1
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Mininni CJ, Zanutto BS. Constructing neural networks with pre-specified dynamics. Sci Rep 2024; 14:18860. [PMID: 39143351 PMCID: PMC11324765 DOI: 10.1038/s41598-024-69747-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 08/08/2024] [Indexed: 08/16/2024] Open
Abstract
A main goal in neuroscience is to understand the computations carried out by neural populations that give animals their cognitive skills. Neural network models allow to formulate explicit hypotheses regarding the algorithms instantiated in the dynamics of a neural population, its firing statistics, and the underlying connectivity. Neural networks can be defined by a small set of parameters, carefully chosen to procure specific capabilities, or by a large set of free parameters, fitted with optimization algorithms that minimize a given loss function. In this work we alternatively propose a method to make a detailed adjustment of the network dynamics and firing statistic to better answer questions that link dynamics, structure, and function. Our algorithm-termed generalised Firing-to-Parameter (gFTP)-provides a way to construct binary recurrent neural networks whose dynamics strictly follows a user pre-specified transition graph that details the transitions between population firing states triggered by stimulus presentations. Our main contribution is a procedure that detects when a transition graph is not realisable in terms of a neural network, and makes the necessary modifications in order to obtain a new transition graph that is realisable and preserves all the information encoded in the transitions of the original graph. With a realisable transition graph, gFTP assigns values to the network firing states associated with each node in the graph, and finds the synaptic weight matrices by solving a set of linear separation problems. We test gFTP performance by constructing networks with random dynamics, continuous attractor-like dynamics that encode position in 2-dimensional space, and discrete attractor dynamics. We then show how gFTP can be employed as a tool to explore the link between structure, function, and the algorithms instantiated in the network dynamics.
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Affiliation(s)
- Camilo J Mininni
- Instituto de Biología y Medicina Experimental, Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina.
| | - B Silvano Zanutto
- Instituto de Biología y Medicina Experimental, Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina
- Instituto de Ingeniería Biomédica, Universidad de Buenos Aires, Buenos Aires, Argentina
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2
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Dyer EL, Kording K. Why the simplest explanation isn't always the best. Proc Natl Acad Sci U S A 2023; 120:e2319169120. [PMID: 38117857 PMCID: PMC10756184 DOI: 10.1073/pnas.2319169120] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2023] Open
Affiliation(s)
- Eva L. Dyer
- Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA30332
| | - Konrad Kording
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA19104
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3
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Weiss O, Bounds HA, Adesnik H, Coen-Cagli R. Modeling the diverse effects of divisive normalization on noise correlations. PLoS Comput Biol 2023; 19:e1011667. [PMID: 38033166 PMCID: PMC10715670 DOI: 10.1371/journal.pcbi.1011667] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Revised: 12/12/2023] [Accepted: 11/07/2023] [Indexed: 12/02/2023] Open
Abstract
Divisive normalization, a prominent descriptive model of neural activity, is employed by theories of neural coding across many different brain areas. Yet, the relationship between normalization and the statistics of neural responses beyond single neurons remains largely unexplored. Here we focus on noise correlations, a widely studied pairwise statistic, because its stimulus and state dependence plays a central role in neural coding. Existing models of covariability typically ignore normalization despite empirical evidence suggesting it affects correlation structure in neural populations. We therefore propose a pairwise stochastic divisive normalization model that accounts for the effects of normalization and other factors on covariability. We first show that normalization modulates noise correlations in qualitatively different ways depending on whether normalization is shared between neurons, and we discuss how to infer when normalization signals are shared. We then apply our model to calcium imaging data from mouse primary visual cortex (V1), and find that it accurately fits the data, often outperforming a popular alternative model of correlations. Our analysis indicates that normalization signals are often shared between V1 neurons in this dataset. Our model will enable quantifying the relation between normalization and covariability in a broad range of neural systems, which could provide new constraints on circuit mechanisms of normalization and their role in information transmission and representation.
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Affiliation(s)
- Oren Weiss
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, New York, United States of America
| | - Hayley A. Bounds
- Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California, United States of America
| | - Hillel Adesnik
- Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California, United States of America
- Department of Molecular and Cell Biology, University of California, Berkeley, Berkeley, California, United States of America
| | - Ruben Coen-Cagli
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, New York, United States of America
- Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, New York, United States of America
- Department of Ophthalmology and Visual Sciences, Albert Einstein College of Medicine, Bronx, New York, United States of America
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4
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White SM, Morningstar MD, De Falco E, Linsenbardt DN, Ma B, Parks MA, Czachowski CL, Lapish CC. Flexible coding schemes in dorsomedial prefrontal cortex underlie decision-making during delay discounting. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.06.15.545101. [PMID: 37398190 PMCID: PMC10312702 DOI: 10.1101/2023.06.15.545101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/04/2023]
Abstract
Determining how an agent decides between a small, immediate versus a larger, delayed reward has provided insight into the psychological and neural basis of decision-making. The tendency to excessively discount the value of delayed rewards is thought to reflect deficits in brain regions critical for impulse control such as the prefrontal cortex (PFC). This study tested the hypothesis that dorsomedial PFC (dmPFC) is critically involved in flexibly managing neural representations of strategies that limit impulsive choices. Optogenetic silencing of neurons in the rat dmPFC increased impulsive choices at an 8 sec, but not 4 sec, delay. Neural recordings from dmPFC ensembles revealed that, at the 8-sec delay, the encoding landscape transitions to reflect a deliberative-like process rather than the schema-like processes observed at the 4-sec delay. These findings show that changes in the encoding landscape reflect changes in task demands and that dmPFC is uniquely involved in decisions requiring deliberation.
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5
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Hu B, Guan ZH, Chen G, Chen CLP. Neuroscience and Network Dynamics Toward Brain-Inspired Intelligence. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:10214-10227. [PMID: 33909581 DOI: 10.1109/tcyb.2021.3071110] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications.
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6
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Miller CT, Gire D, Hoke K, Huk AC, Kelley D, Leopold DA, Smear MC, Theunissen F, Yartsev M, Niell CM. Natural behavior is the language of the brain. Curr Biol 2022; 32:R482-R493. [PMID: 35609550 PMCID: PMC10082559 DOI: 10.1016/j.cub.2022.03.031] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The breadth and complexity of natural behaviors inspires awe. Understanding how our perceptions, actions, and internal thoughts arise from evolved circuits in the brain has motivated neuroscientists for generations. Researchers have traditionally approached this question by focusing on stereotyped behaviors, either natural or trained, in a limited number of model species. This approach has allowed for the isolation and systematic study of specific brain operations, which has greatly advanced our understanding of the circuits involved. At the same time, the emphasis on experimental reductionism has left most aspects of the natural behaviors that have shaped the evolution of the brain largely unexplored. However, emerging technologies and analytical tools make it possible to comprehensively link natural behaviors to neural activity across a broad range of ethological contexts and timescales, heralding new modes of neuroscience focused on natural behaviors. Here we describe a three-part roadmap that aims to leverage the wealth of behaviors in their naturally occurring distributions, linking their variance with that of underlying neural processes to understand how the brain is able to successfully navigate the everyday challenges of animals' social and ecological landscapes. To achieve this aim, experimenters must harness one challenge faced by all neurobiological systems, namely variability, in order to gain new insights into the language of the brain.
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Affiliation(s)
- Cory T Miller
- Cortical Systems and Behavior Laboratory, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92039, USA.
| | - David Gire
- Department of Psychology, University of Washington, Guthrie Hall, Seattle, WA 98105, USA
| | - Kim Hoke
- Department of Biology, Colorado State University, 1878 Campus Delivery, Fort Collins, CO 80523, USA
| | - Alexander C Huk
- Center for Perceptual Systems, Departments of Neuroscience and Psychology, University of Texas at Austin, 116 Inner Campus Drive, Austin, TX 78712, USA
| | - Darcy Kelley
- Department of Biological Sciences, Columbia University, 1212 Amsterdam Avenue, New York, NY 10027, USA
| | - David A Leopold
- Section of Cognitive Neurophysiology and Imaging, National Institute of Mental Health, 49 Convent Drive, Bethesda, MD 20892, USA
| | - Matthew C Smear
- Department of Psychology and Institute of Neuroscience, University of Oregon, 1227 University Street, Eugene, OR 97403, USA
| | - Frederic Theunissen
- Department of Psychology, University of California Berkeley, 2121 Berkeley Way, Berkeley, CA 94720, USA
| | - Michael Yartsev
- Department of Bioengineering, University of California Berkeley, 306 Stanley Hall, Berkeley, CA 94720, USA
| | - Cristopher M Niell
- Department of Biology and Institute of Neuroscience, University of Oregon, 222 Huestis Hall, Eugene, OR 97403, USA.
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7
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Sokoloski S, Aschner A, Coen-Cagli R. Modelling the neural code in large populations of correlated neurons. eLife 2021; 10:64615. [PMID: 34608865 PMCID: PMC8577837 DOI: 10.7554/elife.64615] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Accepted: 10/01/2021] [Indexed: 01/02/2023] Open
Abstract
Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper, we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.
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Affiliation(s)
- Sacha Sokoloski
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, United States.,Institute for Ophthalmic Research, University of Tübingen, Tübingen, Germany
| | - Amir Aschner
- Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, United States
| | - Ruben Coen-Cagli
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, United States.,Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, United States
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8
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Hurwitz C, Kudryashova N, Onken A, Hennig MH. Building population models for large-scale neural recordings: Opportunities and pitfalls. Curr Opin Neurobiol 2021; 70:64-73. [PMID: 34411907 DOI: 10.1016/j.conb.2021.07.003] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 06/11/2021] [Accepted: 07/14/2021] [Indexed: 11/15/2022]
Abstract
Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here, we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide.
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Affiliation(s)
- Cole Hurwitz
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom
| | - Nina Kudryashova
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom
| | - Arno Onken
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom
| | - Matthias H Hennig
- University of Edinburgh, Institute for Adaptive and Neural Computation Edinburgh, EH8 9AB, United Kingdom.
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9
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Quinn KR, Seillier L, Butts DA, Nienborg H. Decision-related feedback in visual cortex lacks spatial selectivity. Nat Commun 2021; 12:4473. [PMID: 34294703 PMCID: PMC8298450 DOI: 10.1038/s41467-021-24629-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 06/22/2021] [Indexed: 11/21/2022] Open
Abstract
Feedback in the brain is thought to convey contextual information that underlies our flexibility to perform different tasks. Empirical and computational work on the visual system suggests this is achieved by targeting task-relevant neuronal subpopulations. We combine two tasks, each resulting in selective modulation by feedback, to test whether the feedback reflected the combination of both selectivities. We used visual feature-discrimination specified at one of two possible locations and uncoupled the decision formation from motor plans to report it, while recording in macaque mid-level visual areas. Here we show that although the behavior is spatially selective, using only task-relevant information, modulation by decision-related feedback is spatially unselective. Population responses reveal similar stimulus-choice alignments irrespective of stimulus relevance. The results suggest a common mechanism across tasks, independent of the spatial selectivity these tasks demand. This may reflect biological constraints and facilitate generalization across tasks. Our findings also support a previously hypothesized link between feature-based attention and decision-related activity. Feedback modulates visual neurons, thought to help achieve flexible task performance. Here, the authors show decision-related feedback is not only relayed to task-relevant neurons, suggesting a broader mechanism and supporting a previously hypothesized link to feature-based attention.
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Affiliation(s)
| | | | - Daniel A Butts
- Department of Biology and Program in Neuroscience and Cognitive Science, University of Maryland, College Park, MD, USA
| | - Hendrikje Nienborg
- Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health, Bethesda, MD, USA.
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10
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Niell CM, Scanziani M. How Cortical Circuits Implement Cortical Computations: Mouse Visual Cortex as a Model. Annu Rev Neurosci 2021; 44:517-546. [PMID: 33914591 PMCID: PMC9925090 DOI: 10.1146/annurev-neuro-102320-085825] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The mouse, as a model organism to study the brain, gives us unprecedented experimental access to the mammalian cerebral cortex. By determining the cortex's cellular composition, revealing the interaction between its different components, and systematically perturbing these components, we are obtaining mechanistic insight into some of the most basic properties of cortical function. In this review, we describe recent advances in our understanding of how circuits of cortical neurons implement computations, as revealed by the study of mouse primary visual cortex. Further, we discuss how studying the mouse has broadened our understanding of the range of computations performed by visual cortex. Finally, we address how future approaches will fulfill the promise of the mouse in elucidating fundamental operations of cortex.
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Affiliation(s)
- Cristopher M. Niell
- Department of Biology and Institute of Neuroscience, University of Oregon, Eugene, Oregon 97403, USA
| | - Massimo Scanziani
- Department of Physiology and Howard Hughes Medical Institute, University of California San Francisco, San Francisco, California 94158, USA;
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11
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Abstract
Complex behaviors are often driven by an internal model, which integrates sensory information over time and facilitates long-term planning to reach subjective goals. A fundamental challenge in neuroscience is, How can we use behavior and neural activity to understand this internal model and its dynamic latent variables? Here we interpret behavioral data by assuming an agent behaves rationally—that is, it takes actions that optimize its subjective reward according to its understanding of the task and its relevant causal variables. We apply a method, inverse rational control (IRC), to learn an agent’s internal model and reward function by maximizing the likelihood of its measured sensory observations and actions. This thereby extracts rational and interpretable thoughts of the agent from its behavior. We also provide a framework for interpreting encoding, recoding, and decoding of neural data in light of this rational model for behavior. When applied to behavioral and neural data from simulated agents performing suboptimally on a naturalistic foraging task, this method successfully recovers their internal model and reward function, as well as the Markovian computational dynamics within the neural manifold that represent the task. This work lays a foundation for discovering how the brain represents and computes with dynamic latent variables.
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Affiliation(s)
- Zhengwei Wu
- Department of Neuroscience, Baylor College of Medicine, Houston, TX 77030
- Department of Electrical and Computer Engineering, Rice University, Houston, TX 77030
- Center for Neuroscience and Artificial Intelligence, Baylor College of Medicine, Houston, TX 77030
| | - Minhae Kwon
- Department of Neuroscience, Baylor College of Medicine, Houston, TX 77030
- Department of Electrical and Computer Engineering, Rice University, Houston, TX 77030
- Center for Neuroscience and Artificial Intelligence, Baylor College of Medicine, Houston, TX 77030
| | - Saurabh Daptardar
- Department of Electrical and Computer Engineering, Rice University, Houston, TX 77030
- Geo Core Data, Atomic Maps, Google, Mountain View, CA 94043
| | - Paul Schrater
- Department of Psychology, University of Minnesota, Minneapolis, MN 55455
- Department of Computer Science, University of Minnesota, Minneapolis, MN 55455
| | - Xaq Pitkow
- Department of Neuroscience, Baylor College of Medicine, Houston, TX 77030;
- Department of Electrical and Computer Engineering, Rice University, Houston, TX 77030
- Center for Neuroscience and Artificial Intelligence, Baylor College of Medicine, Houston, TX 77030
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12
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Johnson JK, Geng S, Hoffman MW, Adesnik H, Wessel R. Precision multidimensional neural population code recovered from single intracellular recordings. Sci Rep 2020; 10:15997. [PMID: 32994474 PMCID: PMC7524839 DOI: 10.1038/s41598-020-72936-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Accepted: 08/20/2020] [Indexed: 11/08/2022] Open
Abstract
Neurons in sensory cortices are more naturally and deeply integrated than any current neural population recording tools (e.g. electrode arrays, fluorescence imaging). Two concepts facilitate efforts to observe population neural code with single-cell recordings. First, even the highest quality single-cell recording studies find a fraction of the stimulus information in high-dimensional population recordings. Finding any of this missing information provides proof of principle. Second, neurons and neural populations are understood as coupled nonlinear differential equations. Therefore, fitted ordinary differential equations provide a basis for single-trial single-cell stimulus decoding. We obtained intracellular recordings of fluctuating transmembrane current and potential in mouse visual cortex during stimulation with drifting gratings. We use mean deflection from baseline when comparing to prior single-cell studies because action potentials are too sparse and the deflection response to drifting grating stimuli (e.g. tuning curves) are well studied. Equation-based decoders allowed more precise single-trial stimulus discrimination than tuning-curve-base decoders. Performance varied across recorded signal types in a manner consistent with population recording studies and both classification bases evinced distinct stimulus-evoked phases of population dynamics, providing further corroboration. Naturally and deeply integrated observations of population dynamics would be invaluable. We offer proof of principle and a versatile framework.
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Affiliation(s)
| | | | | | | | - Ralf Wessel
- Washington University in St. Louis, St. Louis, USA
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13
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Pollock E, Jazayeri M. Engineering recurrent neural networks from task-relevant manifolds and dynamics. PLoS Comput Biol 2020; 16:e1008128. [PMID: 32785228 PMCID: PMC7446915 DOI: 10.1371/journal.pcbi.1008128] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Revised: 08/24/2020] [Accepted: 07/08/2020] [Indexed: 12/11/2022] Open
Abstract
Many cognitive processes involve transformations of distributed representations in neural populations, creating a need for population-level models. Recurrent neural network models fulfill this need, but there are many open questions about how their connectivity gives rise to dynamics that solve a task. Here, we present a method for finding the connectivity of networks for which the dynamics are specified to solve a task in an interpretable way. We apply our method to a working memory task by synthesizing a network that implements a drift-diffusion process over a ring-shaped manifold. We also use our method to demonstrate how inputs can be used to control network dynamics for cognitive flexibility and explore the relationship between representation geometry and network capacity. Our work fits within the broader context of understanding neural computations as dynamics over relatively low-dimensional manifolds formed by correlated patterns of neurons.
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Affiliation(s)
- Eli Pollock
- Department of Brain & Cognitive Sciences, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Mehrdad Jazayeri
- Department of Brain & Cognitive Sciences, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
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14
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Abstract
With modern neurophysiological methods able to record neural activity throughout the visual pathway in the context of arbitrarily complex visual stimulation, our understanding of visual system function is becoming limited by the available models of visual neurons that can be directly related to such data. Different forms of statistical models are now being used to probe the cellular and circuit mechanisms shaping neural activity, understand how neural selectivity to complex visual features is computed, and derive the ways in which neurons contribute to systems-level visual processing. However, models that are able to more accurately reproduce observed neural activity often defy simple interpretations. As a result, rather than being used solely to connect with existing theories of visual processing, statistical modeling will increasingly drive the evolution of more sophisticated theories.
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Affiliation(s)
- Daniel A. Butts
- Department of Biology and Program in Neuroscience and Cognitive Science, University of Maryland, College Park, Maryland 20742, USA
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