Modeling active electrolocation in weakly electric fish

In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem and derive the approximate boundary conditions on the skin of the fish. Then we provide a dipole approximation for small targets away from the fish. Based on this approximation, we obtain a non-iterative location search algorithm using multi-frequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure

Shape recognition and classification in electro-sensing

This paper aims at advancing the field of electro-sensing. It exhibits the physical mechanism underlying shape perception for weakly electric fish. These fish orient themselves at night in complete darkness by employing their active electrolocation system. They generate a stable, high-frequency, weak electric field and perceive the transdermal potential modulations caused by a nearby target with different admittivity than the surrounding water. In this paper, we explain how weakly electric fish might identify and classify a target, knowing by advance that the latter belongs to a certain collection of shapes. Our model of the weakly electric fish relies on differential imaging, i.e., by forming an image from the perturbations of the field due to targets, and physics-based classification. The electric fish would first locate the target using a specific location search algorithm. Then it could extract, from the perturbations of the electric field, generalized (or high-order) polarization tensors of the target. Computing, from the extracted features, invariants under rigid motions and scaling yields shape descriptors. The weakly electric fish might classify a target by comparing its invariants with those of a set of learned shapes. On the other hand, when measurements are taken at multiple frequencies, the fish might exploit the shifts and use the spectral content of the generalized polarization tensors to dramatically improve the stability with respect to measurement noise of the classification procedure in electro-sensing. Surprisingly, it turns out that the first-order polarization tensor at multiple frequencies could be enough for the purpose of classification. A procedure to eliminate the background field in the case where the permittivity of the surrounding medium can be neglected, and hence improve further the stability of the classification process, is also discussed.Comment: 10 pages, 15 figure

Fish Geometry and Electric Organ Discharge Determine Functional Organization of the Electrosensory Epithelium

Active electroreception in Gymnotus omarorum is a sensory modality that perceives the changes that nearby objects cause in a self generated electric field. The field is emitted as repetitive stereotyped pulses that stimulate skin electroreceptors. Differently from mormyriformes electric fish, gymnotiformes have an electric organ distributed along a large portion of the body, which fires sequentially. As a consequence shape and amplitude of both, the electric field generated and the image of objects, change during the electric pulse. To study how G. omarorum constructs a perceptual representation, we developed a computational model that allows the determination of the self-generated field and the electric image. We verify and use the model as a tool to explore image formation in diverse experimental circumstances. We show how the electric images of objects change in shape as a function of time and position, relative to the fish's body. We propose a theoretical framework about the organization of the different perceptive tasks made by electroreception: 1) At the head region, where the electrosensory mosaic presents an electric fovea, the field polarizing nearby objects is coherent and collimated. This favors the high resolution sampling of images of small objects and perception of electric color. Besides, the high sensitivity of the fovea allows the detection and tracking of large faraway objects in rostral regions. 2) In the trunk and tail region a multiplicity of sources illuminate different regions of the object, allowing the characterization of the shape and position of a large object. In this region, electroreceptors are of a unique type and capacitive detection should be based in the pattern of the afferents response. 3) Far from the fish, active electroreception is not possible but the collimated field is suitable to be used for electrocommunication and detection of large objects at the sides and caudally

First results on a sensor bio-inspired by electric fish

This article presents the first results of a work which aims at designing an active sensor inspired by the electric fish. Its interest is its potential for robotics underwater navigation and exploration tasks in conditions where vision and sonar would meet difficulty. It could also be used as a complementary omnidirectional, short range sense to vision and sonar. Combined with a well defined engine geometry, this sensor can be modeled analytically. In this article, we focus on a particular measurement mode where one electrode of the sensor acts as a current emitter and the others as current receivers. In spite of the high sensitivity required by electric sense, the first results show that we can obtain a detection range of the order of the sensor length, which suggests that this sensor principle could be used in future for robotics obstacle avoidance

3-Dimensional Scene Perception during Active Electrolocation in a Weakly Electric Pulse Fish

Weakly electric fish use active electrolocation for object detection and orientation in their environment even in complete darkness. The African mormyrid Gnathonemus petersii can detect object parameters, such as material, size, shape, and distance. Here, we tested whether individuals of this species can learn to identify 3-dimensional objects independently of the training conditions and independently of the object's position in space (rotation-invariance; size-constancy). Individual G. petersii were trained in a two-alternative forced-choice procedure to electrically discriminate between a 3-dimensional object (S+) and several alternative objects (S−). Fish were then tested whether they could identify the S+ among novel objects and whether single components of S+ were sufficient for recognition. Size-constancy was investigated by presenting the S+ together with a larger version at different distances. Rotation-invariance was tested by rotating S+ and/or S− in 3D. Our results show that electrolocating G. petersii could (1) recognize an object independently of the S− used during training. When only single components of a complex S+ were offered, recognition of S+ was more or less affected depending on which part was used. (2) Object-size was detected independently of object distance, i.e. fish showed size-constancy. (3) The majority of the fishes tested recognized their S+ even if it was rotated in space, i.e. these fishes showed rotation-invariance. (4) Object recognition was restricted to the near field around the fish and failed when objects were moved more than about 4 cm away from the animals. Our results indicate that even in complete darkness our G. petersii were capable of complex 3-dimensional scene perception using active electrolocation

Mathematical models of depth perception in weakly electric fish

Weakly electric fish use electrolocation - the detection of electric fields - to sense their environment. The task of electrolocation involves the decoding of the third dimension - depth - from a two-dimensional electric image. In this work we present three advances in the area of depth-perception. First, we develop a model for electrolocation based on a single parameter, namely the width of the electric image. In contrast to previous suggested algorithms, our algorithm would only require a single narrow tuned topographic map to accurately estimate distance. This model is used to study the effects of electromagnetic noise and the presence of stochastic resonance. Second, considering the problem of depth perception from the perspective of information constraints, we ask how much information is necessary for location disambiguation? That is, what is the minimum amount of information that fish would need to localize an object? This inverse problem approach gives us insight into biological electrolocation and provides a guide for future experimental work. Our final contribution is to provide a mathematical foundation for two of the most accepted depth perception models currently in use

Shape recognition and classification in electro-sensing

This paper aims at advancing the field of electro-sensing. It exhibits physical mechanisms underlying shape perception for weakly electric fish. These fish orient themselves at night in complete darkness by using their active electrolocation system. They generate a stable, relatively high-frequency, weak electric field and perceive the transdermal potential modulations caused by a nearby target with different electromagnetic properties than the surrounding water. The main result of this paper is a scheme that explains how weakly electric fish might identify and classify a target, knowing in advance that the latter belongs to a certain collection of shapes. The scheme is designed to recognize living biological organisms. It exploits the frequency dependence of the electromagnetic properties of living organisms, which comes from the capacitive effects generated by the cell membrane structure. When measurements are taken at multiple frequencies, the fish might use the spectral content of the perceived transdermal potential modulations to classify the living target. inverse conductivity problem | polarization tensor | shape classification I n the turbid rivers of Africa and South America, some species of fish generate a stable, relatively high-frequency (0.1-10 kHz), weakly electric (≤100 mV/cm) field that is not enough for defense against predators. In 1958, Lissmann and Machin (1) discovered that the emitted electrical signal is in fact used for active electro-sensing. The weakly electric fish have thousands of receptors at the surface of their skins. A nearby target with different admittivity than the surrounding water perturbs the transdermal potential induced by the electric organ discharge (2, 3). Targets with large permittivity cause appreciable phase shifts, which can be measured by receptors called T-type units (4). It is an important input for the fish, and thus it will be the central point in this paper for shape classification. Active electro-sensing has driven an increasing number of experimental, behavioral, biological, and computational studies since Lissmann and Machin's work (5-12). Behavioral experiments have shown that weakly electric fish are able to locate a target (12) and discriminate between targets with different shapes (13) or/and electric parameters (conductivity and permittivity) (14). The growing interest in electro-sensing could be explained not only by the curiosity of discovering a sixth sense, electric perception, that is not accessible by our own senses, but also by potential bio-inspired applications in underwater robotics. It is challenging to equip robots with electric perception and provide them, by mimicking weakly electric fish, with imaging and classification capabilities in dark or turbid environments Mathematically speaking, the problem is to locate the target and identify its shape and material parameters given the current distribution over the skin. Due to the fundamental ill-posedness of this imaging problem, it is very intriguing to see how much information weakly electric fish are able to recover. The electric field perturbation due to the target is a complicated highly nonlinear function of its shape, admittivity, and distance from the fish. Thus, understanding analytically this electric sensing is likely to give us insight in this regard (5-7, 9, 13, 18, 21). Although locating targets from the electric field perturbations induced on the skin of the fish is now understood (17, 22), identifying and classifying their shapes are considered to be some of the most challenging problems in electro-sensing. Although the neuroethology of these fish has been significantly advanced recently (see ref. 23 and references therein), the neural mechanisms encoding the shape of a target are far beyond the scope of our study. Rather, this work focuses on the physical feasibility of such a process, which was not explained before. In ref. 22, a rigorous model for the electro-location of a target around the fish was derived. Using the fact that the electric current produced by the electric organ is time harmonic with a known fundamental frequency, a space-frequency location search algorithm was introduced. Its robustness with respect to measurement noise and its sensitivity with respect to the number of frequencies, the number of sensors, and the distance to the target were illustrated. In the case of disk-and ellipse-shaped targets, the conductivity, the permittivity, and the size of the targets can be reconstructed separately from multifrequency measurements. Such measurements have been used successfully in transadmittance scanners of breast tumors (24-26). The main result of this paper is the presentation and analysis of a scheme that allows to recognize and classify targets from multifrequency measurements of the electric field perturbations induced by the targets. To explain how the shape information is encoded in measured data, we distinguish two cases: recognition of nonbiological targets and recognition of living organisms. Most of the nonbiological objects have very low permittivities, and therefore, their electromagnetic parameters are frequency independent. Living targets have frequency-dependent electromagnetic parameters because their cell membrane structures induce capacitive effects (27), and therefore it is possible to exploit the spectral content of the data. We will mostly focus our attention on the second situation, but we first explain the strategy for the first one. Our model in this paper of the weakly electric fish relies on differential imaging, i.e., by forming an image from the perturbations of the field due to the target. The method is based on the multipole expansion for the perturbations of the electric field induced by a nearby target in terms of the characteristic size of the target. The asymptotic expansion derived in refs. 22 and 28 generalizes Rasnow's equation (29) in two directions: (i) it is a higher-order approximation of the effect of a nearby target, and it is valid for an arbitrary shape and admittivity contrast; and (ii) it also takes into account the body of the fish. As was first shown in ref. 22, one can reduce the Significance Weakly electric fish orient themselves in complete darkness by using their active electrolocation system. They generate a weak electric field and perceive the transdermal potential modulations caused by a nearby target with different electromagnetic properties than the surrounding water. The main result of this paper is a scheme that explains how weakly electric fish might identify and classify living biological organisms. This scheme exploits the frequency dependence of the electromagnetic properties of living organisms, which comes from the capacitive effects generated by the cell membrane structure

ELECTROLOCATION-BASED OBSTACLE AVOIDANCE AND AUTONOMOUS NAVIGATION IN UNDERWATER ENVIRONMENTS

Weakly electric fish are capable of performing obstacle avoidance in dark and complex aquatic environments efficiently using a navigation technique known as \emph{electrolocation}. That is, electric fish infer relevant information about surrounding obstacles from the perturbations that these obstacles impart to their self-generated electric field. This dissertation draws inspiration from electrolocation to demonstrate unmapped reflexive obstacle avoidance in underwater environments. The perturbation signal, called the \emph{electric image}, contains the spatial information of the perturbing objects regarding their location, size, conductivity etc. Electrostatic equations elucidate the concept of electrolocation and the mechanism of obstacle detection using electric field perturbations. Spatial decomposition of an electric image using Wide-Field Integration processing extracts relative proximity information about the obstacles. The electric field source is changed to an oscillatory one and a quasistatic approach is taken. Simulations were performed in straight tunnel, cluttered corridor and an obstacle field. Experimental validation was conducted with a setup comprising a tank, a computer-controlled gantry system and an electro-sensor. Consistency between the simulations and the experiments was maintained by recreating similar environments. Simulations using both the electrostatic and the quasistatic approach demonstrate that the algorithm is capable of performing various maneuvers like tunnel centering, wall following and clutter navigation. The experimental results agree with the simulation results and validate the efficacy of the approach in performing obstacle avoidance. The presented approach is computationally lightweight and readily implementable, making underwater autonomous navigation in real-time feasible

Dynamics of sensorimotor behavior in electrolocation and electrocommunication

Pedraja F. Dynamics of sensorimotor behavior in electrolocation and electrocommunication. Bielefeld: Universität Bielefeld; 2019.How are external sensory stimuli perceived, integrated and represented within the central nervous system? How does the nervous system generate appropriate behavioral responses based on this input and how does this behavior affect perception? The above questions have in common that they view sensory input and motor control as two sides of the sensorimotor loop. In this closed-loop system, actions inevitably generate sensory flow that can serve to organize behavior. To look, to smell, to touch, etc. are perceptual acts that depend on the interaction, coordination and interpretation of motor and sensory information through neural mechanisms. Active sensory systems are particularly amenable to the study of the reciprocal relations of motor and sensory components, as parts of closed loop control structures. A notable advantage of these sensory systems is the experimental accessibility of their sensory input, both in terms of its measurement and in terms of detailed modeling reconstructions of the input. In the case of weakly electric fish studied in this thesis, the animals sense and process environmental perturbations of a self-generated electric field. The fact that this field serves as the carrier of sensory information and at the same time is controlled by the animal, enables to precisely determine aspects of sensing that are often hard to obtain or quantify in sensory systems that do not actively generate the carrier: where, when and what an animal samples. Drawing on these benefits, my thesis focuses on the role of motor and electromotor behavior in sensorimotor integration. For this, a biophysical model for the active and passive electroreception was combined with physiological recordings and behavioral approaches. The central topics addressed are: (i) Object detection and sensorimotor learning. The sensory information obtained by the African species Gnathonemus petersii while learning a detection task was computationally reconstructed using boundary element methods (BEM). This revealed that the improved task performance was paralleled by an enhancement of the quality of the sensory information, which was mediated by changes of the electromotor patterns. The versatile manner in which the fish changed the spatial and temporal allocation of otherwise stable motor components not only improved the quality of the sensory input, but also resulted in shifts of the animals' attention towards the object. (ii) Dynamic choice of optimal behavior. Extending on the above results, I next explored how changing the distance of an object to be detected by the fish influenced the electromotor behavior. With increasing complexity (distance), the fish resorted to a new motor strategy. This consisted in first approaching a salient element in the arena, from where the fish then made a perceptually-guided decision. This interpretation is backed up by analyzing the trajectories in the context of attractors, revealing that the focus of attention was altered in a task-dependent manner. (iii) Distance estimation using a non-visual form of motion parallax. In the above experiments it is implicitly assumed that electric fish acquire spatial information like the position and distance of a target. How this is achieved dynamically has been addressed recently. Based on the properties of the electric field geometry, theoretical considerations indicated that relative movements might provide depth information. In a behavioral assay, I show that this novel form of electric parallax exists and is used across phylogenetically distant taxa of weakly electric fish (Apteronotus albifrons, Eigenmania virescens and Gnathonemus petersii). Notably, these species electrically sample the environment in temporally distinct ways (using discrete pulses or quasi-sinusoidal waves), suggesting an ubiquitous role for parallax in electric sensing. (iv) The role of multi-modal integration in socially relevant agonistic behaviour. Extending on the above results, I next addressed if passive as well as active electric sensory information can be used to evaluate more complex features of the environment. For this I turned to social interactions of the South American species Gymnotus omarorum to study if an electrical assessment of a competitor is possible. Based on modeling the sensory consequences of dyadic encounters, I showed that passive as well as active sensory information can drive agonistic interactions. This suggests that aggressive interactions may be triggered by information about contenders obtained through the active and passive electrosensory system. (v) Hierarchy as a social consequence of electric interactions. The above analysis indicated that active as well as passive electrolocation may contribute in a non-reciprocal manner to social interactions. Gymnotus omarorum then was tested in intra- and intersexual dyads in small plain arenas. A sex-independent dominant-subordinate status emerged after highly aggressive contests. Subordinates signaled their submission by retreating and emitting specific (submissive) electric signals. The emergence of a dominant-subordinate status was also observed in a larger arena after longer but milder contests with rare electric signaling of submission with a unique consequence: the persistence of dominance over time with no outcome reversion