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Dabaghian Y. Grid cells, border cells, and discrete complex analysis. Front Comput Neurosci 2023; 17:1242300. [PMID: 37881247 PMCID: PMC10595009 DOI: 10.3389/fncom.2023.1242300] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Accepted: 09/22/2023] [Indexed: 10/27/2023] Open
Abstract
We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity toward the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.
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Affiliation(s)
- Yuri Dabaghian
- Department of Neurology, The University of Texas, McGovern Medical Center at Houston, Houston, TX, United States
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2
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Abstract
A schema refers to a structured body of prior knowledge that captures common patterns across related experiences. Schemas have been studied separately in the realms of episodic memory and spatial navigation across different species and have been grounded in theories of memory consolidation, but there has been little attempt to integrate our understanding across domains, particularly in humans. We propose that experiences during navigation with many similarly structured environments give rise to the formation of spatial schemas (for example, the expected layout of modern cities) that share properties with but are distinct from cognitive maps (for example, the memory of a modern city) and event schemas (such as expected events in a modern city) at both cognitive and neural levels. We describe earlier theoretical frameworks and empirical findings relevant to spatial schemas, along with more targeted investigations of spatial schemas in human and non-human animals. Consideration of architecture and urban analytics, including the influence of scale and regionalization, on different properties of spatial schemas may provide a powerful approach to advance our understanding of spatial schemas.
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Abstract
A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.
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Dabaghian Y. From Topological Analyses to Functional Modeling: The Case of Hippocampus. Front Comput Neurosci 2021; 14:593166. [PMID: 33505262 PMCID: PMC7829363 DOI: 10.3389/fncom.2020.593166] [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: 08/09/2020] [Accepted: 12/02/2020] [Indexed: 11/13/2022] Open
Abstract
Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.
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Affiliation(s)
- Yuri Dabaghian
- Department of Neurology, The University of Texas McGovern Medical School, Houston, TX, United States
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5
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Brown RE. Donald O. Hebb and the Organization of Behavior: 17 years in the writing. Mol Brain 2020; 13:55. [PMID: 32252813 PMCID: PMC7137474 DOI: 10.1186/s13041-020-00567-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 02/18/2020] [Indexed: 02/06/2023] Open
Abstract
The Organization of Behavior has played a significant part in the development of behavioural neuroscience for the last 70 years. This book introduced the concepts of the "Hebb synapse", the "Hebbian cell assembly" and the "Phase sequence". The most frequently cited of these is the Hebb synapse, but the cell assembly may be Hebb's most important contribution. Even after 70 years, Hebb's theory is still relevant because it is a general framework for relating behavior to synaptic organization through the development of neural networks. The Organization of Behavior was Hebb's 40th publication. His first published papers in 1937 were on the innate organization of the visual system and he first used the phrase "the organization of behavior" in 1938. However, Hebb wrote a number of unpublished papers between 1932 and 1945 in which he developed the ideas published in The Organization of Behavior. Thus, the concept of the neural organization of behavior was central to Hebb's thinking from the beginning of his academic career. But his thinking about the organization of behavior in 1949 was different from what it was between 1932 and 1937. This paper examines Hebb's early ideas on the neural basis of behavior and attempts to trace the rather arduous series of steps through which he developed these ideas into the book that was published as The Organization of Behavior. Using the 1946 typescript and Hebb's correspondence we can see a number of changes made in the book before it was published. Finally, a number of issues arising from the book, and the importance of the book today are discussed.
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Affiliation(s)
- Richard E Brown
- Department of Psychology and Neuroscience, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada.
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Momennejad I. Learning Structures: Predictive Representations, Replay, and Generalization. Curr Opin Behav Sci 2020; 32:155-166. [DOI: 10.1016/j.cobeha.2020.02.017] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
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Babichev A, Morozov D, Dabaghian Y. Replays of spatial memories suppress topological fluctuations in cognitive map. Netw Neurosci 2019; 3:707-724. [PMID: 31410375 PMCID: PMC6663216 DOI: 10.1162/netn_a_00076] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Accepted: 12/18/2018] [Indexed: 11/04/2022] Open
Abstract
The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space-a cognitive map. These cells do not only exhibit location-specific spiking during navigation, but also may rapidly replay the navigated routs through endogenous dynamics of the hippocampal network. Physiologically, such reactivations are viewed as manifestations of "memory replays" that help to learn new information and to consolidate previously acquired memories by reinforcing synapses in the parahippocampal networks. Below we propose a computational model of these processes that allows assessing the effect of replays on acquiring a robust topological map of the environment and demonstrate that replays may play a key role in stabilizing the hippocampal representation of space.
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Affiliation(s)
- Andrey Babichev
- Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA
| | | | - Yuri Dabaghian
- Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA
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Dabaghian Y. Through synapses to spatial memory maps via a topological model. Sci Rep 2019; 9:572. [PMID: 30679520 PMCID: PMC6345962 DOI: 10.1038/s41598-018-36807-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2018] [Accepted: 11/22/2018] [Indexed: 12/16/2022] Open
Abstract
Various neurophysiological and cognitive functions are based on transferring information between spiking neurons via a complex system of synaptic connections. In particular, the capacity of presynaptic inputs to influence the postsynaptic outputs–the efficacy of the synapses–plays a principal role in all aspects of hippocampal neurophysiology. However, a direct link between the information processed at the level of individual synapses and the animal’s ability to form memories at the organismal level has not yet been fully understood. Here, we investigate the effect of synaptic transmission probabilities on the ability of the hippocampal place cell ensembles to produce a cognitive map of the environment. Using methods from algebraic topology, we find that weakening synaptic connections increase spatial learning times, produce topological defects in the large-scale representation of the ambient space and restrict the range of parameters for which place cell ensembles are capable of producing a map with correct topological structure. On the other hand, the results indicate a possibility of compensatory phenomena, namely that spatial learning deficiencies may be mitigated through enhancement of neuronal activity.
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Affiliation(s)
- Yuri Dabaghian
- Department of Neurology, The University of Texas McGovern Medical School, 6431 Fannin St, Houston, TX, 77030, USA.
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Babichev A, Morozov D, Dabaghian Y. Robust spatial memory maps encoded by networks with transient connections. PLoS Comput Biol 2018; 14:e1006433. [PMID: 30226836 PMCID: PMC6161922 DOI: 10.1371/journal.pcbi.1006433] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Revised: 09/28/2018] [Accepted: 08/15/2018] [Indexed: 11/25/2022] Open
Abstract
The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space—a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long period. However, the neuronal substrate that produces this map is transient: the synaptic connections in the hippocampus and in the downstream neuronal networks never cease to form and to deteriorate at a rapid rate. How can the brain maintain a robust, reliable representation of space using a network that constantly changes its architecture? We address this question using a computational framework that allows evaluating the effect produced by the decaying connections between simulated hippocampal neurons on the properties of the cognitive map. Using novel Algebraic Topology techniques, we demonstrate that emergence of stable cognitive maps produced by networks with transient architectures is a generic phenomenon. The model also points out that deterioration of the cognitive map caused by weakening or lost connections between neurons may be compensated by simulating the neuronal activity. Lastly, the model explicates the importance of the complementary learning systems for processing spatial information at different levels of spatiotemporal granularity. The reliability of our memories is nothing short of remarkable. Synaptic connections between neurons appear and disappear at a rapid rate, and the resulting networks constantly change their architecture due to various forms of neural plasticity. How can the brain develop a reliable representation of the world, learn and retain memories despite, or perhaps due to, such complex dynamics? Below we address these questions by modeling mechanisms of spatial learning in the hippocampal network, using novel algebraic topology methods. We demonstrate that although the functional units of the hippocampal network—the place cell assemblies—are unstable structures that may appear and disappear, the spatial memory map produced by a sufficiently large population of such assemblies robustly captures the topological structure of the environment.
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Affiliation(s)
- Andrey Babichev
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas, United States of America
| | - Dmitriy Morozov
- Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Berkeley Institute for Data Science, University of California - Berkeley, Berkeley, California, United States of America
| | - Yuri Dabaghian
- Department of Neurology, The University of Texas McGovern Medical School, Houston, Texas, United States of America
- * E-mail:
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Zhao M. Human spatial representation: what we cannot learn from the studies of rodent navigation. J Neurophysiol 2018; 120:2453-2465. [PMID: 30133384 DOI: 10.1152/jn.00781.2017] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Studies of human and rodent navigation often reveal a remarkable cross-species similarity between the cognitive and neural mechanisms of navigation. Such cross-species resemblance often overshadows some critical differences between how humans and nonhuman animals navigate. In this review, I propose that a navigation system requires both a storage system (i.e., representing spatial information) and a positioning system (i.e., sensing spatial information) to operate. I then argue that the way humans represent spatial information is different from that inferred from the cellular activity observed during rodent navigation. Such difference spans the whole hierarchy of spatial representation, from representing the structure of an environment to the representation of subregions of an environment, routes and paths, and the distance and direction relative to a goal location. These cross-species inconsistencies suggest that what we learn from rodent navigation does not always transfer to human navigation. Finally, I argue for closing the loop for the dominant, unidirectional animal-to-human approach in navigation research so that insights from behavioral studies of human navigation may also flow back to shed light on the cellular mechanisms of navigation for both humans and other mammals (i.e., a human-to-animal approach).
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Affiliation(s)
- Mintao Zhao
- School of Psychology, University of East Anglia , Norwich , United Kingdom.,Department of Human Perception, Cognition, and Action, Max Planck Institute for Biological Cybernetics , Tübingen , Germany
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Babichev A, Dabaghian YA. Topological Schemas of Memory Spaces. Front Comput Neurosci 2018; 12:27. [PMID: 29740306 PMCID: PMC5928258 DOI: 10.3389/fncom.2018.00027] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Accepted: 04/04/2018] [Indexed: 11/19/2022] Open
Abstract
Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.
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Affiliation(s)
- Andrey Babichev
- Department of Computational and Applied Mathematics, Rice University, Houston, TX, United States
| | - Yuri A Dabaghian
- Department of Computational and Applied Mathematics, Rice University, Houston, TX, United States.,Department of Neurology, The University of Texas McGovern Medical School, Houston, TX, United States
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12
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Abstract
One of the mysteries of memory is that it can last despite changes in the underlying synaptic architecture. How can we, for example, maintain an internal spatial map of an environment over months or years when the underlying network is full of transient connections? In the following, we propose a computational model for describing the emergence of the hippocampal cognitive map in a network of transient place cell assemblies and demonstrate, using methods of algebraic topology, how such a network can maintain spatial memory over time.
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Basso E, Arai M, Dabaghian Y. Gamma Synchronization Influences Map Formation Time in a Topological Model of Spatial Learning. PLoS Comput Biol 2016; 12:e1005114. [PMID: 27636199 PMCID: PMC5026372 DOI: 10.1371/journal.pcbi.1005114] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Accepted: 08/20/2016] [Indexed: 12/30/2022] Open
Abstract
The mammalian hippocampus plays a crucial role in producing a cognitive map of space-an internalized representation of the animal's environment. We have previously shown that it is possible to model this map formation using a topological framework, in which information about the environment is transmitted through the temporal organization of neuronal spiking activity, particularly those occasions in which the firing of different place cells overlaps. In this paper, we discuss how gamma rhythm, one of the main components of the extracellular electrical field potential affects the efficiency of place cell map formation. Using methods of algebraic topology and the maximal entropy principle, we demonstrate that gamma modulation synchronizes the spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales.
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Affiliation(s)
- Edward Basso
- Department of Physics, Rice University, Houston, Texas, United States of America
| | - Mamiko Arai
- Department of Mathematics, Tokyo Women’s Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo, Japan
| | - Yuri Dabaghian
- Jan and Dan Duncan Neurological Research Institute, Baylor College of Medicine, Houston, Texas, United States of America
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas, United States of America
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Hoffman K, Babichev A, Dabaghian Y. A model of topological mapping of space in bat hippocampus. Hippocampus 2016; 26:1345-53. [PMID: 27312850 DOI: 10.1002/hipo.22610] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2016] [Revised: 06/06/2016] [Accepted: 06/07/2016] [Indexed: 11/10/2022]
Abstract
The mammalian hippocampus plays a key role in spatial learning and memory, but the exact nature of the hippocampal representation of space is still being explored. Recently, there has been a fair amount of success in modeling hippocampal spatial maps in rats, assuming a topological perspective on spatial information processing. In this article, we use the topological approach to study the formation of a 3D spatial map in bats, which produces several insights into neurophysiological mechanisms of the hippocampal spatial leaning. First, we demonstrate that, in order to produce accurate maps of the environment, place cell should be organized into functional groups, which can be interpreted as cell assemblies. Second, the model suggests that the readout neurons in these cell assemblies should function as integrators of synaptic inputs, rather than detectors of place cells' coactivity, which allows estimating the integration time window. Lastly, the model suggests that, in contrast with relatively slow moving rats, suppressing θ-precession in bats improves the place cells capacity to encode spatial maps, which is consistent with the experimental observations. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Kentaro Hoffman
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas
| | - Andrey Babichev
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas.,Baylor College of Medicine, Jan and Dan Duncan Neurological Research Institute, Department of Pediatrics Neurology, Houston, Texas, USA
| | - Yuri Dabaghian
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas. .,Baylor College of Medicine, Jan and Dan Duncan Neurological Research Institute, Department of Pediatrics Neurology, Houston, Texas, USA.
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Babichev A, Ji D, Mémoli F, Dabaghian YA. A Topological Model of the Hippocampal Cell Assembly Network. Front Comput Neurosci 2016; 10:50. [PMID: 27313527 PMCID: PMC4889593 DOI: 10.3389/fncom.2016.00050] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2015] [Accepted: 05/17/2016] [Indexed: 12/22/2022] Open
Abstract
It is widely accepted that the hippocampal place cells' spiking activity produces a cognitive map of space. However, many details of this representation's physiological mechanism remain unknown. For example, it is believed that the place cells exhibiting frequent coactivity form functionally interconnected groups-place cell assemblies-that drive readout neurons in the downstream networks. However, the sheer number of coactive combinations is extremely large, which implies that only a small fraction of them actually gives rise to cell assemblies. The physiological processes responsible for selecting the winning combinations are highly complex and are usually modeled via detailed synaptic and structural plasticity mechanisms. Here we propose an alternative approach that allows modeling the cell assembly network directly, based on a small number of phenomenological selection rules. We then demonstrate that the selected population of place cell assemblies correctly encodes the topology of the environment in biologically plausible time, and may serve as a schematic model of the hippocampal network.
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Affiliation(s)
- Andrey Babichev
- Jan and Dan Duncan Neurological Research Institute, Baylor College of MedicineHouston, TX, USA; Department of Computational and Applied Mathematics, Rice UniversityHouston, TX, USA
| | - Daoyun Ji
- Department of Neuroscience, Baylor College of Medicine Houston, TX, USA
| | - Facundo Mémoli
- Department of Mathematics, Ohio State University Columbus, OH, USA
| | - Yuri A Dabaghian
- Jan and Dan Duncan Neurological Research Institute, Baylor College of MedicineHouston, TX, USA; Department of Computational and Applied Mathematics, Rice UniversityHouston, TX, USA
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