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Manu S. Madhav

Other affiliations: University of British Columbia
Bio: Manu S. Madhav is an academic researcher from Johns Hopkins University. The author has contributed to research in topics: Electric fish & Jamming avoidance response. The author has an hindex of 9, co-authored 19 publications receiving 372 citations. Previous affiliations of Manu S. Madhav include University of British Columbia.

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TL;DR: In this article, the authors focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations.
Abstract: Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with feedback regulation, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations. We use examples from aquatic (electric fish station keeping and jamming avoidance), terrestrial (cockroach wall following) and aerial environments (flight control in moths) to highlight how one can use control theory to understand how feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

101 citations

Journal ArticleDOI
TL;DR: This work focuses on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations.
Abstract: Synopsis Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with regulation via feedback, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here, we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism’s response to perturbations. We use examples from aquatic (two behaviors performed by electric fish), terrestrial (following of walls by cockroaches), and aerial environments (flight control by moths) to highlight how one can use control theory to understand the way feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

97 citations

Journal ArticleDOI
01 Feb 2019-Nature
TL;DR: It is proposed that this rapid plasticity keeps the positional update in register with the movement of the rat in the external world over behavioural timescales, and shows that path-integration gain, previously thought to be a constant factor in the computation of location, is flexible and can be rapidly fine-tuned.
Abstract: Hippocampal place cells are spatially tuned neurons that serve as elements of a 'cognitive map' in the mammalian brain1. To detect the animal's location, place cells are thought to rely upon two interacting mechanisms: sensing the position of the animal relative to familiar landmarks2,3 and measuring the distance and direction that the animal has travelled from previously occupied locations4-7. The latter mechanism-known as path integration-requires a finely tuned gain factor that relates the animal's self-movement to the updating of position on the internal cognitive map, as well as external landmarks to correct the positional error that accumulates8,9. Models of hippocampal place cells and entorhinal grid cells based on path integration treat the path-integration gain as a constant9-14, but behavioural evidence in humans suggests that the gain is modifiable15. Here we show, using physiological evidence from rat hippocampal place cells, that the path-integration gain is a highly plastic variable that can be altered by persistent conflict between self-motion cues and feedback from external landmarks. In an augmented-reality system, visual landmarks were moved in proportion to the movement of a rat on a circular track, creating continuous conflict with path integration. Sustained exposure to this cue conflict resulted in predictable and prolonged recalibration of the path-integration gain, as estimated from the place cells after the landmarks were turned off. We propose that this rapid plasticity keeps the positional update in register with the movement of the rat in the external world over behavioural timescales. These results also demonstrate that visual landmarks not only provide a signal to correct cumulative error in the path-integration system4,8,16-19, but also rapidly fine-tune the integration computation itself.

63 citations

Journal ArticleDOI
TL;DR: The Social Envelope Response (SER) generally resulted in an increase of the envelope frequency during the course of a trial, suggesting that this behavior may be a mechanism for avoiding low-frequency social envelopes.
Abstract: SUMMARY Recent studies have shown that central nervous system neurons in weakly electric fish respond to artificially constructed electrosensory envelopes, but the behavioral relevance of such stimuli is unclear. Here we investigate the possibility that social context creates envelopes that drive behavior. When Eigenmannia virescens are in groups of three or more, the interactions between their pseudo-sinusoidal electric fields can generate ‘social envelopes’. We developed a simple mathematical prediction for how fish might respond to such social envelopes. To test this prediction, we measured the responses of E. virescens to stimuli consisting of two sinusoids, each outside the range of the Jamming Avoidance Response (JAR), that when added to the fish9s own electric field produced low-frequency (below 10 Hz) social envelopes. Fish changed their electric organ discharge (EOD) frequency in response to these envelopes, which we have termed the Social Envelope Response (SER). In 99% of trials, the direction of the SER was consistent with the mathematical prediction. The SER was strongest in response to the lowest initial envelope frequency tested (2 Hz) and depended on stimulus amplitude. The SER generally resulted in an increase of the envelope frequency during the course of a trial, suggesting that this behavior may be a mechanism for avoiding low-frequency social envelopes. Importantly, the direction of the SER was not predicted by the superposition of two JAR responses: the SER was insensitive to the amplitude ratio between the sinusoids used to generate the envelope, but was instead predicted by the sign of the difference of difference frequencies.

46 citations

Journal ArticleDOI
TL;DR: This work overcame the instability of the JAR in Eigenmannia virescens by closing a feedback loop around the behavioral response of the animal, and examined the intrinsic nonlinearity of the behavior using clamped frequency difference experiments to extend the model beyond the neighborhood of the equilibrium.
Abstract: The Jamming Avoidance Response, or JAR, in the weakly electric fish has been analyzed at all levels of organization, from whole-organism behavior down to specific ion channels. Nevertheless, a parsimonious description of the JAR behavior in terms of a dynamical system model has not been achieved at least in part due to the fact that 'avoidance' behaviors are both intrinsically unstable and nonlinear. We overcame the instability of the JAR in Eigenmannia virescens by closing a feedback loop around the behavioral response of the animal. Specifically, the instantaneous frequency of a jamming stimulus was tied to the fish's own electrogenic frequency by a feedback law. Without feedback, the fish's own frequency diverges from the stimulus frequency, but appropriate feedback stabilizes the behavior. After stabilizing the system, we measured the responses in the fish's instantaneous frequency to various stimuli. A delayed first-order linear system model fitted the behavior near the equilibrium. Coherence to white noise stimuli together with quantitative agreement across stimulus types supported this local linear model. Next, we examined the intrinsic nonlinearity of the behavior using clamped frequency difference experiments to extend the model beyond the neighborhood of the equilibrium. The resulting nonlinear model is composed of competing motor return and sensory escape terms. The model reproduces responses to step and ramp changes in the difference frequency (df) and predicts a 'snap-through' bifurcation as a function of dF that we confirmed experimentally.

32 citations


Cited by
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Journal Article
TL;DR: In this paper, two major figures in adaptive control provide a wealth of material for researchers, practitioners, and students to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs.
Abstract: This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

1,814 citations

Journal Article
TL;DR: In this paper, an archaeal light-driven chloride pump (NpHR) was developed for temporally precise optical inhibition of neural activity, allowing either knockout of single action potentials, or sustained blockade of spiking.
Abstract: Our understanding of the cellular implementation of systems-level neural processes like action, thought and emotion has been limited by the availability of tools to interrogate specific classes of neural cells within intact, living brain tissue. Here we identify and develop an archaeal light-driven chloride pump (NpHR) from Natronomonas pharaonis for temporally precise optical inhibition of neural activity. NpHR allows either knockout of single action potentials, or sustained blockade of spiking. NpHR is compatible with ChR2, the previous optical excitation technology we have described, in that the two opposing probes operate at similar light powers but with well-separated action spectra. NpHR, like ChR2, functions in mammals without exogenous cofactors, and the two probes can be integrated with calcium imaging in mammalian brain tissue for bidirectional optical modulation and readout of neural activity. Likewise, NpHR and ChR2 can be targeted together to Caenorhabditis elegans muscle and cholinergic motor neurons to control locomotion bidirectionally. NpHR and ChR2 form a complete system for multimodal, high-speed, genetically targeted, all-optical interrogation of living neural circuits.

1,520 citations

Book
01 Sep 2014
TL;DR: It is quite impossible to include in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages, so it becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer.
Abstract: WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

881 citations

01 Jul 2005

852 citations