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} $
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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 |
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.
Mathematics Subject Classification:
35R30, 35J05, 31B10, 35C20, 78A30.
Citation:
Andrea Scapin. Electrocommunication for weakly electric fish. Inverse Problems and 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. |
| [2] |
H. Ammari, T. Boulier and J. Garnier,
Modeling active electrolocation in weakly electric fish, SIAM J. Imaging Sci., 6 (2013), 285-321.
doi: 10.1137/12086858X. |
| [3] |
H. Ammari, T. Boulier, J. Garnier, W. Jing, H. 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. |
| [4] |
H. Ammari, T. Boulier, J. 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. |
| [5] |
H. Ammari, T. Boulier, J. 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. |
| [6] |
H. Ammari, J. Garnier, H. Kang, M. Lim and S. Yu,
Generalized polarization tensors for shape description, Numer. Math., 126 (2014), 199-224.
doi: 10.1007/s00211-013-0561-5. |
| [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. |
| [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. |
| [9] |
D. Babineau, A. 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. |
| [10] |
Y. Bai, I. D. Neveln, M. 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. |
| [11] |
E. Bonnetier, F. 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. |
| [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.
|
| [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. |
| [14] |
A. A. Caputi,
The bioinspiring potential of weakly electric fish, Bioinspir. Biomim., 12 (2017).
doi: 10.1088/1748-3190/12/2/025004. |
| [15] |
L. Chen, J. L. House, R. 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. |
| [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. |
| [17] |
O. M. Curet, N. A. Patankar, G. 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. |
| [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. |
| [19] |
B. He, T. Musha, Y. Okamoto, S. Homma, Y. 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. |
| [20] |
W. Heiligenberg,
Theoretical and experimental approaches to spatial aspects of electrolocation, J. Comp. Physiol., 103 (1975), 247-272.
doi: 10.1007/BF00612021. |
| [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. |
| [22] |
W. Heiligenberg, C. 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. |
| [23] |
N. Hoshimiya, K. Shogen, T. Matsuo and S. Chichibu,
The Apteronotus EOD field: Waveform and EOD field simulation, J. Comp. Physiol., 135 (1980), 283-290.
doi: 10.1007/BF00657644. |
| [24] |
B. Kramer, Electroreception and Communication in Fishes, Progress in Zoology, 42, Gustav Fischer, Stuttgart, 1996. |
| [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.
|
| [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. |
| [27] |
M. A. MacIver, N. 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.
|
| [28] |
P. Moller, Electric Fish: History and Behavior, Chapman and Hall, London, 1995. |
| [29] |
J. C. Mosher, P. 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. |
| [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. |
| [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. |
| [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. |
| [33] |
A. Scapin,
Electro-sensing of inhomogeneous targets, J. Math. Anal. Appl., 472 (2019), 1872-1901.
doi: 10.1016/j.jmaa.2018.12.027. |
| [34] |
K. Sekihara, D. Poeppel, A. Marantz, H. 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. |
| [35] |
G. von der Emde, S. Schwarz, L. Gomez, R. Budelli and K. Grant,
Electric fish measure distance in the dark, Nature, 395 (1998), 890-894.
doi: 10.1038/27655. |
| [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. |
| [37] |
G. von der Emde,
Active electrolocation of objects in weakly electric fish, J. Exp. Biol., 202 (1999), 1205-1215.
|
| [38] |
H. Wang, Shape identification in electro-sensing., Available from: https://github.com/yanncalec/SIES. |
| [39] |
W. Wang et al., A bio-inspired electrocommunication system for small underwater robots, Bioinspir. Biomim., 12 (2017).
doi: 10.1088/1748-3190/aa61c3. |
| [40] |
X. Zheng,
Artificial lateral line based local sensing between two adjacent robotic fish, Bioinspir. Biomim., 13 (2017).
doi: 10.1088/1748-3190/aa8f2e. |
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. |
| [2] |
H. Ammari, T. Boulier and J. Garnier,
Modeling active electrolocation in weakly electric fish, SIAM J. Imaging Sci., 6 (2013), 285-321.
doi: 10.1137/12086858X. |
| [3] |
H. Ammari, T. Boulier, J. Garnier, W. Jing, H. 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. |
| [4] |
H. Ammari, T. Boulier, J. 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. |
| [5] |
H. Ammari, T. Boulier, J. 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. |
| [6] |
H. Ammari, J. Garnier, H. Kang, M. Lim and S. Yu,
Generalized polarization tensors for shape description, Numer. Math., 126 (2014), 199-224.
doi: 10.1007/s00211-013-0561-5. |
| [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. |
| [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. |
| [9] |
D. Babineau, A. 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. |
| [10] |
Y. Bai, I. D. Neveln, M. 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. |
| [11] |
E. Bonnetier, F. 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. |
| [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.
|
| [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. |
| [14] |
A. A. Caputi,
The bioinspiring potential of weakly electric fish, Bioinspir. Biomim., 12 (2017).
doi: 10.1088/1748-3190/12/2/025004. |
| [15] |
L. Chen, J. L. House, R. 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. |
| [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. |
| [17] |
O. M. Curet, N. A. Patankar, G. 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. |
| [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. |
| [19] |
B. He, T. Musha, Y. Okamoto, S. Homma, Y. 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. |
| [20] |
W. Heiligenberg,
Theoretical and experimental approaches to spatial aspects of electrolocation, J. Comp. Physiol., 103 (1975), 247-272.
doi: 10.1007/BF00612021. |
| [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. |
| [22] |
W. Heiligenberg, C. 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. |
| [23] |
N. Hoshimiya, K. Shogen, T. Matsuo and S. Chichibu,
The Apteronotus EOD field: Waveform and EOD field simulation, J. Comp. Physiol., 135 (1980), 283-290.
doi: 10.1007/BF00657644. |
| [24] |
B. Kramer, Electroreception and Communication in Fishes, Progress in Zoology, 42, Gustav Fischer, Stuttgart, 1996. |
| [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.
|
| [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. |
| [27] |
M. A. MacIver, N. 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.
|
| [28] |
P. Moller, Electric Fish: History and Behavior, Chapman and Hall, London, 1995. |
| [29] |
J. C. Mosher, P. 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. |
| [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. |
| [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. |
| [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. |
| [33] |
A. Scapin,
Electro-sensing of inhomogeneous targets, J. Math. Anal. Appl., 472 (2019), 1872-1901.
doi: 10.1016/j.jmaa.2018.12.027. |
| [34] |
K. Sekihara, D. Poeppel, A. Marantz, H. 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. |
| [35] |
G. von der Emde, S. Schwarz, L. Gomez, R. Budelli and K. Grant,
Electric fish measure distance in the dark, Nature, 395 (1998), 890-894.
doi: 10.1038/27655. |
| [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. |
| [37] |
G. von der Emde,
Active electrolocation of objects in weakly electric fish, J. Exp. Biol., 202 (1999), 1205-1215.
|
| [38] |
H. Wang, Shape identification in electro-sensing., Available from: https://github.com/yanncalec/SIES. |
| [39] |
W. Wang et al., A bio-inspired electrocommunication system for small underwater robots, Bioinspir. Biomim., 12 (2017).
doi: 10.1088/1748-3190/aa61c3. |
| [40] |
X. Zheng,
Artificial lateral line based local sensing between two adjacent robotic fish, Bioinspir. Biomim., 13 (2017).
doi: 10.1088/1748-3190/aa8f2e. |
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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