Navigating with grid and place cells in cluttered environments

A spatial transformation-based CAN model for information integration within grid cell modules

The hippocampal-entorhinal circuit is considered to play an important role in the spatial cognition of animals. However, the mechanism of the information flow within the circuit and its contribution to the function of the grid-cell module are still topics of discussion. Prevailing theories suggest that grid cells are primarily influenced by self-motion inputs from the Medial Entorhinal Cortex, with place cells serving a secondary role by contributing to the visual calibration of grid cells. However, recent evidence suggests that both self-motion inputs and visual cues may collaboratively contribute to the formation of grid-like patterns. In this paper, we introduce a novel Continuous Attractor Network model based on a spatial transformation mechanism. This mechanism enables the integration of self-motion inputs and visual cues within grid-cell modules, synergistically driving the formation of grid-like patterns. From the perspective of individual neurons within the network, our model successfully replicates grid firing patterns. From the view of neural population activity within the network, the network can form and drive the activated bump, which describes the characteristic feature of grid-cell modules, namely, path integration. Through further exploration and experimentation, our model can exhibit significant performance in path integration. This study provides a new insight into understanding the mechanism of how the self-motion and visual inputs contribute to the neural activity within grid-cell modules. Furthermore, it provides theoretical support for achieving accurate path integration, which holds substantial implications for various applications requiring spatial navigation and mapping.

A theory of hippocampal function: New developments

We develop further here the only quantitative theory of the storage of information in the hippocampal episodic memory system and its recall back to the neocortex. The theory is upgraded to account for a revolution in understanding of spatial representations in the primate, including human, hippocampus, that go beyond the place where the individual is located, to the location being viewed in a scene. This is fundamental to much primate episodic memory and navigation: functions supported in humans by pathways that build 'where' spatial view representations by feature combinations in a ventromedial visual cortical stream, separate from those for 'what' object and face information to the inferior temporal visual cortex, and for reward information from the orbitofrontal cortex. Key new computational developments include the capacity of the CA3 attractor network for storing whole charts of space; how the correlations inherent in self-organizing continuous spatial representations impact the storage capacity; how the CA3 network can combine continuous spatial and discrete object and reward representations; the roles of the rewards that reach the hippocampus in the later consolidation into long-term memory in part via cholinergic pathways from the orbitofrontal cortex; and new ways of analysing neocortical information storage using Potts networks.

Two what, two where, visual cortical streams in humans

ROLLS, E. T. Two What, Two Where, Visual Cortical Streams in Humans. NEUROSCI BIOBEHAV REV 2024. Recent cortical connectivity investigations lead to new concepts about 'What' and 'Where' visual cortical streams in humans, and how they connect to other cortical systems. A ventrolateral 'What' visual stream leads to the inferior temporal visual cortex for object and face identity, and provides 'What' information to the hippocampal episodic memory system, the anterior temporal lobe semantic system, and the orbitofrontal cortex emotion system. A superior temporal sulcus (STS) 'What' visual stream utilising connectivity from the temporal and parietal visual cortex responds to moving objects and faces, and face expression, and connects to the orbitofrontal cortex for emotion and social behaviour. A ventromedial 'Where' visual stream builds feature combinations for scenes, and provides 'Where' inputs via the parahippocampal scene area to the hippocampal episodic memory system that are also useful for landmark-based navigation. The dorsal 'Where' visual pathway to the parietal cortex provides for actions in space, but also provides coordinate transforms to provide inputs to the parahippocampal scene area for self-motion update of locations in scenes in the dark or when the view is obscured.

Mice identify subgoal locations through an action-driven mapping process

Mammals form mental maps of the environments by exploring their surroundings. Here, we investigate which elements of exploration are important for this process. We studied mouse escape behavior, in which mice are known to memorize subgoal locations-obstacle edges-to execute efficient escape routes to shelter. To test the role of exploratory actions, we developed closed-loop neural-stimulation protocols for interrupting various actions while mice explored. We found that blocking running movements directed at obstacle edges prevented subgoal learning; however, blocking several control movements had no effect. Reinforcement learning simulations and analysis of spatial data show that artificial agents can match these results if they have a region-level spatial representation and explore with object-directed movements. We conclude that mice employ an action-driven process for integrating subgoals into a hierarchical cognitive map. These findings broaden our understanding of the cognitive toolkit that mammals use to acquire spatial knowledge.

Subgraph Learning for Topological Geolocalization with Graph Neural Networks

One of the challenges of spatial cognition, such as self-localization and navigation, is to develop an efficient learning approach capable of mimicking human ability. This paper proposes a novel approach for topological geolocalization on the map using motion trajectory and graph neural networks. Specifically, our learning method learns an embedding of the motion trajectory encoded as a path subgraph where the node and edge represent turning direction and relative distance information by training a graph neural network. We formulate the subgraph learning as a multi-class classification problem in which the output node IDs are interpreted as the object's location on the map. After training using three map datasets with small, medium, and large sizes, the node localization tests on simulated trajectories generated from the map show 93.61%, 95.33%, and 87.50% accuracy, respectively. We also demonstrate similar accuracy for our approach on actual trajectories generated by visual-inertial odometry. The key benefits of our approach are as follows: (1) we take advantage of the powerful graph-modeling ability of neural graph networks, (2) it only requires a map in the form of a 2D graph, and (3) it only requires an affordable sensor that generates relative motion trajectory.

Hippocampal spatial view cells for memory and navigation, and their underlying connectivity in humans

Hippocampal and parahippocampal gyrus spatial view neurons in primates respond to the spatial location being looked at. The representation is allocentric, in that the responses are to locations "out there" in the world, and are relatively invariant with respect to retinal position, eye position, head direction, and the place where the individual is located. The underlying connectivity in humans is from ventromedial visual cortical regions to the parahippocampal scene area, leading to the theory that spatial view cells are formed by combinations of overlapping feature inputs self-organized based on their closeness in space. Thus, although spatial view cells represent "where" for episodic memory and navigation, they are formed by ventral visual stream feature inputs in the parahippocampal gyrus in what is the parahippocampal scene area. A second "where" driver of spatial view cells are parietal inputs, which it is proposed provide the idiothetic update for spatial view cells, used for memory recall and navigation when the spatial view details are obscured. Inferior temporal object "what" inputs and orbitofrontal cortex reward inputs connect to the human hippocampal system, and in macaques can be associated in the hippocampus with spatial view cell "where" representations to implement episodic memory. Hippocampal spatial view cells also provide a basis for navigation to a series of viewed landmarks, with the orbitofrontal cortex reward inputs to the hippocampus providing the goals for navigation, which can then be implemented by hippocampal connectivity in humans to parietal cortex regions involved in visuomotor actions in space. The presence of foveate vision and the highly developed temporal lobe for object and scene processing in primates including humans provide a basis for hippocampal spatial view cells to be key to understanding episodic memory in the primate and human hippocampus, and the roles of this system in primate including human navigation.

Optrode recording of an entorhinal-cortical circuit in freely moving mice

The deep layers of medial entorhinal cortex (MEC) are considered a crucial station for spatial cognition and memory. The deep sublayer Va of MEC (MECVa) serves as the output stage of the entorhinal-hippocampal system and sends extensive projections to brain cortical areas. However, the functional heterogeneity of these efferent neurons in MECVa is poorly understood, due to the difficulty of performing single-neuron activity recording from the narrow band of cell population while the animals are behaving. In the current study, we combined multi-electrode electrophysiological recording and optical stimulation to record cortical-projecting MECVa neurons at single-neuron resolution in freely moving mice. First, injection of a viral Cre-LoxP system was used to express channelrhodopsin-2 specifically in MECVa neurons that project to the medial part of the secondary visual cortex (V2M-projecting MECVa neurons). Then, a lightweight, self-made optrode was implanted into MECVa to identify the V2M-projecting MECVa neurons and to enable single-neuron activity recordings in mice performing the open field test and 8-arm radial maze. Our results demonstrate that optrode approach is an accessible and reliable method for single-neuron recording of V2M-projecting MECVa neurons in freely moving mice, paving the way for future circuit studies designed to characterize the activity of MECVa neurons during specific tasks.

Entropy and a sub-group of geometric measures of paths predict the navigability of an environment

Despite extensive research on navigation, it remains unclear which features of an environment predict how difficult it will be to navigate. We analysed 478,170 trajectories from 10,626 participants who navigated 45 virtual environments in the research app-based game Sea Hero Quest. Virtual environments were designed to vary in a range of properties such as their layout, number of goals, visibility (varying fog) and map condition. We calculated 58 spatial measures grouped into four families: task-specific metrics, space syntax configurational metrics, space syntax geometric metrics, and general geometric metrics. We used Lasso, a variable selection method, to select the most predictive measures of navigation difficulty. Geometric features such as entropy, area of navigable space, number of rings and closeness centrality of path networks were among the most significant factors determining the navigational difficulty. By contrast a range of other measures did not predict difficulty, including measures of intelligibility. Unsurprisingly, other task-specific features (e.g. number of destinations) and fog also predicted navigation difficulty. These findings have implications for the study of spatial behaviour in ecological settings, as well as predicting human movements in different settings, such as complex buildings and transport networks and may aid the design of more navigable environments.

Importance of Path Planning Variability: A Simulation Study

Individuals vary in the way they navigate through space. Some take novel shortcuts, while others rely on known routes to find their way around. We wondered how and why there is so much variation in the population. To address this, we first compared the trajectories of 368 human subjects navigating a virtual maze with simulated trajectories. The simulated trajectories were generated by strategy-based path planning algorithms from robotics. Based on the similarities between human trajectories and different strategy-based simulated trajectories, we found that there is a variation in the type of strategy individuals apply to navigate space, as well as variation within individuals on a trial-by-trial basis. Moreover, we observed variation within a trial when subjects occasionally switched the navigation strategies halfway through a trajectory. In these cases, subjects started with a route strategy, in which they followed a familiar path, and then switched to a survey strategy, in which they took shortcuts by considering the layout of the environment. Then we simulated a second set of trajectories using five different but comparable artificial maps. These trajectories produced the similar pattern of strategy variation within and between trials. Furthermore, we varied the relative cost, that is, the assumed mental effort or required timesteps to choose a learned route over alternative paths. When the learned route was relatively costly, the simulated agents tended to take shortcuts. Conversely, when the learned route was less costly, the simulated agents showed preference toward a route strategy. We suggest that cost or assumed mental effort may be the reason why in previous studies, subjects used survey knowledge when instructed to take the shortest path. We suggest that this variation we observe in humans may be beneficial for robotic swarms or collections of autonomous agents during information gathering.

Adapting hippocampus multi-scale place field distributions in cluttered environments optimizes spatial navigation and learning

Extensive studies in rodents show that place cells in the hippocampus have firing patterns that are highly correlated with the animal's location in the environment and are organized in layers of increasing field sizes or scales along its dorsoventral axis. In this study, we use a spatial cognition model to show that different field sizes could be exploited to adapt the place cell representation to different environments according to their size and complexity. Specifically, we provide an in-depth analysis of how to distribute place cell fields according to the obstacles in cluttered environments to optimize learning time and path optimality during goal-oriented spatial navigation tasks. The analysis uses a reinforcement learning (RL) model that assumes that place cells allow encoding the state. While previous studies have suggested exploiting different field sizes to represent areas requiring different spatial resolutions, our work analyzes specific distributions that adapt the representation to the environment, activating larger fields in open areas and smaller fields near goals and subgoals (e.g., obstacle corners). In addition to assessing how the multi-scale representation may be exploited in spatial navigation tasks, our analysis and results suggest place cell representations that can impact the robotics field by reducing the total number of cells for path planning without compromising the quality of the paths learned.

A space of goals: the cognitive geometry of informationally bounded agents

Traditionally, Euclidean geometry is treated by scientists as a priori and objective. However, when we take the position of an agent, the problem of selecting a best route should also factor in the abilities of the agent, its embodiment and particularly its cognitive effort. In this paper, we consider geometry in terms of travel between states within a world by incorporating information processing costs with the appropriate spatial distances. This induces a geometry that increasingly differs from the original geometry of the given world as information costs become increasingly important. We visualize this 'cognitive geometry' by projecting it onto two- and three-dimensional spaces showing distinct distortions reflecting the emergence of epistemic and information-saving strategies as well as pivot states. The analogies between traditional cost-based geometries and those induced by additional informational costs invite a generalization of the notion of geodesics as cheapest routes towards the notion of infodesics. In this perspective, the concept of infodesics is inspired by the property of geodesics that, travelling from a given start location to a given goal location along a geodesic, not only the goal, but all points along the way are visited at optimal cost from the start.

A fuzzy-oscillatory model of medial prefrontal cortex control function in spatial memory retrieval in human navigation function

Navigation can be broadly defined as the process of moving from an origin to a destination through path-planning. Previous research has shown that navigation is mainly related to the function of the medial temporal lobe (MTL), including the hippocampus (HPC), and medial prefrontal cortex (mPFC), which controls retrieval of the spatial memories from this region. In this study, we suggested a cognitive and computational model of human navigation with a focus on mutual interactions between the hippocampus (HPC) and the mPFC using the concept of synchrony. The Van-der-pol oscillator was used to model the synchronous process of receiving and processing “what stream” information. A fuzzy lookup table system was applied for modeling the controlling function of the mPFC in retrieving spatial information from the HPC. The effect of attention level was also included and simulated. The performance of the model was evaluated using information reported in previous experimental research. Due to the inherent stability of the proposed fuzzy-oscillatory model, it is less sensitive to the exact values of the initial conditions, and therefore, it is shown that it is consistent with the actual human performance in real environments. Analyzing the proposed cognitive and fuzzy-oscillatory computational model demonstrates that the model is able to reproduce certain cognitive and functional disturbances in navigation in related diseases such as Alzheimer’s disease (AD). We have shown that an increase in the bifurcation parameter of the Van-der-pol equation represents an increase in the low-frequency spectral power density and a decrease in the high-frequency spectral power as occurs in AD due to an increase in the amyloid plaques in the brain. These changes in the frequency characteristics of neuronal activity, in turn, lead to impaired recall and retrieval of landmarks information and learned routes upon encountering them. As a result, and because of the wrong frequency code being transmitted, the relevant set of rules in the mPFC is not activated, or another unrelated set will be activated, which leads to forgetfulness and erroneous decisions in routing and eventually losing the route in Alzheimer’s patients.

The hippocampus, ventromedial prefrontal cortex, and episodic and semantic memory

The human ventromedial prefrontal cortex (vmPFC)/anterior cingulate cortex is implicated in reward and emotion, but also in memory. It is shown how the human orbitofrontal cortex connecting with the vmPFC and anterior cingulate cortex provide a route to the hippocampus for reward and emotional value to be incorporated into episodic memory, enabling memory of where a reward was seen. It is proposed that this value component results in primarily episodic memories with some value component to be repeatedly recalled from the hippocampus so that they are more likely to become incorporated into neocortical semantic and autobiographical memories. The same orbitofrontal and anterior cingulate regions also connect in humans to the septal and basal forebrain cholinergic nuclei, thereby helping to consolidate memory, and helping to account for why damage to the vMPFC impairs memory. The human hippocampus and vmPFC thus contribute in complementary ways to forming episodic and semantic memories.

A Bionic Spatial Cognition Model and Method for Robots Based on the Hippocampus Mechanism

The hippocampus and its accessory are the main areas for spatial cognition. It can integrate paths and form environmental cognition based on motion information and then realize positioning and navigation. Learning from the hippocampus mechanism is a crucial way forward for research in robot perception, so it is crucial to building a calculation method that conforms to the biological principle. In addition, it should be easy to implement on a robot. This paper proposes a bionic cognition model and method for mobile robots, which can realize precise path integration and cognition of space. Our research can provide the basis for the cognition of the environment and autonomous navigation for bionic robots.

Spatial goal coding in the hippocampal formation

The mammalian hippocampal formation contains several distinct populations of neurons involved in representing self-position and orientation. These neurons, which include place, grid, head direction, and boundary-vector cells, are thought to collectively instantiate cognitive maps supporting flexible navigation. However, to flexibly navigate, it is necessary to also maintain internal representations of goal locations, such that goal-directed routes can be planned and executed. Although it has remained unclear how the mammalian brain represents goal locations, multiple neural candidates have recently been uncovered during different phases of navigation. For example, during planning, sequential activation of spatial cells may enable simulation of future routes toward the goal. During travel, modulation of spatial cells by the prospective route, or by distance and direction to the goal, may allow maintenance of route and goal-location information, supporting navigation on an ongoing basis. As the goal is approached, an increased activation of spatial cells may enable the goal location to become distinctly represented within cognitive maps, aiding goal localization. Lastly, after arrival at the goal, sequential activation of spatial cells may represent the just-taken route, enabling route learning and evaluation. Here, we review and synthesize these and other evidence for goal coding in mammalian brains, relate the experimental findings to predictions from computational models, and discuss outstanding questions and future challenges.

Deep entorhinal cortex: from circuit organization to spatial cognition and memory

The deep layers of the entorhinal cortex are important for spatial cognition, as well as memory storage, consolidation and retrieval. A long-standing hypothesis is that deep-layer neurons relay spatial and memory-related signals between the hippocampus and telencephalon. We review the implications of recent circuit-level analyses that suggest more complex roles. The organization of deep entorhinal layers is consistent with multi-stage processing by specialized cell populations; in this framework, hippocampal, neocortical, and subcortical inputs are integrated to generate representations for use by targets in the telencephalon and for feedback to the superficial entorhinal cortex and hippocampus. Addressing individual sublayers of the deep entorhinal cortex in future experiments and models will be important for establishing systems-level mechanisms for spatial cognition and episodic memory.

Dynamical self-organization and efficient representation of space by grid cells

To plan trajectories and navigate, animals must maintain a mental representation of the environment and their own position within it. This "cognitive map" is thought to be supported in part by the entorhinal cortex, where grid cells are active when an animal occupies the vertices of a scaling hierarchy of periodic lattices of locations in an enclosure. Here, we review computational developments which suggest that the grid cell network is: (a) efficient, providing required spatial resolution with a minimum number of neurons, (b) self-organizing, dynamically coordinating the structure and scale of the responses, and (c) adaptive, re-organizing in response to changes in landmarks and the structure of the boundaries of spaces. We consider these ideas in light of recent discoveries of similar structures in the mental representation of abstract spaces of shapes and smells, and in other brain areas, and highlight promising directions for future research.

Mice learn multi-step routes by memorizing subgoal locations

The behavioral strategies that mammals use to learn multi-step routes are unknown. In this study, we investigated how mice navigate to shelter in response to threats when the direct path is blocked. Initially, they fled toward the shelter and negotiated obstacles using sensory cues. Within 20 min, they spontaneously adopted a subgoal strategy, initiating escapes by running directly to the obstacle's edge. Mice continued to escape in this manner even after the obstacle had been removed, indicating use of spatial memory. However, standard models of spatial learning-habitual movement repetition and internal map building-did not explain how subgoal memories formed. Instead, mice used a hybrid approach: memorizing salient locations encountered during spontaneous 'practice runs' to the shelter. This strategy was also used during a geometrically identical food-seeking task. These results suggest that subgoal memorization is a fundamental strategy by which rodents learn efficient multi-step routes in new environments.

Learning Invariant Object and Spatial View Representations in the Brain Using Slow Unsupervised Learning

First, neurophysiological evidence for the learning of invariant representations in the inferior temporal visual cortex is described. This includes object and face representations with invariance for position, size, lighting, view and morphological transforms in the temporal lobe visual cortex; global object motion in the cortex in the superior temporal sulcus; and spatial view representations in the hippocampus that are invariant with respect to eye position, head direction, and place. Second, computational mechanisms that enable the brain to learn these invariant representations are proposed. For the ventral visual system, one key adaptation is the use of information available in the statistics of the environment in slow unsupervised learning to learn transform-invariant representations of objects. This contrasts with deep supervised learning in artificial neural networks, which uses training with thousands of exemplars forced into different categories by neuronal teachers. Similar slow learning principles apply to the learning of global object motion in the dorsal visual system leading to the cortex in the superior temporal sulcus. The learning rule that has been explored in VisNet is an associative rule with a short-term memory trace. The feed-forward architecture has four stages, with convergence from stage to stage. This type of slow learning is implemented in the brain in hierarchically organized competitive neuronal networks with convergence from stage to stage, with only 4-5 stages in the hierarchy. Slow learning is also shown to help the learning of coordinate transforms using gain modulation in the dorsal visual system extending into the parietal cortex and retrosplenial cortex. Representations are learned that are in allocentric spatial view coordinates of locations in the world and that are independent of eye position, head direction, and the place where the individual is located. This enables hippocampal spatial view cells to use idiothetic, self-motion, signals for navigation when the view details are obscured for short periods.

A unified energy-optimality criterion predicts human navigation paths and speeds

Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality criterion that predicts disparate non-straight-line walking phenomena, with straight-line walking as a special case. We first characterized the metabolic cost of turning, deriving the cost landscape as a function of turning radius and rate. We then generalized this cost landscape to arbitrarily complex trajectories, allowing the velocity direction to deviate from body orientation (holonomic walking). We used this generalized optimality criterion to mathematically predict movement patterns in multiple contexts of varying complexity: walking on prescribed paths, turning in place, navigating an angled corridor, navigating freely with end-point constraints, walking through doors, and navigating around obstacles. In these tasks, humans moved at speeds and paths predicted by our optimality criterion, slowing down to turn and never using sharp turns. We show that the shortest path between two points is, counterintuitively, often not energy-optimal, and, indeed, humans do not use the shortest path in such cases. Thus, we have obtained a unified theoretical account that predicts human walking paths and speeds in diverse contexts. Our model focuses on walking in healthy adults; future work could generalize this model to other human populations, other animals, and other locomotor tasks.

Neuro4PD: An Initial Neurorobotics Model of Parkinson's Disease

In this work, we present the first steps toward the creation of a new neurorobotics model of Parkinson's Disease (PD) that embeds, for the first time in a real robot, a well-established computational model of PD. PD mostly affects the modulation of movement in humans. The number of people suffering from this neurodegenerative disease is set to double in the next 15 years and there is still no cure. With the new model we were capable to further explore the dynamics of the disease using a humanoid robot. Results show that the embedded model under both conditions, healthy and parkinsonian, was capable of performing a simple behavioural task with different levels of motor disturbance. We believe that this neurorobotics model is a stepping stone to the development of more sophisticated models that could eventually test and inform new PD therapies and help to reduce and replace animals in research.

Why grid cells function as a metric for space

The brain is able to calculate the distance and direction to the desired position based on grid cells. Extensive neurophysiological studies of rodent navigation have postulated the grid cells function as a metric for space, and have inspired many computational studies to develop innovative navigation approaches. Furthermore, grid cells may provide a general encoding scheme for high-order nonspatial information. Built upon existing neuroscience and machine learning work, this paper provides theoretical clarity on that the grid cell population codes can be taken as a metric for space. The metric is generated by a shift-invariant positive definite kernel via kernel distance method and embeds isometrically in a Euclidean space, and the inner product of the grid cell population code exponentially converges to the kernel. We also provide a method to learn the distribution of grid cell population efficiently. Grid cells, as a scalable position encoding method, can encode the spatial relationships of places and enable grid cells to outperform place cells in navigation. Further, we extend the grid cell to images encoding and find that grid cells embed images into a mental map, where geometric relationships are conceptual relationships of images. The theoretical model and analysis would contribute to establishing the grid cell code as a generic coding scheme for both spatial and conceptual spaces, and is promising for a multitude of problems across spatial cognition, machine learning and semantic cognition.

Neurons including hippocampal spatial view cells, and navigation in primates including humans

A new theory is proposed of mechanisms of navigation in primates including humans in which spatial view cells found in the primate hippocampus and parahippocampal gyrus are used to guide the individual from landmark to landmark. The navigation involves approach to each landmark in turn (taxis), using spatial view cells to identify the next landmark in the sequence, and does not require a topological map. Two other cell types found in primates, whole body motion cells, and head direction cells, can be utilized in the spatial view cell navigational mechanism, but are not essential. If the landmarks become obscured, then the spatial view representations can be updated by self-motion (idiothetic) path integration using spatial coordinate transform mechanisms in the primate dorsal visual system to transform from egocentric to allocentric spatial view coordinates. A continuous attractor network or time cells or working memory is used in this approach to navigation to encode and recall the spatial view sequences involved. I also propose how navigation can be performed using a further type of neuron found in primates, allocentric-bearing-to-a-landmark neurons, in which changes of direction are made when a landmark reaches a particular allocentric bearing. This is useful if a landmark cannot be approached. The theories are made explicit in models of navigation, which are then illustrated by computer simulations. These types of navigation are contrasted with triangulation, which requires a topological map. It is proposed that the first strategy utilizing spatial view cells is used frequently in humans, and is relatively simple because primates have spatial view neurons that respond allocentrically to locations in spatial scenes. An advantage of this approach to navigation is that hippocampal spatial view neurons are also useful for episodic memory, and for imagery.

Structuring Knowledge with Cognitive Maps and Cognitive Graphs

Humans and animals use mental representations of the spatial structure of the world to navigate. The classical view is that these representations take the form of Euclidean cognitive maps, but alternative theories suggest that they are cognitive graphs consisting of locations connected by paths. We review evidence suggesting that both map-like and graph-like representations exist in the mind/brain that rely on partially overlapping neural systems. Maps and graphs can operate simultaneously or separately, and they may be applied to both spatial and nonspatial knowledge. By providing structural frameworks for complex information, cognitive maps and cognitive graphs may provide fundamental organizing schemata that allow us to navigate in physical, social, and conceptual spaces.

Perception of urban subdivisions in pedestrian movement simulation

The perception of urban subdivisions, deriving from regionalisation processes and the identification of separating elements (barriers), has proven to dynamically shape peoples’ cognitive representations of space and route choice behaviour in cities. However, existing Agent-Based Models (ABMs) for pedestrian simulation have not accounted for these particular cognitive mapping processes. The aim of this paper is to explore the behaviour of pedestrian agents endowed with knowledge about urban subdivisions. Drawing from literature in spatial cognition, we adapted a region-based route choice model, which contemplates a high- and a local planning level, and advanced a barrier-based route choice model, wherein the influence of separating elements is manipulated. Finally, we combined these two approaches in a region-barrier based model. The patterns emerging from the movement of agents employing such approaches were examined in the city centres of London and Paris. The introduction of regions in the routing mechanisms reduced the unbalanced concentration of agents across the street network brought up by the widely employed least cumulative angular change model (-.08 Gini coefficient). The inclusion of barriers further raised the dispersal of the agents through secondary roads, while leading agents to walk along waterfronts and across parks; it also yielded a more regular usage of pedestrian roads. Moreover, the region- and the region-barrier based routes showed deviation ratio values from the road distance shortest path (region-based: 1.18 London, 1.16 Paris, region-barrier based: 1.43 London, 1.33 Paris) consistent with empirical observations from pedestrian behaviour research. A further evaluation of the model with macro-level observational data may enhance the understanding of pedestrian dynamics and help tuning the interplay amongst urban salient elements at the agent level. Yet, we consider the movement flows arising from our current implementation insightful for assessing the distribution of pedestrians and testing possible interventions for the design of legible and walkable spaces.

Introduction to part two of the special issue on computational models of hippocampus and related structures

Extensive computational modeling has focused on the hippocampal formation and related cortical structures. This introduction describes the topics addressed by individual articles in part two of this special issue of the journal Hippocampus on the topic of computational models of the hippocampus and related structures.

Spatial inference without a cognitive map: the role of higher-order path integration

The cognitive map has been taken as the standard model for how agents infer the most efficient route to a goal location. Alternatively, path integration - maintaining a homing vector during navigation - constitutes a primitive and presumably less-flexible strategy than cognitive mapping because path integration relies primarily on vestibular stimuli and pace counting. The historical debate as to whether complex spatial navigation is ruled by associative learning or cognitive map mechanisms has been challenged by experimental difficulties in successfully neutralizing path integration. To our knowledge, there are only three studies that have succeeded in resolving this issue, all showing clear evidence of novel route taking, a behaviour outside the scope of traditional associative learning accounts. Nevertheless, there is no mechanistic explanation as to how animals perform novel route taking. We propose here a new model of spatial learning that combines path integration with higher-order associative learning, and demonstrate how it can account for novel route taking without a cognitive map, thus resolving this long-standing debate. We show how our higher-order path integration (HOPI) model can explain spatial inferences, such as novel detours and shortcuts. Our analysis suggests that a phylogenetically ancient, vector-based navigational strategy utilizing associative processes is powerful enough to support complex spatial inferences.

Neuronal vector coding in spatial cognition

Several types of neurons involved in spatial navigation and memory encode the distance and direction (that is, the vector) between an agent and items in its environment. Such vectorial information provides a powerful basis for spatial cognition by representing the geometric relationships between the self and the external world. Here, we review the explicit encoding of vectorial information by neurons in and around the hippocampal formation, far from the sensory periphery. The parahippocampal, retrosplenial and parietal cortices, as well as the hippocampal formation and striatum, provide a plethora of examples of vector coding at the single neuron level. We provide a functional taxonomy of cells with vectorial receptive fields as reported in experiments and proposed in theoretical work. The responses of these neurons may provide the fundamental neural basis for the (bottom-up) representation of environmental layout and (top-down) memory-guided generation of visuospatial imagery and navigational planning.

Overview of computational models of hippocampus and related structures: Introduction to the special issue

Extensive computational modeling has focused on the hippocampal formation and associated cortical structures. This overview describes some of the factors that have motivated the strong focus on these structures, including major experimental findings and their impact on computational models. This overview provides a framework for describing the topics addressed by individual articles in this special issue of the journal Hippocampus.