Challenges for identifying the neural mechanisms that support spatial navigation: the impact of spatial scale.

Spatial navigation is a fascinating behavior that is essential for our everyday lives. It involves nearly all sensory systems, it requires numerous parallel computations, and it engages multiple memory systems. One of the key problems in this field pertains to the question of reference frames: spatial information such as direction or distance can be coded egocentrically-relative to an observer-or allocentrically-in a reference frame independent of the observer. While many studies have associated striatal and parietal circuits with egocentric coding and entorhinal/hippocampal circuits with allocentric coding, this strict dissociation is not in line with a growing body of experimental data. In this review, we discuss some of the problems that can arise when studying the neural mechanisms that are presumed to support different spatial reference frames. We argue that the scale of space in which a navigation task takes place plays a crucial role in determining the processes that are being recruited. This has important implications, particularly for the inferences that can be made from animal studies in small scale space about the neural mechanisms supporting human spatial navigation in large (environmental) spaces. Furthermore, we argue that many of the commonly used tasks to study spatial navigation and the underlying neuronal mechanisms involve different types of reference frames, which can complicate the interpretation of neurophysiological data

Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ~10–100 meters and ~1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

No advantage for remembering horizontal over vertical spatial locations learned from a single viewpoint

Previous behavioral and neurophysiological research has shown better memory for horizontal than for vertical locations. In these studies, participants navigated toward these locations. In the present study we investigated whether the orientation of the spatial plane per se was responsible for this difference. We thus had participants learn locations visually from a single perspective and retrieve them from multiple viewpoints. In three experiments, participants studied colored tags on a horizontally or vertically oriented board within a virtual room and recalled these locations with different layout orientations (Exp. 1) or from different room-based perspectives (Exps. 2 and 3). All experiments revealed evidence for equal recall performance in horizontal and vertical memory. In addition, the patterns for recall from different test orientations were rather similar. Consequently, our results suggest that memory is qualitatively similar for both vertical and horizontal two-dimensional locations, given that these locations are learned from a single viewpoint. Thus, prior differences in spatial memory may have originated from the structure of the space or the fact that participants navigated through it. Additionally, the strong performance advantages for perspective shifts (Exps. 2 and 3) relative to layout rotations (Exp. 1) suggest that configurational judgments are not only based on memory of the relations between target objects, but also encompass the relations between target objects and the surrounding room—for example, in the form of a memorized view

Spatial navigation deficits — overlooked cognitive marker for preclinical Alzheimer disease?

Detection of incipient Alzheimer disease (AD) pathophysiology is critical to identify preclinical individuals and target potentially disease-modifying therapies towards them. Current neuroimaging and biomarker research is strongly focused in this direction, with the aim of establishing AD fingerprints to identify individuals at high risk of developing this disease. By contrast, cognitive fingerprints for incipient AD are virtually non-existent as diagnostics and outcomes measures are still focused on episodic memory deficits as the gold standard for AD, despite their low sensitivity and specificity for identifying at-risk individuals. This Review highlights a novel feature of cognitive evaluation for incipient AD by focusing on spatial navigation and orientation deficits, which are increasingly shown to be present in at-risk individuals. Importantly, the navigation system in the brain overlaps substantially with the regions affected by AD in both animal models and humans. Notably, spatial navigation has fewer verbal, cultural and educational biases than current cognitive tests and could enable a more uniform, global approach towards cognitive fingerprints of AD and better cognitive treatment outcome measures in future multicentre trials. The current Review appraises the available evidence for spatial navigation and/or orientation deficits in preclinical, prodromal and confirmed AD and identifies research gaps and future research priorities

Dual coding with STDP in a spiking recurrent neural network model of the hippocampus.

The firing rate of single neurons in the mammalian hippocampus has been demonstrated to encode for a range of spatial and non-spatial stimuli. It has also been demonstrated that phase of firing, with respect to the theta oscillation that dominates the hippocampal EEG during stereotype learning behaviour, correlates with an animal's spatial location. These findings have led to the hypothesis that the hippocampus operates using a dual (rate and temporal) coding system. To investigate the phenomenon of dual coding in the hippocampus, we examine a spiking recurrent network model with theta coded neural dynamics and an STDP rule that mediates rate-coded Hebbian learning when pre- and post-synaptic firing is stochastic. We demonstrate that this plasticity rule can generate both symmetric and asymmetric connections between neurons that fire at concurrent or successive theta phase, respectively, and subsequently produce both pattern completion and sequence prediction from partial cues. This unifies previously disparate auto- and hetero-associative network models of hippocampal function and provides them with a firmer basis in modern neurobiology. Furthermore, the encoding and reactivation of activity in mutually exciting Hebbian cell assemblies demonstrated here is believed to represent a fundamental mechanism of cognitive processing in the brain

Modular Open-Source Design of Pyrolysis Reactor Monitoring and Control Electronics

Industrial pilot projects often rely on proprietary and expensive electronic hardware to control and monitor experiments. This raises costs and retards innovation. Open-source hardware tools exist for implementing these processes individually; however, they are not easily integrated with other designs. The Broadly Reconfigurable and Expandable Automation Device (BREAD) is a framework that provides many open-source devices which can be connected to create more complex data acquisition and control systems. This article explores the feasibility of using BREAD plug-and-play open hardware to quickly design and test monitoring and control electronics for an industrial materials processing prototype pyrolysis reactor. Generally, pilot-scale pyrolysis plants are expensive custom designed systems. The plug-and-play prototype approach was first tested by connecting it to the pyrolysis reactor and ensuring that it can measure temperature and actuate heaters and a stirring motor. Next, a single circuit board system was created and tested using the designs from the BREAD prototype to reduce the number of microcontrollers required. Both open-source control systems were capable of reliably running the pyrolysis reactor continuously, achieving equivalent performance to a state-of-the-art commercial controller with a ten-fold reduction in the overall cost of control. Open-source, plug-and-play hardware provides a reliable avenue for researchers to quickly develop data acquisition and control electronics for industrial-scale experiments

Ensemble Place Codes in Hippocampus: CA1, CA3, and Dentate Gyrus Place Cells Have Multiple Place Fields in Large Environments

Previously we reported that the hippocampus place code must be an ensemble code because place cells in the CA1 region of hippocampus have multiple place fields in a more natural, larger-than-standard enclosure with stairs that permitted movements in 3-D. Here, we further investigated the nature of hippocampal place codes by characterizing the spatial firing properties of place cells in the CA1, CA3, and dentate gyrus (DG) hippocampal subdivisions as rats foraged in a standard 76-cm cylinder as well as a larger-than-standard box (1.8 m×1.4 m) that did not have stairs or any internal structure to permit movements in 3-D. The rats were trained to forage continuously for 1 hour using computer-controlled food delivery. We confirmed that most place cells have single place fields in the standard cylinder and that the positional firing pattern remapped between the cylinder and the large enclosure. Importantly, place cells in the CA1, CA3 and DG areas all characteristically had multiple place fields that were irregularly spaced, as we had reported previously for CA1. We conclude that multiple place fields are a fundamental characteristic of hippocampal place cells that simplifies to a single field in sufficiently small spaces. An ensemble place code is compatible with these observations, which contradict any dedicated coding scheme

Non-hexagonal neural dynamics in vowel space

Are the grid cells discovered in rodents relevant to human cognition? Following up on two seminal studies by others, we aimed to check whether an approximate 6-fold, grid-like symmetry shows up in the cortical activity of humans who "navigate" between vowels, given that vowel space can be approximated with a continuous trapezoidal 2D manifold, spanned by the first and second formant frequencies. We created 30 vowel trajectories in the assumedly flat central portion of the trapezoid. Each of these trajectories had a duration of 240 milliseconds, with a steady start and end point on the perimeter of a "wheel". We hypothesized that if the neural representation of this "box" is similar to that of rodent grid units, there should be an at least partial hexagonal (6-fold) symmetry in the EEG response of participants who navigate it. We have not found any dominant n-fold symmetry, however, but instead, using PCAs, we find indications that the vowel representation may reflect phonetic features, as positioned on the vowel manifold. The suggestion, therefore, is that vowels are encoded in relation to their salient sensory-perceptual variables, and are not assigned to arbitrary gridlike abstract maps. Finally, we explored the relationship between the first PCA eigenvector and putative vowel attractors for native Italian speakers, who served as the subjects in our study