Pub Date : 2002-07-22DOI: 10.1109/CNNA.2002.1035030
M. Gilli, T. Roska, L. Chua, P. Civalleri
The relationship between cellular neural/nonlinear networks (CNNs) and partial differential equations (PDEs) is investigated. The equivalence between a discrete-space CNN model and a continuous-space PDE model is rigorously defined. The problem of the equivalence is split into two sub-problems: approximation and topological equivalence, that can be explicitly studied for any CNN models. It is known that each PDE can be approximated by a space difference scheme, i.e. a CNN model, that presents a similar dynamic behavior. It is shown, through examples, that there exist CNN models that are not equivalent to any PDEs, either because they do not approximate any PDE models, or because they have a different dynamic behavior (i.e. they are not topologically equivalent to the PDE, that approximate). This proves that the spatio-temporal CNN dynamics is broader than that described by PDEs.
{"title":"On the relationship between CNNs and PDEs","authors":"M. Gilli, T. Roska, L. Chua, P. Civalleri","doi":"10.1109/CNNA.2002.1035030","DOIUrl":"https://doi.org/10.1109/CNNA.2002.1035030","url":null,"abstract":"The relationship between cellular neural/nonlinear networks (CNNs) and partial differential equations (PDEs) is investigated. The equivalence between a discrete-space CNN model and a continuous-space PDE model is rigorously defined. The problem of the equivalence is split into two sub-problems: approximation and topological equivalence, that can be explicitly studied for any CNN models. It is known that each PDE can be approximated by a space difference scheme, i.e. a CNN model, that presents a similar dynamic behavior. It is shown, through examples, that there exist CNN models that are not equivalent to any PDEs, either because they do not approximate any PDE models, or because they have a different dynamic behavior (i.e. they are not topologically equivalent to the PDE, that approximate). This proves that the spatio-temporal CNN dynamics is broader than that described by PDEs.","PeriodicalId":387716,"journal":{"name":"Proceedings of the 2002 7th IEEE International Workshop on Cellular Neural Networks and Their Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2002-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130115026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/CNNA.2002.1035047
S.T. Kes, L. Orzó, T. Roska
Within thc programmable opto-electronic analogic computer (POAC) framework B new, feed forward only optical CNN-UM implementation has been introduced. It is grounded on an innovative semi-incoherent optical correlator architecture. Angular coding of the template pixels determines the operation o f this optical CNN implementation, therefore it is rcal time and flexibly programmable. We have demonstrated its feasibility and operation by an experimental setup. Our correlator architecture makes it possible to execute algorithms real time, which cannot be done by any other existing optical conclator so far. Our architechue unifies the advantages of coherent and incoherent optical correlators, provides a more robust frame and avoids their main hindrances. In the POAC framework the resulting conelogram is measured by a programmable adaptive sensor array, a special visual CNN-UM chip. So, local parallel programs fulfill both the necessary pre and post processing with the required adaptive thrcsholdiog. HOWCVCI, because of the limited resolution of available visual CNN chips ( 28x 28), all-optical optical prcandpost-precessing will be used, as well.
{"title":"Programmable optical CNN implementation based on the template pixels' angular coding","authors":"S.T. Kes, L. Orzó, T. Roska","doi":"10.1109/CNNA.2002.1035047","DOIUrl":"https://doi.org/10.1109/CNNA.2002.1035047","url":null,"abstract":"Within thc programmable opto-electronic analogic computer (POAC) framework B new, feed forward only optical CNN-UM implementation has been introduced. It is grounded on an innovative semi-incoherent optical correlator architecture. Angular coding of the template pixels determines the operation o f this optical CNN implementation, therefore it is rcal time and flexibly programmable. We have demonstrated its feasibility and operation by an experimental setup. Our correlator architecture makes it possible to execute algorithms real time, which cannot be done by any other existing optical conclator so far. Our architechue unifies the advantages of coherent and incoherent optical correlators, provides a more robust frame and avoids their main hindrances. In the POAC framework the resulting conelogram is measured by a programmable adaptive sensor array, a special visual CNN-UM chip. So, local parallel programs fulfill both the necessary pre and post processing with the required adaptive thrcsholdiog. HOWCVCI, because of the limited resolution of available visual CNN chips ( 28x 28), all-optical optical prcandpost-precessing will be used, as well.","PeriodicalId":387716,"journal":{"name":"Proceedings of the 2002 7th IEEE International Workshop on Cellular Neural Networks and Their Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125625981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/CNNA.2002.1035028
D. Bálya, C. Rekeczky, T. Roska
Some parallel channels of the mammalian retina are illustrated schematically. The different decomposition possibilities are indicated by the cyan blocks. The different neuron types in the retina are organized into two-dimensional stmta modeled with CNN layers, which are represented by the spheres. A neuron in a given layer effects another neuron in another layer through synapses while the arrows represent the connections. The layers have different time and space constants and the synapses produce non-linear transfer functions.
{"title":"Basic mammalian retinal effects on the prototype complex cell CNN universal machine","authors":"D. Bálya, C. Rekeczky, T. Roska","doi":"10.1109/CNNA.2002.1035028","DOIUrl":"https://doi.org/10.1109/CNNA.2002.1035028","url":null,"abstract":"Some parallel channels of the mammalian retina are illustrated schematically. The different decomposition possibilities are indicated by the cyan blocks. The different neuron types in the retina are organized into two-dimensional stmta modeled with CNN layers, which are represented by the spheres. A neuron in a given layer effects another neuron in another layer through synapses while the arrows represent the connections. The layers have different time and space constants and the synapses produce non-linear transfer functions.","PeriodicalId":387716,"journal":{"name":"Proceedings of the 2002 7th IEEE International Workshop on Cellular Neural Networks and Their Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124492407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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