEEE}, 102(5):699--716, May 2014. \bibitem{schemmel_wafer-scale_2010} Johannes Schemmel, Daniel Briiderle, Andreas Griibl, Matthias Hock, Karlheinz Meier, and Sebastian Millner. \newblock A wafer-scale neuromorphic hardware system for large-scale neural modeling. \newblock pages 1947--1950. IEEE, May 2010. \bibitem{bichler_design_2013} O.~Bichler, D.~Roclin, C.~Gamrat, and D.~Querlioz. \newblock Design exploration methodology for memristor-based spiking neuromorphic architectures with the {Xnet} event-driven simulator. \newblock In {\em 2013 {IEEE}/{ACM} {International} {Symposium} on {Nanoscale} {Architectures} ({NANOARCH})}, pages 7--12, July 2013. \bibitem{hinton_training_2002} Geoffrey~E. Hinton. \newblock Training {Products} of {Experts} by {Minimizing} {Contrastive} {Divergence}. \newblock {\em Neural Computation}, 14(8):1771--1800, August 2002. \bibitem{gerstner2014neuronal} Wulfram Gerstner, Werner~M Kistler, Richard Naud, and Liam Paninski. \newblock {\em Neuronal dynamics: From single neurons to networks and models of cognition}. \newblock Cambridge University Press, 2014. \bibitem{LiH10} Hai (Helen)~Li and Miao Hu. \newblock Compact model of memristors and its application in computing systems. \newblock pages 673--678, March 2010. \bibitem{ferro} Andr\'{e} Chanthbouala, Vincent Garcia, Ryan~O. Cherifi, Karim Bouzehouane, St\'{e}phane Fusil, Xavier Moya, St\'{e}phane Xavier, Hiroyuki Yamada, Cyrile Deranlot, Neil~D. Mathur, Manuel Bibes, Agn\`{e}s Barth\'{e}l\'{e}my, and Julie Grollier. \newblock {A ferroelectric memristor}, June 2012. \bibitem{Berzina-poly} T.~Berzina, S.~Erokhina, P.~Camorani, O.~Konovalov, V.~Erokhin, and M.P. Fontana. \newblock Electrochemical control of the conductivity in an organic memristor: A time-resolved x-ray fluorescence study of ionic drift as a function of the applied voltage. \newblock {\em ACS Applied Materials and Interfaces}, 1(10):2115--2118, 2009. \bibitem{spin1} Yurij~V. Pershin and Massimiliano~D. Ventra. \newblock {Spin Memristive systems}. \newblock {\em Physical Review B.}, 78:113309, 2008. \bibitem{alibart_organic_2010} Fabien Alibart, Stéphane Pleutin, David Guérin, Christophe Novembre, Stéphane Lenfant, Kamal Lmimouni, Christian Gamrat, and Dominique Vuillaume. \newblock An {Organic} {Nanoparticle} {Transistor} {Behaving} as a {Biological} {Spiking} {Synapse}. \newblock {\em Advanced Functional Materials}, 20(2):330--337, January 2010. \bibitem{Biolek2009} Z.~Biolek, D.~Biolek, and V.~Biolková. \newblock Spice model of memristor with nonlinear dopant drift. \newblock {\em Radioengineering}, 18(2):210--214, 2009. \bibitem{Wei-syn-mem} Sung~H. Jo, Ting Chang, Idongesit Ebong, Bhavitavya~B. Bhadviya, Pinaki Mazumder, and Wei Lu. \newblock {Nanoscale Memristor Device as Synapse in Neuromorphic Systems}. \newblock {\em Nano Lett.}, 10(4):1297--1301, March 2010. \bibitem{Yan2011240} H.~Yan, H.S. Choe, S.~Nam, Y.~Hu, S.~Das, J.F. Klemic, J.C. Ellenbogen, and C.M. Lieber. \newblock Programmable nanowire circuits for nanoprocessors. \newblock {\em Nature}, 470(7333):240--244, 2011. \bibitem{indiveri_integration_2013-1} Giacomo Indiveri, Bernabe Linares-Barranco, Robert Legenstein, George Deligeorgis, and Themistoklis Prodromakis. \newblock Integration of nanoscale memristor synapses in neuromorphic computing architectures. \newblock {\em Nanotechnology}, 24(38):384010, September 2013. \newblock arXiv: 1302.7007. \bibitem{Williams-missingmem} R.~Williams. \newblock How we found the missing memristor. \newblock {\em IEEE Spectr.}, 45(12):28--35, December 2008. \bibitem{chua-76} L.O. Chua and Sung~Mo Kang. \newblock Memristive devices and systems. \newblock {\em Proceedings of the IEEE}, 64(2):209--223, Feb. 1976. \bibitem{Gee-Kim} Wan Gee~Kim, Min Gyu~Sung, Sook Joo~Kim, Jong Hee~Yoo, Te~One~Youn, Jang Won~Oh, Jung Nam~Kim, Byung Gu~Gyun, Taeh Wan~Kim, Chi Ho~Kim, Jun Young~Byun, Won Kim, Moon Sig~Joo, Jae Sung~Roh, and Sung Ki~Park. \newblock Dependence of the switching characteristics of resistance random access memory on the type of transition metal oxide; tio2, zro2, and hfo2. \newblock {\em Journal of The Electrochemical Society}, 158(4):H417--H422, 2011. \bibitem{waser_redox-based_2009} Rainer Waser, Regina Dittmann, Georgi Staikov, and Kristof Szot. \newblock Redox-{Based} {Resistive} {Switching} {Memories}-{Nanoionic} {Mechanisms}, {Prospects}, and {Challenges}. \newblock {\em Advanced Materials}, 21(25-26):2632--2663, July 2009. \bibitem{HP-speed} A.C. Torrezan, J.P. Strachan, G.~Medeiros-Ribeiro, and R.S. Williams. \newblock Sub-nanosecond switching of a tantalum oxide memristor. \newblock {\em Nanotechnology}, 22(48):485203, 2011. \bibitem{si-mem} S.H. Jo, K.-H. Kim, T.~Chang, S.~Gaba, and W.~Lu. \newblock Si memristive devices applied to memory and neuromorphic circuits. \newblock pages 13--16, 2010. \bibitem{Wang2009Spintronic} Xiaobin Wang, Yiran Chen, Haiwen Xi, Hai Li, and D.~Dimitrov. \newblock {Spintronic Memristor Through Spin-Torque-Induced Magnetization Motion}. \newblock {\em Electron Device Letters, IEEE}, 30(3):294--297, March 2009. \bibitem{spin2} Xiaobin Wang and Yiran Chen. \newblock Spintronic memristor devices and application. \newblock In {\em Proceedings of the Conference on Design, Automation and Test in Europe}, DATE '10, pages 667--672, 3001 Leuven, Belgium, Belgium, 2010. European Design and Automation Association. \bibitem{poly2005} Victor Erokhin, Tatiana Berzina, and Marco~P. Fontana. \newblock Hybrid electronic device based on polyaniline-polyethyleneoxide junction. \newblock {\em Journal of Applied Physics}, 97(6):064501, 2005. \bibitem{organic2} F.~{Pincella}, P.~{Camorani}, and V.~{Erokhin}. \newblock {Electrical properties of an organic memristive system}. \newblock {\em Applied Physics A: Materials Science \& Processing}, 104:1039--1046, September 2011. \bibitem{Organic3} Victor Erokhin and Marco~P. Fontana. \newblock Organic memristive device and its application for the information processing. \newblock In {\em ICECS}, pages 926--929. IEEE, 2010. \bibitem{wang_next_2014} L.~Wang and S.~Gai. \newblock The next generation mass storage devices - {Physical} principles and current status. \newblock {\em Contemporary Physics}, 55(2):75--93, April 2014. \bibitem{Ferro2} Y.~Kaneko, H.~Tanaka, M.~Ueda, Y.~Kato, and E.~Fujii. \newblock A novel ferroelectric memristor enabling nand-type analog memory characteristics. \newblock In {\em Device Research Conference (DRC), 2010}, pages 257 --258, june 2010. \bibitem{ferro3} S.-M. Yoon, S.~Yang, S.-W. Jung, C.-W. Byun, M.-K. Ryu, W.-S. Cheong, B.H. Kim, H.C. Oh, S.-H.K. Park, C.-S. Hwang, S.-Y. Kang, H.-J. Ryu, and B.-G. Yu. \newblock Polymeric ferroelectric and oxide semiconductor-based fully transparent memristor cell. \newblock {\em Applied Physics A: Materials Science and Processing}, 102(4):983--990, 2011. \bibitem{wang_overview_2015} Lei Wang, CiHui Yang, Jing Wen, Shan Gai, and YuanXiu Peng. \newblock Overview of emerging memristor families from resistive memristor to spintronic memristor. \newblock {\em Journal of Materials Science: Materials in Electronics}, 26(7):4618--4628, March 2015. \bibitem{hu_multilayer_2015} Xiaofang Hu, Gang Feng, Shukai Duan, and Lu~Liu. \newblock Multilayer {RTD}-memristor-based cellular neural networks for color image processing. \newblock {\em Neurocomputing}, 162:150--162, August 2015. \bibitem{Hamdioui1_mem} S.~Hamdioui, L.~Xie, H.A.~Du Nguyen, M.~Taouil, and K.L.M. Bertels. \newblock Memristor based computation-in-memory architecture for data-intensive applications. \newblock In {\em Proc. 18th Design, Automation \& Test in Europe conference}, Grenoble, France, March 2015. \bibitem{RRAM} Cong Xu, Xiangyu Dong, Norman~P. Jouppi, and Yuan Xie. \newblock Design implications of memristor-based rram cross-point structures. \newblock In {\em DATE}, pages 734--739. IEEE, 2011. \bibitem{driscoll_phase-transition_2009} T.~Driscoll, H.-T. Kim, B.-G. Chae, M.~Di Ventra, and D.~N. Basov. \newblock Phase-transition driven memristive system. \newblock {\em Applied Physics Letters}, 95(4):043503, July 2009. \bibitem{liu_controllable_2010} Qi~Liu, Shibing Long, Hangbing Lv, Wei Wang, Jiebin Niu, Zongliang Huo, Junning Chen, and Ming Liu. \newblock Controllable {Growth} of {Nanoscale} {Conductive} {Filaments} in {Solid}-{Electrolyte}-{Based} {ReRAM} by {Using} a {Metal} {Nanocrystal} {Covered} {Bottom} {Electrode}. \newblock {\em ACS Nano}, 4(10):6162--6168, October 2010. \bibitem{MRAM} Hai Li and Yiran Chen. \newblock An overview of non-volatile memory technology and the implication for tools and architectures. \newblock In {\em DATE}, pages 731--736, 2009. \bibitem{Logic-Wiliams} Qiangfei Xia, Warren Robinett, Micheal~W. Cumbie, Neel Banarjee, Thomas~J. Cardinali, Joshua~J. Yang, Wei Wu, Xuema Li, William~M. Tong, Dmitri~B. Strukov, Gregosry~S. Snider, Gilberto Medeiros=Ribeiro, and R.~Stanley Williams. \newblock {Memristor-CMOS Hybrid Integrated circuits for reconfigurable logic}. \newblock {\em Nanoletters}, 2009. \bibitem{FPGA} Jason Cong and Bingjun Xiao. \newblock mrfpga: A novel fpga architecture with memristor-based reconfiguration. \newblock In {\em Proceedings of the 2011 IEEE/ACM International Symposium on Nanoscale Architectures}, NANOARCH '11, pages 1--8, Washington, DC, USA, 2011. IEEE Computer Society. \bibitem{analog1} Yogesh~N. Joglekar and Stephen~J. Wolf. \newblock {The elusive memristor: properties of basic electrical circuits}. \bibitem{Amplifier} T.A. Wey and W.D. Jemison. \newblock Variable gain amplifier circuit using titanium dioxide memristors. \newblock {\em IET Circuits, Devices and Systems}, 5(1):59--65, 2011. \bibitem{Oscillator} M.~Itoh and L.O. Chua. \newblock Memristor oscillators. \newblock {\em International Journal of Bifurcation and Chaos}, 18(11):3183--3206, 2008. \bibitem{analogICs} S.~Shin, K.~Kim, and S.-M. Kang. \newblock Memristor applications for programmable analog ics. \newblock {\em IEEE Transactions on Nanotechnology}, 10(2):266--274, 2011. \bibitem{chaotic} B.~Muthuswamy. \newblock Implementing memristor based chaotic circuits. \newblock {\em International Journal of Bifurcation and Chaos}, 20(5):1335--1350, 2010. \bibitem{Afifi-stdp} A.~Afifi, A.~Ayatollahi, and F.~Raissi. \newblock Implementation of biologically plausible spiking neural network models on the memristor crossbar-based cmos/nano circuits. \newblock pages 563--566, 2009. \bibitem{Image} X.~Hu, S.~Duan, L.~Wang, and X.~Liao. \newblock Memristive crossbar array with applications in image processing. \newblock {\em Science China Information Sciences}, 55(2):461--472, 2012. \bibitem{Quantum} Y.V. Pershin and M.~Di~Ventra. \newblock Neuromorphic, digital, and quantum computation with memory circuit elements. \newblock {\em Proceedings of the IEEE}, 100(6):2071 --2080, june 2012. \bibitem{Arith} Farnood Merrikh-Bayat and Saeed~Bagheri Shouraki. \newblock Memristor-based circuits for performing basic arithmetic operations. \newblock {\em Procedia CS}, 3:128--132, 2011. \bibitem{Fuzzy} F.~Merrikh-Bayat and S.~Bagheri~Shouraki. \newblock Memristive neuro-fuzzy system. \newblock {\em IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics}, 2012. \bibitem{principa_1927} Alfred~North Whitehead and Bertrand Russell. \newblock {\em Principia Mathematica}. \newblock 1927. \newblock 2nd Edition). \bibitem{RajaM10} Tezaswi Raja and Samiha Mourad. \newblock Digital logic implementation in memristor-based crossbars - a tutorial. \newblock {\em Electronic Design, Test and Applications, IEEE International Workshop on}, 0:303--309, 2010. \bibitem{selfprog1} Julien Borghetti, Zhiyong Li, Joseph Straznicky, Xuema Li, Douglas A.~A. Ohlberg, Wei Wu, and Duncan~R. Stewart. \newblock {A hybrid nanomemristor/transistor logic circuit capable of self-programming}. \newblock {\em PNAS}, 106, 2009. \bibitem{lehtonen_stateful_2009} E.~Lehtonen and M.~Laiho. \newblock Stateful implication logic with memristors. \newblock In {\em 2009 {IEEE}/{ACM} {International} {Symposium} on {Nanoscale} {Architectures}}, pages 33--36, July 2009. \bibitem{xie_boolean_2016} L.~Xie, H.~A.~D. Nguyen, M.~Taouil, S.~Hamdioui, and K.~Bertels. \newblock Boolean logic gate exploration for memristor crossbar. \newblock In {\em 2016 {International} {Conference} on {Design} and {Technology} of {Integrated} {Systems} in {Nanoscale} {Era} ({DTIS})}, pages 1--6, April 2016. \bibitem{marranghello_factored_2015} F.~S. Marranghello, V.~Callegaro, M.~G.~A. Martins, A.~I. Reis, and R.~P. Ribas. \newblock Factored {Forms} for {Memristive} {Material} {Implication} {Stateful} {Logic}. \newblock {\em IEEE Journal on Emerging and Selected Topics in Circuits and Systems}, 5(2):267--278, June 2015. \bibitem{snider-cross} G.~Snider. \newblock {Computing with hysteretic resistor crossbars}. \newblock {\em Applied Physics A}, 80:1165--1172, 2005. \bibitem{vourkas_alternative_2016} I.~Vourkas, D.~Stathis, G.~C. Sirakoulis, and S.~Hamdioui. \newblock Alternative {Architectures} {Toward} {Reliable} {Memristive} {Crossbar} {Memories}. \newblock {\em IEEE Transactions on Very Large Scale Integration (VLSI) Systems}, 24(1):206--217, January 2016. \bibitem{lapicque_recherches_1907} L~Lapicque. \newblock Recherches quantitatives sur l'excitation electrique des nerfs traitee comme une polarization. \newblock {\em J Physiol Pathol Gen}, 9:620--635, 1907. \bibitem{mead_neuromorphic_1990} C.~Mead. \newblock Neuromorphic electronic systems. \newblock {\em Proceedings of the IEEE}, 78(10):1629--1636, October 1990. \bibitem{mahowald_silicon_1991} M.~A. Mahowald and C.~Mead. \newblock The silicon retina. \newblock {\em Scientific American}, 264(5):76--82, May 1991. \bibitem{delbruck_adaptive_1994} T.~Delbruck and C.~A. Mead. \newblock Adaptive photoreceptor with wide dynamic range. \newblock In {\em Proceedings of {IEEE} {International} {Symposium} on {Circuits} and {Systems} - {ISCAS} '94}, volume~4, pages 339--342 vol.4, May 1994. \bibitem{sarpeshkar_low-power_1998} Rahul Sarpeshkar, Richard~F. Lyon, and Carver Mead. \newblock A {Low}-{Power} {Wide}-{Dynamic}-{Range} {Analog} {VLSI} {Cochlea}. \newblock In Tor~Sverre Lande, editor, {\em Neuromorphic {Systems} {Engineering} : {Neural} {Networks} in {Silicon}}, pages 49--103. Kluwer Academic, Boston, MA, 1998. \bibitem{chiu_towards_2013} Shih-Wen Chiu and Kea-Tiong Tang. \newblock Towards a {Chemiresistive} {Sensor}-{Integrated} {Electronic} {Nose}: {A} {Review}. \newblock {\em Sensors}, 13(10):14214--14247, October 2013. \bibitem{liu_asynchronous_2014} S.~C. Liu, A.~van Schaik, B.~A. Minch, and T.~Delbruck. \newblock Asynchronous {Binaural} {Spatial} {Audition} {Sensor} {With} 2 64 4 {Channel} {Output}. \newblock {\em IEEE Transactions on Biomedical Circuits and Systems}, 8(4):453--464, August 2014. \bibitem{vanarse_review_2016} Anup Vanarse, Adam Osseiran, and Alexander Rassau. \newblock A {Review} of {Current} {Neuromorphic} {Approaches} for {Vision}, {Auditory}, and {Olfactory} {Sensors}. \newblock {\em Frontiers in Neuroscience}, 10, March 2016. \bibitem{shi_development_2015} L.~Shi, J.~Pei, N.~Deng, D.~Wang, L.~Deng, Y.~Wang, Y.~Zhang, F.~Chen, M.~Zhao, S.~Song, F.~Zeng, G.~Li, H.~Li, and C.~Ma. \newblock Development of a neuromorphic computing system. \newblock In {\em 2015 {IEEE} {International} {Electron} {Devices} {Meeting} ({IEDM})}, pages 4.3.1--4.3.4, December 2015. \bibitem{oconnor_real-time_2013} Peter O'Connor, Daniel Neil, Shih-Chii Liu, Tobi Delbruck, and Michael Pfeiffer. \newblock Real-time classification and sensor fusion with a spiking deep belief network. \newblock {\em Neuromorphic Engineering}, 7:178, 2013. \bibitem{prezioso_training_2015} Mirko Prezioso, Farnood Merrikh-Bayat, Brian Hoskins, Gina Adam, Konstantin~K. Likharev, and Dmitri~B. Strukov. \newblock Training and {Operation} of an {Integrated} {Neuromorphic} {Network} {Based} on {Metal}-{Oxide} {Memristors}. \newblock {\em Nature}, 521(7550):61--64, May 2015. \newblock arXiv: 1412.0611. \bibitem{mcculloch_logical_1943} Warren~S. McCulloch and Walter Pitts. \newblock A logical calculus of the ideas immanent in nervous activity. \newblock {\em The bulletin of mathematical biophysics}, 5(4):115--133, December 1943. \bibitem{vanrullen_spike_2005} Rufin VanRullen, Rudy Guyonneau, and Simon~J. Thorpe. \newblock Spike times make sense. \newblock {\em Trends in Neurosciences}, 28(1):1--4, January 2005. \bibitem{brette_philosophy_2015} Romain Brette. \newblock Philosophy of the {Spike}: {Rate}-{Based} vs. {Spike}-{Based} {Theories} of the {Brain}. \newblock {\em Frontiers in Systems Neuroscience}, page 151, 2015. \bibitem{bohte_evidence_2004} Sander~M. Bohte. \newblock The evidence for neural information processing with precise spike-times: {A} survey. \newblock {\em Natural Computing}, 3(2):195--206, June 2004. \bibitem{ponulak_supervised_2010} Filip Ponulak and Andrzej Kasiński. \newblock Supervised learning in spiking neural networks with {ReSuMe}: sequence learning, classification, and spike shifting. \newblock {\em Neural Computation}, 22(2):467--510, February 2010. \bibitem{masquelier_oscillations_2009} T.~Masquelier, E.~Hugues, G.~Deco, and S.J. Thorpe. \newblock Oscillations, phase-of-firing coding, and spike timing-dependent plasticity: {An} efficient learning scheme. \newblock {\em Journal of Neuroscience}, 29(43):13484--13493, 2009. \bibitem{chen_spike_2011} H.~T. Chen, K.~T. Ng, A.~Bermak, M.~K. Law, and D.~Martinez. \newblock Spike {Latency} {Coding} in {Biologically} {Inspired} {Microelectronic} {Nose}. \newblock {\em IEEE Transactions on Biomedical Circuits and Systems}, 5(2):160--168, April 2011. \bibitem{thorpe_spike-based_2001} Simon Thorpe, Arnaud Delorme, and Rufin Van~Rullen. \newblock Spike-based strategies for rapid processing. \newblock {\em Neural Networks}, 14(6-7):715--725, July 2001. \bibitem{shamir_emerging_2014} Maoz Shamir. \newblock Emerging principles of population coding: in search for the neural code. \newblock {\em Current Opinion in Neurobiology}, 25:140--148, April 2014. \bibitem{olshausen_emergence_1996} Bruno~A. Olshausen and David~J. Field. \newblock Emergence of simple-cell receptive field properties by learning a sparse code for natural images. \newblock {\em Nature}, 381(6583):607--609, June 1996. \bibitem{haykin_neural_1998} Simon Haykin. \newblock {\em Neural {Networks}: {A} {Comprehensive} {Foundation}}. \newblock Prentice Hall PTR, Upper Saddle River, NJ, USA, 2nd edition, 1998. \bibitem{lipton_critical_2015} Zachary~C. Lipton, John Berkowitz, and Charles Elkan. \newblock A {Critical} {Review} of {Recurrent} {Neural} {Networks} for {Sequence} {Learning}. \newblock {\em arXiv:1506.00019 [cs]}, May 2015. \newblock arXiv: 1506.00019. \bibitem{hopfield_neural_1982} J.~J. Hopfield. \newblock Neural networks and physical systems with emergent collective computational abilities. \newblock {\em Proceedings of the National Academy of Sciences}, 79(8):2554--2558, April 1982. \bibitem{elman_finding_1990} Jeffrey~L. Elman. \newblock Finding {Structure} in {Time}. \newblock {\em Cognitive Science}, 14(2):179--211, March 1990. \bibitem{krizhevsky_imagenet_2012} A.~Krizhevsky, I.~Sutskever, and G.E. Hinton. \newblock {ImageNet} classification with deep convolutional neural networks. \newblock volume~2, pages 1097--1105, 2012. \bibitem{neil_minitaur_2014} D.~Neil and S.~C. Liu. \newblock Minitaur, an {Event}-{Driven} {FPGA}-{Based} {Spiking} {Network} {Accelerator}. \newblock {\em IEEE Transactions on Very Large Scale Integration (VLSI) Systems}, 22(12):2621--2628, December 2014. \bibitem{hodgkin_quantitative_1952} A.~L. Hodgkin and A.~F. Huxley. \newblock A quantitative description of membrane current and its application to conduction and excitation in nerve. \newblock {\em The Journal of Physiology}, 117(4):500--544, August 1952. \bibitem{chicca_vlsi_2003} E.~Chicca, D.~Badoni, V.~Dante, M.~D'Andreagiovanni, G.~Salina, L.~Carota, S.~Fusi, and P.~Del Giudice. \newblock A {VLSI} recurrent network of integrate-and-fire neurons connected by plastic synapses with long-term memory. \newblock {\em IEEE Transactions on Neural Networks}, 14(5):1297--1307, September 2003. \bibitem{liu_temporal_2004} Shih-Chii Liu and R.~Douglas. \newblock Temporal coding in a silicon network of integrate-and-fire neurons. \newblock {\em IEEE Transactions on Neural Networks}, 15(5):1305--1314, September 2004. \bibitem{LIF1999} Wolfgang Maass and Christopher~M. Bishop, editors. \newblock {\em Pulsed Neural Networks}. \newblock MIT Press, Cambridge, MA, USA, 1999. \bibitem{brette_simulation_2007} Romain Brette, Michelle Rudolph, Ted Carnevale, Michael Hines, David Beeman, James~M. Bower, Markus Diesmann, Abigail Morrison, Philip~H. Goodman, Frederick~C. Harris, Milind Zirpe, Thomas Natschläger, Dejan Pecevski, Bard Ermentrout, Mikael Djurfeldt, Anders Lansner, Olivier Rochel, Thierry Vieville, Eilif Muller, Andrew~P. Davison, Sami El~Boustani, and Alain Destexhe. \newblock Simulation of networks of spiking neurons: a review of tools and strategies. \newblock {\em Journal of Computational Neuroscience}, 23(3):349--398, December 2007. \bibitem{izhikevich_simple_2003} E.~M. Izhikevich. \newblock Simple model of spiking neurons. \newblock {\em IEEE transactions on neural networks / a publication of the IEEE Neural Networks Council}, 14(6):1569--1572, 2003. \bibitem{hu_gap_2003} Edward~H. Hu and Stewart~A. Bloomfield. \newblock Gap junctional coupling underlies the short-latency spike synchrony of retinal alpha ganglion cells. \newblock {\em The Journal of Neuroscience: The Official Journal of the Society for Neuroscience}, 23(17):6768--6777, July 2003. \bibitem{drachman_we_2005} David~A. Drachman. \newblock Do we have brain to spare? \newblock {\em Neurology}, 64(12):2004--2005, June 2005. \bibitem{morris_d.o._1999} R.~G. Morris. \newblock D.{O}. {Hebb}: {The} {Organization} of {Behavior}, {Wiley}: {New} {York}; 1949. \newblock {\em Brain Research Bulletin}, 50(5-6):437, December 1999. \bibitem{clark_organization_1950} D.O. Hebb. \newblock The organization of behavior: {A} neuropsychological theory. {D}. {O}. {Hebb}. {John}. \newblock {\em Wiley, New York}, (3), 1949. \bibitem{morrison_phenomenological_2008} Abigail Morrison, Markus Diesmann, and Wulfram Gerstner. \newblock Phenomenological models of synaptic plasticity based on spike timing. \newblock {\em Biological Cybernetics}, 98(6):459--478, June 2008. \bibitem{dayan_theoretical_2005} Peter Dayan and L.~F. Abbott. \newblock {\em Theoretical {Neuroscience}: {Computational} and {Mathematical} {Modeling} of {Neural} {Systems}}. \newblock The MIT Press, 2005. \bibitem{yger_models_2015} Pierre Yger and Matthieu Gilson. \newblock Models of {Metaplasticity}: {A} {Review} of {Concepts}. \newblock {\em Frontiers in Computational Neuroscience}, page 138, 2015. \bibitem{zhang_critical_1998} Li~I. Zhang, Huizhong~W. Tao, Christine~E. Holt, William~A. Harris, and Mu-ming Poo. \newblock A critical window for cooperation and competition among developing retinotectal synapses. \newblock {\em Nature}, 395(6697):37--44, September 1998. \bibitem{wang_coactivation_2005} Huai-Xing Wang, Richard~C. Gerkin, David~W. Nauen, and Guo-Qiang Bi. \newblock Coactivation and timing-dependent integration of synaptic potentiation and depression. \newblock {\em Nature Neuroscience}, 8(2):187--193, February 2005. \bibitem{babadi_stability_2016} Baktash Babadi and L.~F. Abbott. \newblock Stability and {Competition} in {Multi}-spike {Models} of {Spike}-{Timing} {Dependent} {Plasticity}. \newblock {\em PLOS Comput Biol}, 12(3):e1004750, March 2016. \bibitem{pfister_triplets_2006} Jean-Pascal Pfister and Wulfram Gerstner. \newblock Triplets of {Spikes} in a {Model} of {Spike} {Timing}-{Dependent} {Plasticity}. \newblock {\em The Journal of Neuroscience}, 26(38):9673--9682, September 2006. \bibitem{bienenstock_theory_1982} E.~L. Bienenstock, L.~N. Cooper, and P.~W. Munro. \newblock Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. \newblock {\em The Journal of Neuroscience: The Official Journal of the Society for Neuroscience}, 2(1):32--48, January 1982. \bibitem{froemke_spike-timing-dependent_2002} Robert~C. Froemke and Yang Dan. \newblock Spike-timing-dependent synaptic modification induced by natural spike trains. \newblock {\em Nature}, 416(6879):433--438, March 2002. \bibitem{sjostrom_endocannabinoid-dependent_2004} Per~Jesper Sjöström, Gina~G. Turrigiano, and Sacha~B. Nelson. \newblock Endocannabinoid-dependent neocortical layer-5 {LTD} in the absence of postsynaptic spiking. \newblock {\em Journal of Neurophysiology}, 92(6):3338--3343, December 2004. \bibitem{senn_algorithm_2001} W.~Senn, H.~Markram, and M.~Tsodyks. \newblock An algorithm for modifying neurotransmitter release probability based on pre- and postsynaptic spike timing. \newblock {\em Neural Computation}, 13(1):35--67, January 2001. \bibitem{fregnac_activity-dependent_1999} Y.~Frégnac and D.~E. Shulz. \newblock Activity-dependent regulation of receptive field properties of cat area 17 by supervised {Hebbian} learning. \newblock {\em Journal of Neurobiology}, 41(1):69--82, October 1999. \bibitem{pfister_optimal_2006} Jean-Pascal Pfister, Taro Toyoizumi, David Barber, and Wulfram Gerstner. \newblock Optimal spike-timing-dependent plasticity for precise action potential firing in supervised learning. \newblock {\em Neural Computation}, 18(6):1318--1348, June 2006. \bibitem{boahen_point--point_2000} K.A. Boahen. \newblock Point-to-point connectivity between neuromorphic chips using address events. \newblock {\em IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing}, 47(5):416--434, May 2000. \bibitem{wendt_graph_2008} Karsten Wendt, Matthias Ehrlich, and René Schüffny. \newblock A {Graph} {Theoretical} {Approach} for a {Multistep} {Mapping} {Software} for the {FACETS} {Project}. \newblock In {\em Proceedings of the 2Nd {WSEAS} {International} {Conference} on {Computer} {Engineering} and {Applications}}, {CEA}'08, pages 189--194, Stevens Point, Wisconsin, USA, 2008. World Scientific and Engineering Academy and Society (WSEAS). \bibitem{HP_2008-switch} J.J. Yang, M.D. Pickett, X.~Li, D.A.A. Ohlberg, D.R. Stewart, and R.S. Williams. \newblock Memristive switching mechanism for metal/oxide/metal nanodevices. \newblock {\em Nature Nanotechnology}, 3(7):429--433, 2008. \bibitem{marder_variability_2006} Eve Marder and Jean-Marc Goaillard. \newblock Variability, compensation and homeostasis in neuron and network function. \newblock {\em Nature Reviews Neuroscience}, 7(7):563--574, July 2006. \bibitem{li_review_2016} C.~Li and Y.~Li. \newblock A {Review} on {Synergistic} {Learning}. \newblock {\em IEEE Access}, 4:119--134, 2016. \bibitem{grossberg_adaptive_1976} S.~Grossberg. \newblock Adaptive pattern classification and universal recoding: {I}. {Parallel} development and coding of neural feature detectors. \newblock {\em Biological Cybernetics}, 23(3), 1976. \bibitem{maass_computational_2000} Wolfgang Maass. \newblock On the {Computational} {Power} of {Winner}-{Take}-{All}. \newblock {\em Neural Computation}, 12(11):2519--2535, November 2000. \bibitem{hafliger_adaptive_2007} P.~Hafliger. \newblock Adaptive {WTA} {With} an {Analog} {VLSI} {Neuromorphic} {Learning} {Chip}. \newblock {\em IEEE Transactions on Neural Networks}, 18(2):551--572, March 2007. \bibitem{markram_human_2012} Henry Markram. \newblock The human brain project. \newblock {\em Scientific American}, 306(6):50--55, June 2012. \bibitem{ananthanarayanan_cat_2009} R.~Ananthanarayanan, S.~K. Esser, H.~D. Simon, and D.~S. Modha. \newblock The cat is out of the bag: cortical simulations with 109 neurons, 1013 synapses. \newblock In {\em Proceedings of the {Conference} on {High} {Performance} {Computing} {Networking}, {Storage} and {Analysis}}, pages 1--12, November 2009. \bibitem{paugam-moisy_computing_2012} Hélène Paugam-Moisy and Sander Bohte. \newblock Computing with {Spiking} {Neuron} {Networks}. \newblock In Grzegorz Rozenberg, Thomas Bäck, and Joost~N. Kok, editors, {\em Handbook of {Natural} {Computing}}, pages 335--376. Springer Berlin Heidelberg, 2012. \newblock DOI: 10.1007/978-3-540-92910-9\_10. \bibitem{goodman_brian:_2008} Dan F.~M. Goodman, Romain Brette, Dan Goodman, and Romain Brette. \newblock Brian: a simulator for spiking neural networks in {Python}. \newblock {\em Frontiers in Neuroinformatics}, 2:5, 2008. \bibitem{shahsavari_n2s3_2015} Mahyar Shahsavari, Philippe Devienne, and Pierre Boulet. \newblock N2s3, a {Simulator} for the {Architecture} {Exploration} of {Neuromorphic} {Accelerators}. \newblock In {\em 2nd {International} {Workshop} on {Neuromorphic} and {Brain}-{Based} {Computing} {Systems} ({NeuComp} 2015) in {DATE} {Conference}, {Grenoble}, {France}}, 2015. \bibitem{wyatt_akka_2013} Derek Wyatt. \newblock {\em Akka {Concurrency}}. \newblock Artima Incorporation, USA, 2013. \bibitem{odersky_overview_2006} Martin Odersky, Philippe Altherr, Vincent Cremet, Iulian Dragos, Gilles Dubochet, Burak Emir, Sean McDirmid, Stéphane Micheloud, Nikolay Mihaylov, Michel Schinz, Erik Stenman, Lex Spoon, and Matthias Zenger. \newblock An overview of the {Scala} programming language (2nd {Edition}). \newblock Technical {Report} LAMP-REPORT-2006-001, École Polytechnique Fédérale de Lausanne (EPFL), 2006. \bibitem{martin_synaptic_2000} S.~J. Martin, P.~D. Grimwood, and R.~G. Morris. \newblock Synaptic plasticity and memory: an evaluation of the hypothesis. \newblock {\em Annual Review of Neuroscience}, 23:649--711, 2000. \bibitem{kim_memristor_2012} H.~Kim, M.~P. Sah, C.~Yang, T.~Roska, and L.~O. Chua. \newblock Memristor {Bridge} {Synapses}. \newblock {\em Proceedings of the IEEE}, 100(6):2061--2070, June 2012. \bibitem{querlioz_immunity_2013} D.~Querlioz, O.~Bichler, P.~Dollfus, and C.~Gamrat. \newblock Immunity to {Device} {Variations} in a {Spiking} {Neural} {Network} {With} {Memristive} {Nanodevices}. \newblock {\em IEEE Transactions on Nanotechnology}, 12(3):288--295, May 2013. \bibitem{querlioz_learning_2011} D.~Querlioz, P.~Dollfus, O.~Bichler, and C.~Gamrat. \newblock Learning with memristive devices: {How} should we model their behavior? \newblock In {\em 2011 {IEEE}/{ACM} {International} {Symposium} on {Nanoscale} {Architectures}}, pages 150--156, June 2011. \bibitem{verstraeten_experimental_2007} D.~Verstraeten, B.~Schrauwen, M.~D’Haene, and D.~Stroobandt. \newblock An experimental unification of reservoir computing methods. \newblock {\em Neural Networks}, 20(3):391--403, April 2007. \bibitem{querlioz_bioinspired_2012} D.~Querlioz, W.~S. Zhao, P.~Dollfus, J.-O. Klein, O.~Bichler, and C.~Gamrat. \newblock Bioinspired {Networks} with {Nanoscale} {Memristive} {Devices} that {Combine} the {Unsupervised} and {Supervised} {Learning} {Approaches}. \newblock pages 203--210, 2012. \bibitem{indiveri_integration_2013} Giacomo Indiveri, Bernabe Linares-Barranco, Robert Legenstein, George Deligeorgis, and Themistoklis Prodromakis. \newblock Integration of nanoscale memristor synapses in neuromorphic computing architectures. \newblock {\em Nanotechnology}, 24(38):384010, September 2013. \newblock arXiv: 1302.7007. \bibitem{alibart_memristive_2012} Fabien Alibart, Stéphane Pleutin, Olivier Bichler, Christian Gamrat, Teresa Serrano-Gotarredona, Bernabe Linares-Barranco, and Dominique Vuillaume. \newblock A {Memristive} {Nanoparticle}/{Organic} {Hybrid} {Synapstor} for {Neuroinspired} {Computing}. \newblock {\em Advanced Functional Materials}, 22(3):609--616, February 2012. \bibitem{desbief_low_2015} Simon Desbief, Adrica Kyndiah, David Guérin, Denis Gentili, Mauro Murgia, Stéphane Lenfant, Fabien Alibart, Tobias Cramer, Fabio Biscarini, and Dominique Vuillaume. \newblock Low voltage and time constant organic synapse-transistor. \newblock {\em Organic Electronics}, 21:47--53, June 2015. \bibitem{Indiveri-Bistable-syn} G.~Indiveri. \newblock Neuromorphic bistable {VLSI} synapses with spike-timing-dependent plasticity. \newblock In {\em Advances in Neural Information Processing Systems ({NIPS})}, volume~15, pages 1091--1098, Cambridge, MA, USA, December 2003. MIT Press. \bibitem{salakhutdinov_restricted_2007} Ruslan Salakhutdinov, Andriy Mnih, and Geoffrey Hinton. \newblock Restricted {Boltzmann} {Machines} for {Collaborative} {Filtering}. \newblock In {\em Proceedings of the 24th {International} {Conference} on {Machine} {Learning}}, {ICML} '07, pages 791--798, New York, NY, USA, 2007. ACM. \bibitem{serrano-gotarredona_stdp_2013} Teresa Serrano-Gotarredona, Timothée Masquelier, Themistoklis Prodromakis, Giacomo Indiveri, and Bernabe Linares-Barranco. \newblock {STDP} and {STDP} variations with memristors for spiking neuromorphic learning systems. \newblock {\em Frontiers in Neuroscience}, 7:2, 2013. \bibitem{nessler_stdp_2009} Bernhard Nessler, Michael Pfeiffer, and Wolfgang Maass. \newblock {STDP} enables spiking neurons to detect hidden causes of their inputs. \newblock In Y.~Bengio, D.~Schuurmans, J.~D. Lafferty, C.~K.~I. Williams, and A.~Culotta, editors, {\em Advances in {Neural} {Information} {Processing} {Systems} 22}, pages 1357--1365. Curran Associates, Inc., 2009. \bibitem{MNIST} Yann Lecun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. \newblock Gradient-based learning applied to document recognition. \newblock In {\em Proceedings of the IEEE}, pages 2278--2324, 1998. \bibitem{diehl_unsupervised_2015} Peter~U. Diehl and Matthew Cook. \newblock Unsupervised learning of digit recognition using spike-timing-dependent plasticity. \newblock {\em Frontiers in Computational Neuroscience}, page~99, 2015. \bibitem{eryilmaz_neuromorphic_2016} Sukru~Burc Eryilmaz, Siddharth Joshi, Emre Neftci, Weier Wan, Gert Cauwenberghs, and H.-S.~Philip Wong. \newblock Neuromorphic architectures with electronic synapses. \newblock pages 118--123. IEEE, March 2016. \bibitem{lecun_deep_2015} Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. \newblock Deep learning. \newblock {\em Nature}, 521(7553):436--444, May 2015. \bibitem{eryilmaz_brain-like_2014} Sukru~B. Eryilmaz, Duygu Kuzum, Rakesh Jeyasingh, SangBum Kim, Matthew BrightSky, Chung Lam, and H.-S.~Philip Wong. \newblock Brain-like associative learning using a nanoscale non-volatile phase change synaptic device array. \newblock {\em Neuromorphic Engineering}, 8:205, 2014. \bibitem{ambrogio_unsupervised_2016} Stefano Ambrogio, Nicola Ciocchini, Mario Laudato, Valerio Milo, Agostino Pirovano, Paolo Fantini, and Daniele Ielmini. \newblock Unsupervised {Learning} by {Spike} {Timing} {Dependent} {Plasticity} in {Phase} {Change} {Memory} ({PCM}) {Synapses}. \newblock {\em Neuromorphic Engineering}, page~56, 2016. \bibitem{suri_bio-inspired_2013} Manan Suri, Damien Querlioz, Olivier Bichler, Giorgio Palma, Elisa Vianello, Dominique Vuillaume, Christian Gamrat, and Barbara DeSalvo. \newblock Bio-{Inspired} {Stochastic} {Computing} {Using} {Binary} {CBRAM} {Synapses}. \newblock {\em IEEE Transactions on Electron Devices}, 60(7):2402--2409, July 2013. \bibitem{nishitani_artificial_2014} Y.~Nishitani, Y.~Kaneko, and M.~Ueda. \newblock Artificial synapses using ferroelectric memristors embedded with {CMOS} {Circuit} for image recognition. \newblock In {\em 72nd {Device} {Research} {Conference}}, pages 297--298, June 2014. \bibitem{Gerstner_Why_1993} Wulfram Gerstner, Raphael Ritz, and J.~Leo Hemmen. \newblock Why spikes? hebbian learning and retrieval of time-resolved excitation patterns. \newblock {\em Biological {C}ybernetics}, 69(5-6):503--515, 1993. \bibitem{Markram_regulation_1997} Henry Markram, Joachim Lübke, Michael Frotscher, and Bert Sakmann. \newblock Regulation of synaptic efficacy by coincidence of postsynaptic aps and epsps. \newblock {\em Science}, 275(5297):213--215, 1997. \bibitem{fatahi_evt_mnist:_2016} Mazdak Fatahi, Mahmood Ahmadi, Mahyar Shahsavari, Arash Ahmadi, and Philippe Devienne. \newblock evt\_mnist: {A} spike based version of traditional {MNIST}. \newblock {\em arXiv:1604.06751 [cs]}, April 2016. \newblock arXiv: 1604.06751. \bibitem{drew_extending_2006} Patrick~J. Drew and L.~F. Abbott. \newblock Extending the effects of spike-timing-dependent plasticity to behavioral timescales. \newblock {\em Proceedings of the National Academy of Sciences of the United States of America}, 103(23):8876--8881, June 2006. \bibitem{querlioz_simulation_2011} D.~Querlioz, O.~Bichler, and C.~Gamrat. \newblock Simulation of a memristor-based spiking neural network immune to device variations. \newblock In {\em The 2011 {International} {Joint} {Conference} on {Neural} {Networks} ({IJCNN})}, pages 1775--1781, July 2011. \bibitem{neftci_event-driven_2014} Emre Neftci, Srinjoy Das, Bruno Pedroni, Kenneth Kreutz-Delgado, and Gert Cauwenberghs. \newblock Event-driven contrastive divergence for spiking neuromorphic systems. \newblock {\em Neuromorphic Engineering}, 7:272, 2014. \bibitem{soudry_memristor-based_2015} D.~Soudry, D.~Di Castro, A.~Gal, A.~Kolodny, and S.~Kvatinsky. \newblock Memristor-{Based} {Multilayer} {Neural} {Networks} {With} {Online} {Gradient} {Descent} {Training}. \newblock {\em IEEE Transactions on Neural Networks and Learning Systems}, 26(10):2408--2421, October 2015. \bibitem{siegert_first_1951} Arnold J.~F. Siegert. \newblock On the {First} {Passage} {Time} {Probability} {Problem}. \newblock {\em Physical Review}, 81(4):617--623, February 1951. \bibitem{kempter_intrinsic_2001} R.~Kempter, W.~Gerstner, and J.~L. van Hemmen. \newblock Intrinsic stabilization of output rates by spike-based {Hebbian} learning. \newblock {\em Neural Computation}, 13(12):2709--2741, December 2001. \bibitem{CD_RBM_hinton2002training} Geoffrey~E Hinton. \newblock Training products of experts by minimizing contrastive divergence. \newblock {\em Neural computation}, 14(8):1771--1800, 2002. \bibitem{CD_a_new_welling2002new} Max Welling and Geoffrey~E Hinton. \newblock A new learning algorithm for mean field boltzmann machines. \newblock In {\em Artificial Neural Networks—ICANN 2002}, pages 351--357. Springer, 2002. \bibitem{67_mleczko2015rough} Wojciech~K Mleczko, Tomasz Kapu{\'s}ci{\'n}ski, and Robert~K Nowicki. \newblock Rough deep belief network-application to incomplete handwritten digits pattern classification. \newblock In {\em Information and Software Technologies}, pages 400--411. Springer, 2015. \bibitem{65_taylor2006modeling} Graham~W Taylor, Geoffrey~E Hinton, and Sam~T Roweis. \newblock Modeling human motion using binary latent variables. \newblock In {\em Advances in neural information processing systems}, pages 1345--1352, 2006. \bibitem{sig_jug2012spiking} Florian Jug, Johannes Lengler, Christoph Krautz, and Angelika Steger. \newblock Spiking networks and their rate-based equivalents: does it make sense to use siegert neurons? \newblock {\em Swiss Society for Neuroscience}, 2012. \bibitem{ORL_32_32} Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han, and Thomas Huang. \newblock Learning a spatially smooth subspace for face recognition. \newblock In {\em Proc. IEEE Conf. Computer Vision and Pattern Recognition Machine Learning (CVPR'07)}, 2007. \bibitem{rtguide_hinton2012} Geoffrey~E Hinton. \newblock A practical guide to training restricted boltzmann machines. \newblock In {\em Neural Networks: Tricks of the Trade}, volume 7700, pages 599--619. Springer, 2012. \bibitem{bengio2012practical} Yoshua Bengio. \newblock Practical recommendations for gradient-based training of deep architectures. \newblock In {\em Neural Networks: Tricks of the Trade}, pages 437--478. Springer, 2012. \bibitem{Disc_RBM__larochelle2008classification} Hugo Larochelle and Yoshua Bengio. \newblock Classification using discriminative restricted boltzmann machines. \newblock In {\em Proceedings of the 25th international conference on Machine learning}, pages 536--543. ACM, 2008. \end{thebibliography}