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The problem of how the hippocampus encodes both spatial and nonspatial information at the cellular network level remains largely unresolved. Spatial memory is widely modeled through the theoretical framework of attractor networks, but standard computational models can only represent spaces that are much smaller than the natural habitat of an animal. We propose that hippocampal networks are built on a basic unit called a "megamap," or a cognitive attractor map in which place cells are flexibly recombined to represent a large space. Its inherent flexibility gives the megamap a huge representational capacity and enables the hippocampus to simultaneously represent multiple learned memories and naturally carry nonspatial information at no additional cost. On the other hand, the megamap is dynamically stable, because the underlying network of place cells robustly encodes any location in a large environment given a weak or incomplete input signal from the upstream entorhinal cortex. Our results suggest a general computational strategy by which a hippocampal network enjoys the stability of attractor dynamics without sacrificing the flexibility needed to represent a complex, changing world. [ABSTRACT FROM AUTHOR]

A neural network with symmetric reciprocal connections always admits a Lyapunov function, whose minima correspond to the memory states stored in the network. Networks with suitable asymmetric connections can store and retrieve a sequence ofmemory patterns, but the dynamics of these networks cannot be characterized as readily as that of the symmetric networks due to the lack of established general methods. Here, a reduction method is developed for a class of asymmetric attractor networks that store sequences of activity patterns as associative memories, as in a Hopfield network. The method projects the original activity pattern of the network to a low-dimensional space such that sequential memory retrievals in the original network correspond to periodic oscillations in the reduced system. The reduced system is self-contained and provides quantitative information about the stability and speed of sequential memory retrieval in the original network. The time evolution of the overlaps between the network state and the stored memory patterns can also be determined from extended reduced systems. The reduction procedure can be summarized by a few reduction rules, which are applied to several network models, including coupled networks and networks with time-delayed connections, and the analytical solutions of the reduced systems are confirmed by numerical simulations of the original networks. Finally, a local learning rule that provides an approximation to the connection weights involving the pseudoinverse is also presented. [ABSTRACT FROM AUTHOR]

It is generally unknown when distinct neural networks having different synaptic weights and thresholds implement identical input-output transformations. Determining the exact conditions for structurally distinct yet functionally equivalent networks may shed light on the theoretical constraints on how diverse neural circuits might develop and be maintained to serve identical functions. Such consideration also imposes practical limits on our ability to uniquely infer the structure of underlying neural circuits from stimulus-response measurements. We introduce a biologically inspired mathematical method for determining when the structure of a neural network can be perturbed gradually while preserving functionality. We show that for common three-layer networks with convergent and nondegenerate connection weights, this is possible only when the hidden unit gains are power functions, exponentials, or logarithmic functions, which are known to approximate the gains seen in some biological neurons. For practical applications, our numerical simulations with finite and noisy data show that continuous confounding of parameters due to network functional equivalence tends to occur approximately even when the gain function is not one of the aforementioned three types, suggesting that our analytical results are applicable to more general situations and may help identify a common source of parameter variability in neural network modeling. [ABSTRACT FROM AUTHOR]

Identifying the optimal stimuli for a sensory neuron is often a difficult process involving trial and error. By analyzing the relationship between stimuli and responses in feed forward and stable recurrent neural network models, we find that the stimulus yielding the maximum firing rate response always lies on the topological boundary of the collection of all allowable stimuli, provided that individual neurons have increasing input-output relations or gain functions and that the synaptic connections are convergent between layers with non degenerate weight matrices. This result suggests that in neurophysiological experiments under these conditions, only stimuli on the boundary need to be tested in order to maximize the response, thereby potentially reducing the number of trials needed for finding the most effective stimuli. Even when the gain functions allow firing rate cutoff or saturation, a peak still cannot exist in the stimulus-response relation in the sense that moving away from the optimum stimulus always reduces the response. We further demonstrate that the condition for nondegenerate synaptic connections also implies that proper stimuli can independently perturb the activities of all neurons in the same layer. One example of this type of manipulation is changing the activity of a single neuron in a given processing layer while keeping that of all others constant. Such stimulus perturbations might help experimentally isolate the interactions of selected neurons within a network. [ABSTRACT FROM AUTHOR]

Presents an analytical theory for the gross organization of cortical gray matter and the associated white matter of the cerebral cortex. Close relationship between the volumes of cortical gray matter and the adjacent white matter; Limitation of power law scaling; Three free parameters of the theory.

The dorsomedial entorhinal cortex (dMEC) of the rat brain contains a remarkable population of spatially tuned neurons called grid cells (Hafting et al., 2005). Each grid cell fires selectively at multiple spatial locations, which are geometrically arranged to form a hexagonal lattice that tiles the surface of the rat's environment. Here, we show that grid fields can combine with one another to form moiré interference patterns, referred to as "moiré grids," that replicate the hexagonal lattice over an infinite range of spatial scales. We propose that dMEC grids are actually moiré grids formed by interference between much smaller "theta grids," which are hypothesized to be the primary source of movement-related theta rhythm in the rat brain. The formation of moiré grids from theta grids obeys two scaling laws, referred to as the length and rotational scaling rules. The length scaling rule appears to account for firing properties of grid cells in layer II of dMEC, whereas the rotational scaling rule can better explain properties of layer III grid cells. Moiré grids built from theta grids can be combined to form yet larger grids and can also be used as basis functions to construct memory representations of spatial locations (place cells) or visual images. Memory representations built from moiré grids are automatically endowed with size invariance by the scaling properties of the moiré grids. We therefore propose that moiré interference between grid fields may constitute an important principle of neural computation underlying the construction of scale-invariant memory representations. [ABSTRACT FROM AUTHOR]

Most of the parallel mechanisms (PM) with low coupling degree cannot directly obtain the analytical expression of the positive position solution of the PM, which makes it difficult to carry out the follow-up research on the kinematic accuracy analysis and trajectory planning of the PM. Based on the topological structure theory, this paper analyzes the position and orientation characteristic(POC), DOF and coupling degree of 2PPa-PSS PM. Afterward, the kinematic mathematical model of 2PPa-PSS PM is established based on the order single open chain of kinematic modeling principle. The moving platform of the mechanism is set as an equilateral triangle, and the intermediate variables are solved by combining the constraints of the two chains. The positive position solution of the PM in analytical form is obtained. The correctness of the kinematic model of the mechanism is verified by numerical calculation. Then, according to the positive position solution analytical expression, we can work out the complete workspace of the PM, and the significant influence of the driving increment on the attitude change of the moving platform is analyzed by using the analysis method based on the orthogonal test. According to the results of orthogonal experiment, the best driving range of the mechanism is obtained. [ABSTRACT FROM AUTHOR]

The rodent septohippocampal system contains "theta cells," which burst rhythmically at 4-12Hz, but the functional significance of this rhythm remains poorly understood (Buzsaki, 2006). Theta rhythm commonly modulates the spike trains of spatially tuned neurons such as place (O'Keefe and Dostrovsky, 1971 ), head direction (Tsanov et al., 20lla), grid (Hafting et al., 2005), and border cells ( avelli et al., 2008; Sols tad et al., 2008). An "oscillatory interference" theory has hypothesized that some of these spatially tuned neurons may derive their positional firing from phase interference among theta oscillations with frequencies that are modulated by the speed and direction of translational movements (Burgess et al., 2005, 2007). This theory is supported by studies reporting modulation of theta frequency by movement speed (Rivas et al.,l996; Geisler et al., 2007; Jeewajee et al., 2008a), but modulation of theta frequency by movement direction has never been observed. Here we recorded theta cells from hippocampus, medial septum, and anterior thalamus of freely behaving rats. Theta cell burst frequencies varied as the cosine of the rat's movement direction, and this directional tuning was influenced by landmark cues, in agreement with predictions of the oscillatory interference theory. Computer simulations and mathematical analysis demonstrated how a postsynaptic neuron can detect location-dependent synchrony among inputs from such theta cells, and thereby mimic the spatial tuning properties of place, grid, or border cells. These results suggest that theta cells may serve a high-level computational function by encoding a basis set of oscillatory signals that interfere with one another to synthesize spatial memory representations. [ABSTRACT FROM AUTHOR]