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Çë°ïæ¼ìË÷ÎÄÕµÄSCIÊÕ¼ºÅ£¬ÎÄÕÂÃû£ºQuantification of degeneracy in Hodgkin-Huxley neurons on newman-watts small world network.×÷ÕßMenghua Man,ÔÓÖ¾£ºJournal of theoretical biology.2016,402C,67-74 ·¢×ÔСľ³æAndroid¿Í»§¶Ë |
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Quantification of degeneracy in Hodgkin-Huxley neurons on Newman-Watts small world network ×÷Õß:Man, MH (Man, Menghua)[ 1 ] ; Zhang, Y (Zhang, Ya)[ 1 ] ; Ma, GL (Ma, Guilei)[ 1 ] ; Friston, K (Friston, Karl)[ 2 ] ; Liu, SH (Liu, Shanghe)[ 1 ] JOURNAL OF THEORETICAL BIOLOGY ¾í: 402 í“´a: 62-74 DOI: 10.1016/j.jtbi.2016.05.004 ³ö°æÈÕÆÚ: AUG 7 2016 |
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Quantification of degeneracy in Hodgkin-Huxley neurons on Newman-Watts small world network ×÷Õß:Man, MH (Man, Menghua)[ 1 ] ; Zhang, Y (Zhang, Ya)[ 1 ] ; Ma, GL (Ma, Guilei)[ 1 ] ; Friston, K (Friston, Karl)[ 2 ] ; Liu, SH (Liu, Shanghe)[ 1 ] JOURNAL OF THEORETICAL BIOLOGY ¾í: 402 Ò³: 62-74 DOI: 10.1016/j.jtbi.2016.05.004 ³ö°æÄê: AUG 7 2016 ²é¿´ÆÚ¿¯ÐÅÏ¢ JOURNAL OF THEORETICAL BIOLOGY ³ö°æÉÌ ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 24-28 OVAL RD, LONDON NW1 7DX, ENGLAND ISSN: 0022-5193 eISSN: 1095-8541 Ñо¿ÁìÓò Life Sciences & Biomedicine - Other Topics Mathematical & Computational Biology ÕªÒª Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin-Huxley neuronal networks with Newman-Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus - and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics. (C) 2016 Elsevier Ltd. All rights reserved. ¹Ø¼ü´Ê ×÷Õ߹ؼü´Ê:Complexity; Redundancy; Neuronal networks KeyWords Plus:NON-GAUSSIAN NOISE; FUNCTIONAL CONNECTIVITY; MULTIPLE RESONANCES; COGNITIVE FUNCTIONS; TIME DELAYS; BRAIN; COMPLEXITY; SYSTEMS; INFORMATION; MODEL ×÷ÕßÐÅÏ¢ ͨѶ×÷ÕßµØÖ·: Man, MH (ͨѶ×÷Õß) Mech Engn Coll, Electrostat & Electromagnet Protect Inst, Shijiazhuang, Peoples R China. µØÖ·: [ 1 ] Mech Engn Coll, Electrostat & Electromagnet Protect Inst, Shijiazhuang, Peoples R China [ 2 ] UCL, Inst Neurol, Wellcome Trust Ctr Neuroimaging, Queen Sq, London, England ÔöÇ¿×éÖ¯ÐÅÏ¢µÄÃû³Æ University College London University of London µç×ÓÓʼþµØÖ·:manmenghua@126.com »ù½ð×ÊÖúÖÂл »ù½ð×ÊÖú»ú¹¹ ÊÚȨºÅ National Natural Science Foundation of China 51407194 Wellcome Trust 088130/Z/09/Z ²é¿´»ù½ð×ÊÖúÐÅÏ¢¹Ø±Õ»ù½ð×ÊÖúÐÅÏ¢ Thank anonymous reviewers for constructive comments on this work. We would like to thank Mai Lu and Qian Zhou for helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant no. 51407194). K.F. is funded by the Wellcome Trust (Ref.: 088130/Z/09/Z). ³ö°æÉÌ ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 24-28 OVAL RD, LONDON NW1 7DX, ENGLAND Àà±ð / ·ÖÀà Ñо¿·½Ïò:Life Sciences & Biomedicine - Other Topics; Mathematical & Computational Biology Web of Science Àà±ð:Biology; Mathematical & Computational Biology ÎÄÏ×ÐÅÏ¢ ÎÄÏ×ÀàÐÍ:Article ÓïÖÖ:English Èë²ØºÅ: WOS:000377623700008 PubMed ID: 27155043 ISSN: 0022-5193 eISSN: 1095-8541 ÆäËûÐÅÏ¢ IDS ºÅ: DO2QA Web of Science ºËÐĺϼ¯ÖÐµÄ "ÒýÓõIJο¼ÎÄÏ×": 73 Web of Science ºËÐĺϼ¯ÖÐµÄ "±»ÒýƵ´Î": 0 Ó°ÏìÒò×Ó 2.049 2.156 2015 5 Äê JCR® Àà±ð Àà±ðÖеÄÅÅÐò JCR ·ÖÇø BIOLOGY 25/86 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY 14/56 Q1 Êý¾ÝÀ´×ÔµÚ 2015 °æ Journal Citation Reports® |
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