February  2020, 14(1): 97-115. doi: 10.3934/ipi.2019065

Electrocommunication for weakly electric fish

Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland

* Corresponding author: Andrea Scapin

Received  March 2019 Revised  August 2019 Published  November 2019

Fund Project: The author is supported by SNF grant 200021-172483

This paper addresses the problem of the electro-communication for weakly electric fish. In particular we aim at sheding light on how the fish circumvent the jamming issue for both electro-communication and active electro-sensing. Our main result is a real-time tracking algorithm, which provides a new approach to the communication problem. It finds a natural application in robotics, where efficient communication strategies are needed to be implemented by bio-inspired underwater robots.

Citation: Andrea Scapin. Electrocommunication for weakly electric fish. Inverse Problems & Imaging, 2020, 14 (1) : 97-115. doi: 10.3934/ipi.2019065
References:
[1]

H. Ammari, An Introduction to Mathematics of Emerging Biomedical Imaging, Mathematics & Applications, 62, Springer, Berlin, 2008. doi: 10.1007/978-3-540-79553-7.  Google Scholar

[2]

H. AmmariT. Boulier and J. Garnier, Modeling active electrolocation in weakly electric fish, SIAM J. Imaging Sci., 6 (2013), 285-321.  doi: 10.1137/12086858X.  Google Scholar

[3]

H. AmmariT. BoulierJ. GarnierW. JingH. Kang and H. Wang, Target identification using dictionary matching of generalized polarization tensors, Found. Comput. Math., 14 (2014), 27-62.  doi: 10.1007/s10208-013-9168-6.  Google Scholar

[4]

H. AmmariT. BoulierJ. Garnier and H. Wang, Shape recognition and classification in electro-sensing, Proc. Natl. Acad. Sci. USA, 111 (2014), 11652-11657.  doi: 10.1073/pnas.1406513111.  Google Scholar

[5]

H. AmmariT. BoulierJ. Garnier and H. Wang, Mathematical modelling of the electric sense of fish: The role of multi-frequency measurements and movement, Bioinspir. Biomim., 12 (2017).  doi: 10.1088/1748-3190/aa5296.  Google Scholar

[6]

H. AmmariJ. GarnierH. KangM. Lim and S. Yu, Generalized polarization tensors for shape description, Numer. Math., 126 (2014), 199-224.  doi: 10.1007/s00211-013-0561-5.  Google Scholar

[7]

H. Ammari, M. Putinar and A. Steenkamp et al, Identification of an algebraic domain in two dimensions from a finite number of its generalized polarization tensors, Math. Ann., 375 (2019), 1337-1354. doi: 10.1007/s00208-018-1780-y.  Google Scholar

[8]

C. Assad, Electric Field Maps and Boundary Element Simulations Of Electrolocation in Weakly Electric Fish, Ph.D thesis, California Institute of Technology in Pasadena, CA, 1997. Google Scholar

[9]

D. BabineauA. Longtin and J. E. Lewis, Modeling the electric field of weakly electric fish, J. Exp. Biol., 209 (2006), 3636-3651.  doi: 10.1242/jeb.02403.  Google Scholar

[10]

Y. BaiI. D. NevelnM. Peshkin and M. A. MacIver, Enhanced detection performance in electrosense through capacitive sensing, Bioinspir. Biomim., 11 (2016).  doi: 10.1088/1748-3190/11/5/055001.  Google Scholar

[11]

E. BonnetierF. Triki and C.-H. Tsou, On the electro-sensing of weakly electric fish, J. Math. Anal. Appl., 464 (2018), 280-303.  doi: 10.1016/j.jmaa.2018.04.008.  Google Scholar

[12]

R. Budelli and A. A. Caputi, The electric image in weakly electric fish: Perception of objects of complex impedance, J. Exp. Biol., 203 (2000), 481-492.   Google Scholar

[13]

T. H. Bullock, R. H. Hamstra and H. Scheich, The jamming avoidance response of high frequency electric fish., in How do Brains Work?, Birkhäuser, Boston, MA, 1972,509–534. doi: 10.1007/978-1-4684-9427-3_42.  Google Scholar

[14]

A. A. Caputi, The bioinspiring potential of weakly electric fish, Bioinspir. Biomim., 12 (2017).  doi: 10.1088/1748-3190/12/2/025004.  Google Scholar

[15]

L. ChenJ. L. HouseR. Krahe and M. E. Nelson, Modeling signal and background components of electrosensory scenes, J. Comp. Physiol., 191 (2005), 331-345.  doi: 10.1007/s00359-004-0587-3.  Google Scholar

[16]

M. Christensen and A. Jakobsson, Optimal filter designs for separating and enhancing periodic signals, IEEE Trans. Signal Process., 58 (2010), 5969-5983.  doi: 10.1109/TSP.2010.2070497.  Google Scholar

[17]

O. M. CuretN. A. PatankarG. V. Lauder and M. A. MacIver, Aquatic manoeuvering with counter-propagating waves: A novel locomotive strategy, J. Royal Soc. Interface, 8 (2011), 1041-1050.  doi: 10.1098/rsif.2010.0493.  Google Scholar

[18]

E. Donati et al., Investigation of collective behaviour and electrocommunication in the weakly electric fish, Mormyrus rume, through a biomimetic robotic dummy fish, Bioinspir. Biomim., 11 (2016). doi: 10.1088/1748-3190/11/6/066009.  Google Scholar

[19]

B. HeT. MushaY. OkamotoS. HommaY. Nakajima and T. Sato, Electric dipole tracing in the brain by means of the boundary element method and its accuracy, IEEE Trans. Biomedical Engineering, 34 (1987), 406-414.  doi: 10.1109/TBME.1987.326056.  Google Scholar

[20]

W. Heiligenberg, Theoretical and experimental approaches to spatial aspects of electrolocation, J. Comp. Physiol., 103 (1975), 247-272.  doi: 10.1007/BF00612021.  Google Scholar

[21]

W. Heiligenberg, Principles of Electrolocation and Jamming Avoidance in Electric Fish: A Neuroethological Approach, Studies of Brain Function, 1, Springer-Verlag Berlin Heidelberg, 1977. doi: 10.1007/978-3-642-81161-6.  Google Scholar

[22]

W. HeiligenbergC. Baker and J. Bastian, The jamming avoidance response in gymnotoid pulse-species: A mechanism to minimize the probability of pulse-train coincidence, J. Comparative Physiology, 124 (1978), 211-224.  doi: 10.1007/BF00657053.  Google Scholar

[23]

N. HoshimiyaK. ShogenT. Matsuo and S. Chichibu, The Apteronotus EOD field: Waveform and EOD field simulation, J. Comp. Physiol., 135 (1980), 283-290.  doi: 10.1007/BF00657644.  Google Scholar

[24]

B. Kramer, Electroreception and Communication in Fishes, Progress in Zoology, 42, Gustav Fischer, Stuttgart, 1996. Google Scholar

[25]

H. W. Lissmann and K. E. Machin, The mechanism of object location in Gymnarchus niloticus and similar fish, J. Exp. Biol., 35 (1958), 451-486.   Google Scholar

[26]

M. A. MacIver, The Computational Neuroethology of Weakly Electric Fish: Body Modeling, Motion Analysis, and Sensory Signal Estimation, Ph.D thesis, University of Illinois at Urbana-Champaign in Champaign, IL, 2001. Google Scholar

[27]

M. A. MacIverN. M. Sharabash and M. E. Nelson, Prey-capture behavior in gymnotid electric fish: Motion analysis and effects of water conductivity, J. Exp. Biol., 204 (2001), 543-557.   Google Scholar

[28]

P. Moller, Electric Fish: History and Behavior, Chapman and Hall, London, 1995. Google Scholar

[29]

J. C. MosherP. S. Lewis and R. M. Leahy, Multiple dipole modeling and localization from spatio-temporal MEG data, IEEE Trans. Biomedical Engineering, 39 (1992), 541-557.  doi: 10.1109/10.141192.  Google Scholar

[30]

M. E. Nelson, Target detection, image analysis, and modeling, in Electroreception, Springer Handbook of Auditory Research, 21, Springer, New York, 2005,290–317. doi: 10.1007/0-387-28275-0_11.  Google Scholar

[31]

F. Pedraja et al., Passive and active electroreception during agonistic encounters in the weakly electric fish Gymnotus omarorum, Bioinspir. Biomim., 11 (2016). doi: 10.1088/1748-3190/11/6/065002.  Google Scholar

[32]

B. Rasnow, C. Assad, M. E. Nelson and J. M. Bower, Simulation and measurement of the electric fields generated by weakly electric fish, in Advances in Neural Information Processing Systems, 1, Morgan Kaufmann Publishers, San Mateo, CA, 1989, 436–443. Google Scholar

[33]

A. Scapin, Electro-sensing of inhomogeneous targets, J. Math. Anal. Appl., 472 (2019), 1872-1901.  doi: 10.1016/j.jmaa.2018.12.027.  Google Scholar

[34]

K. SekiharaD. PoeppelA. MarantzH. Koizumi and Y. Miyashita, Noise covariance incorporated MEG-MUSIC algorithm: A method for multiple-dipole estimation tolerant of the influence of background brain activity, IEEE Trans. Biomedical Engineering, 44 (1997), 839-847.  doi: 10.1109/10.623053.  Google Scholar

[35]

G. von der EmdeS. SchwarzL. GomezR. Budelli and K. Grant, Electric fish measure distance in the dark, Nature, 395 (1998), 890-894.  doi: 10.1038/27655.  Google Scholar

[36]

G. von der Emde and S. Fetz, Distance, shape and more: Recognition of object features during active electrolocation in a weakly electric fish, J. Exp. Biol., 210 (2007), 3082-3095.  doi: 10.1242/jeb.005694.  Google Scholar

[37]

G. von der Emde, Active electrolocation of objects in weakly electric fish, J. Exp. Biol., 202 (1999), 1205-1215.   Google Scholar

[38]

H. Wang, Shape identification in electro-sensing., Available from: https://github.com/yanncalec/SIES. Google Scholar

[39]

W. Wang et al., A bio-inspired electrocommunication system for small underwater robots, Bioinspir. Biomim., 12 (2017). doi: 10.1088/1748-3190/aa61c3.  Google Scholar

[40]

X. Zheng, Artificial lateral line based local sensing between two adjacent robotic fish, Bioinspir. Biomim., 13 (2017).  doi: 10.1088/1748-3190/aa8f2e.  Google Scholar

show all references

References:
[1]

H. Ammari, An Introduction to Mathematics of Emerging Biomedical Imaging, Mathematics & Applications, 62, Springer, Berlin, 2008. doi: 10.1007/978-3-540-79553-7.  Google Scholar

[2]

H. AmmariT. Boulier and J. Garnier, Modeling active electrolocation in weakly electric fish, SIAM J. Imaging Sci., 6 (2013), 285-321.  doi: 10.1137/12086858X.  Google Scholar

[3]

H. AmmariT. BoulierJ. GarnierW. JingH. Kang and H. Wang, Target identification using dictionary matching of generalized polarization tensors, Found. Comput. Math., 14 (2014), 27-62.  doi: 10.1007/s10208-013-9168-6.  Google Scholar

[4]

H. AmmariT. BoulierJ. Garnier and H. Wang, Shape recognition and classification in electro-sensing, Proc. Natl. Acad. Sci. USA, 111 (2014), 11652-11657.  doi: 10.1073/pnas.1406513111.  Google Scholar

[5]

H. AmmariT. BoulierJ. Garnier and H. Wang, Mathematical modelling of the electric sense of fish: The role of multi-frequency measurements and movement, Bioinspir. Biomim., 12 (2017).  doi: 10.1088/1748-3190/aa5296.  Google Scholar

[6]

H. AmmariJ. GarnierH. KangM. Lim and S. Yu, Generalized polarization tensors for shape description, Numer. Math., 126 (2014), 199-224.  doi: 10.1007/s00211-013-0561-5.  Google Scholar

[7]

H. Ammari, M. Putinar and A. Steenkamp et al, Identification of an algebraic domain in two dimensions from a finite number of its generalized polarization tensors, Math. Ann., 375 (2019), 1337-1354. doi: 10.1007/s00208-018-1780-y.  Google Scholar

[8]

C. Assad, Electric Field Maps and Boundary Element Simulations Of Electrolocation in Weakly Electric Fish, Ph.D thesis, California Institute of Technology in Pasadena, CA, 1997. Google Scholar

[9]

D. BabineauA. Longtin and J. E. Lewis, Modeling the electric field of weakly electric fish, J. Exp. Biol., 209 (2006), 3636-3651.  doi: 10.1242/jeb.02403.  Google Scholar

[10]

Y. BaiI. D. NevelnM. Peshkin and M. A. MacIver, Enhanced detection performance in electrosense through capacitive sensing, Bioinspir. Biomim., 11 (2016).  doi: 10.1088/1748-3190/11/5/055001.  Google Scholar

[11]

E. BonnetierF. Triki and C.-H. Tsou, On the electro-sensing of weakly electric fish, J. Math. Anal. Appl., 464 (2018), 280-303.  doi: 10.1016/j.jmaa.2018.04.008.  Google Scholar

[12]

R. Budelli and A. A. Caputi, The electric image in weakly electric fish: Perception of objects of complex impedance, J. Exp. Biol., 203 (2000), 481-492.   Google Scholar

[13]

T. H. Bullock, R. H. Hamstra and H. Scheich, The jamming avoidance response of high frequency electric fish., in How do Brains Work?, Birkhäuser, Boston, MA, 1972,509–534. doi: 10.1007/978-1-4684-9427-3_42.  Google Scholar

[14]

A. A. Caputi, The bioinspiring potential of weakly electric fish, Bioinspir. Biomim., 12 (2017).  doi: 10.1088/1748-3190/12/2/025004.  Google Scholar

[15]

L. ChenJ. L. HouseR. Krahe and M. E. Nelson, Modeling signal and background components of electrosensory scenes, J. Comp. Physiol., 191 (2005), 331-345.  doi: 10.1007/s00359-004-0587-3.  Google Scholar

[16]

M. Christensen and A. Jakobsson, Optimal filter designs for separating and enhancing periodic signals, IEEE Trans. Signal Process., 58 (2010), 5969-5983.  doi: 10.1109/TSP.2010.2070497.  Google Scholar

[17]

O. M. CuretN. A. PatankarG. V. Lauder and M. A. MacIver, Aquatic manoeuvering with counter-propagating waves: A novel locomotive strategy, J. Royal Soc. Interface, 8 (2011), 1041-1050.  doi: 10.1098/rsif.2010.0493.  Google Scholar

[18]

E. Donati et al., Investigation of collective behaviour and electrocommunication in the weakly electric fish, Mormyrus rume, through a biomimetic robotic dummy fish, Bioinspir. Biomim., 11 (2016). doi: 10.1088/1748-3190/11/6/066009.  Google Scholar

[19]

B. HeT. MushaY. OkamotoS. HommaY. Nakajima and T. Sato, Electric dipole tracing in the brain by means of the boundary element method and its accuracy, IEEE Trans. Biomedical Engineering, 34 (1987), 406-414.  doi: 10.1109/TBME.1987.326056.  Google Scholar

[20]

W. Heiligenberg, Theoretical and experimental approaches to spatial aspects of electrolocation, J. Comp. Physiol., 103 (1975), 247-272.  doi: 10.1007/BF00612021.  Google Scholar

[21]

W. Heiligenberg, Principles of Electrolocation and Jamming Avoidance in Electric Fish: A Neuroethological Approach, Studies of Brain Function, 1, Springer-Verlag Berlin Heidelberg, 1977. doi: 10.1007/978-3-642-81161-6.  Google Scholar

[22]

W. HeiligenbergC. Baker and J. Bastian, The jamming avoidance response in gymnotoid pulse-species: A mechanism to minimize the probability of pulse-train coincidence, J. Comparative Physiology, 124 (1978), 211-224.  doi: 10.1007/BF00657053.  Google Scholar

[23]

N. HoshimiyaK. ShogenT. Matsuo and S. Chichibu, The Apteronotus EOD field: Waveform and EOD field simulation, J. Comp. Physiol., 135 (1980), 283-290.  doi: 10.1007/BF00657644.  Google Scholar

[24]

B. Kramer, Electroreception and Communication in Fishes, Progress in Zoology, 42, Gustav Fischer, Stuttgart, 1996. Google Scholar

[25]

H. W. Lissmann and K. E. Machin, The mechanism of object location in Gymnarchus niloticus and similar fish, J. Exp. Biol., 35 (1958), 451-486.   Google Scholar

[26]

M. A. MacIver, The Computational Neuroethology of Weakly Electric Fish: Body Modeling, Motion Analysis, and Sensory Signal Estimation, Ph.D thesis, University of Illinois at Urbana-Champaign in Champaign, IL, 2001. Google Scholar

[27]

M. A. MacIverN. M. Sharabash and M. E. Nelson, Prey-capture behavior in gymnotid electric fish: Motion analysis and effects of water conductivity, J. Exp. Biol., 204 (2001), 543-557.   Google Scholar

[28]

P. Moller, Electric Fish: History and Behavior, Chapman and Hall, London, 1995. Google Scholar

[29]

J. C. MosherP. S. Lewis and R. M. Leahy, Multiple dipole modeling and localization from spatio-temporal MEG data, IEEE Trans. Biomedical Engineering, 39 (1992), 541-557.  doi: 10.1109/10.141192.  Google Scholar

[30]

M. E. Nelson, Target detection, image analysis, and modeling, in Electroreception, Springer Handbook of Auditory Research, 21, Springer, New York, 2005,290–317. doi: 10.1007/0-387-28275-0_11.  Google Scholar

[31]

F. Pedraja et al., Passive and active electroreception during agonistic encounters in the weakly electric fish Gymnotus omarorum, Bioinspir. Biomim., 11 (2016). doi: 10.1088/1748-3190/11/6/065002.  Google Scholar

[32]

B. Rasnow, C. Assad, M. E. Nelson and J. M. Bower, Simulation and measurement of the electric fields generated by weakly electric fish, in Advances in Neural Information Processing Systems, 1, Morgan Kaufmann Publishers, San Mateo, CA, 1989, 436–443. Google Scholar

[33]

A. Scapin, Electro-sensing of inhomogeneous targets, J. Math. Anal. Appl., 472 (2019), 1872-1901.  doi: 10.1016/j.jmaa.2018.12.027.  Google Scholar

[34]

K. SekiharaD. PoeppelA. MarantzH. Koizumi and Y. Miyashita, Noise covariance incorporated MEG-MUSIC algorithm: A method for multiple-dipole estimation tolerant of the influence of background brain activity, IEEE Trans. Biomedical Engineering, 44 (1997), 839-847.  doi: 10.1109/10.623053.  Google Scholar

[35]

G. von der EmdeS. SchwarzL. GomezR. Budelli and K. Grant, Electric fish measure distance in the dark, Nature, 395 (1998), 890-894.  doi: 10.1038/27655.  Google Scholar

[36]

G. von der Emde and S. Fetz, Distance, shape and more: Recognition of object features during active electrolocation in a weakly electric fish, J. Exp. Biol., 210 (2007), 3082-3095.  doi: 10.1242/jeb.005694.  Google Scholar

[37]

G. von der Emde, Active electrolocation of objects in weakly electric fish, J. Exp. Biol., 202 (1999), 1205-1215.   Google Scholar

[38]

H. Wang, Shape identification in electro-sensing., Available from: https://github.com/yanncalec/SIES. Google Scholar

[39]

W. Wang et al., A bio-inspired electrocommunication system for small underwater robots, Bioinspir. Biomim., 12 (2017). doi: 10.1088/1748-3190/aa61c3.  Google Scholar

[40]

X. Zheng, Artificial lateral line based local sensing between two adjacent robotic fish, Bioinspir. Biomim., 13 (2017).  doi: 10.1088/1748-3190/aa8f2e.  Google Scholar

Figure 3.  Before the JAR (the EOD frequencies of the two fish are the same). Plot of $ u(x) = u_1(x) + u_2(x) $, where $ u(x,t) = u(x) e^{i\omega_0 t} $
Figure 4.  After the JAR (the EOD frequencies $ \omega_1 $ and $ \omega_2 $ of the two fish are apart from each other)
Figure 1.  Standard shape of the pulse wave $ h(t) $
Figure 5.  The setting. $ \mathfrak{F}{1} $ is acquiring measurements at $ N_s = 150 $ different closely spaced positions
Figure 6.  Estimate of the position and the orientation of $ \mathfrak{F}{2} $, with noise level $ \sigma_0 = 0.1 $. The dashed red curve represents the estimated body of $ \mathfrak{F}{2} $, whereas the green one represents the true body of $ \mathfrak{F}{2} $. The white circle represents a small dielectric object placed between $ \mathfrak{F}{1} $ and $ \mathfrak{F}{2} $
Figure 7.  Plot of the imaging functional $ \mathcal{I}_2 $ that the fish $ \mathfrak{F}{1} $ uses to track $ \mathfrak{F}{2} $
Figure 8.  Plot of the linear trajectory tracking. $ N_{\text{exp}} = 10 $ trials have been considered
Figure 9.  Plot of the trajectory tracking when the leading fish is swimming in circle, clockwisely. $ N_{\text{exp}} = 10 $ trials/realizations have been considered
Figure 10.  Plot of the isopotential lines when $ \mathfrak{F}{2} $ (on the left) is passive (electrically silent) and $ \mathfrak{F}{1} $ (on the right) is active
Figure 11.  Plot of the MUSIC imaging functional used in Algorithm 3 by using $ N_r = 32 $ receptors and $ N_f = 100 $ frequencies, with noise level $ \sigma_0 = 0.1 $. The square and the diamond indicate the approximation of the center and the true center of the target D, respectively. $ \mathfrak{F}{1} $ (right) can image the target despite the presence of $ \mathfrak{F}{2} $ (left), which is estimated by applying Algorithm 2
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