Narrow Results

The grid cells of the rat medial entorhinal cortex (MEC) show an increased firing frequency when the position of the animal correlates with multiple regions of the environment that are arranged in regular triangular grids. Here, we describe an artificial neural network based on a twisted torus topology, which allows for the generation of regular triangular grids. The association of the activity of pre-defined hippocampal place cells with entorhinal grid cells allows for a highly robust-to-noise calibration mechanism, suggesting a role for the hippocampal back-projections to the entorhinal cortex.

In this paper we derive a gauge fixing identity by varying the covariant gauge fixing term in in the background field method of QCD in pure gauge. Using this gauge fixing identity, we establish a relation between in QCD and in background field method of QCD in pure gauge. We show the validity of this gauge fixing identity, in general noncovariant and general Coulomb gauge fixings respectively. This gauge fixing identity is used to prove factorization theorem in QCD at high energy colliders and in nonequilibrium QCD at high energy heavy-ion colliders.

Insects such as ants and bees are capable of surprisingly good navigation, despite the small size and relative simplicity of their brains. Recent experimental research in our laboratory, summarized in this chapter, indicates that honeybees estimate the distance travelled to a food site in terms of the image motion that they experience en route. This finding has inspired us to design and build a robot that navigates using a visually-driven odometer.

This paper develops bridge sampling path integral algorithms for pricing path-dependent options under a new class of nonlinear state dependent volatility models. Path-dependent option pricing is considered within a new (dual) Bessel family of semimartingale diffusion models, as well as the constant elasticity of variance (CEV) diffusion model, arising as a particular case of these models. The transition p.d.f.s or pricing kernels are mapped onto an underlying simpler squared Bessel process and are expressed analytically in terms of modified Bessel functions. We establish precise links between pricing kernels of such models and the randomized gamma distributions, and thereby demonstrate how a squared Bessel bridge process can be used for exact sampling of the Bessel family of paths. A Bessel bridge algorithm is presented which is based on explicit conditional distributions for the Bessel family of volatility models and is similar in spirit to the Brownian bridge algorithm. A special rearrangement and splitting of the path integral variables allows us to combine the Bessel bridge sampling algorithm with either adaptive Monte Carlo algorithms, or quasi-Monte Carlo techniques for significant numerical efficiency improvement. The algorithms are illustrated by pricing Asian-style and lookback options under the Bessel family of volatility models as well as the CEV diffusion model.

Flexible spatial behavior requires the ability to orchestrate the interaction of multiple parallel processes. At the sensory level, multimodal inputs must be combined to produce a robust description of the spatiotemporal properties of the environment. At the action-selection level, multiple concurrent navigation policies must be dynamically weighted in order to adopt the strategy that is the most adapted to the complexity of the task. Different neural substrates mediate the processing of spatial information. Elucidating their anatomo-functional interrelations is fundamental to unravel the overall spatial memory function. Here we first address the multisensory integration issue and we review a series of experimental findings (both behavioral and electrophysiological) concerning the neural bases of spatial learning and the way the brain builds unambiguous spatial representations from incoming multisensory streams. Second, we move at the navigation strategy level and present an overview of experimental data that begin to explain the cooperation-competition between the brain areas involved in spatial navigation. Third, we introduce the spatial cognition function from a computational neuroscience and neuro-robotics viewpoint. We provide an example of neuro-computational model that focuses on the importance of combining multisensory percepts to enable a robot to acquire coherent (spatial) memories of its interaction with the environment.

In this paper, we present a model for the generation of grid cells and the emergence of place cells from multimodal input to the entorhinal cortex (EC). In this model, grid cell activity in the dorsocaudal medial entorhinal cortex (dMEC) [28] results from the operation of a long-distance path integration system located outside the hippocampal formation, presumably in retrosplenial and/or parietal cortex. If the connections between these structures and dMEC are organized as a modulo N operator, the resulting activity of dMEC neurons is a grid cell pattern. Furthermore, a robust high-resolution positional code can be built from a small set of different grid cells if the modulo factors are relatively prime. On the other hand, broad visual place cell activity in the MEC can result from the integration of visual information depending on the view-field of the visual input. The merging of entorhinal visual place cell information and grid cell information in the EC and/or in the dentate gyrus (DG) allows the building of precise and robust "place cells" (e.g., whose activity is maintained if light is suppressed for a short duration). Our model supports our previous proposition that hippocampal "place cell" activity code transitions between two successive states ("transition cells") rather than mere current locations. Furthermore, we discuss the possibility that the hippocampal loop participates in the emergence of grid cell activity but is not sufficient by itself. Finally, path integration at a short time scale (which is reset from one place to the next) would be merged in the subiculum with CA3/CA1 "transition cells" [22] to provide a robust feedback about current action to the deep layer of the entorhinal cortex in order to predict the recognition of the new animal location.

Desert ant (Cataglyphis) is famous for its ability in navigation. In deserts with very few visual and odor information, the ant can return to its den almost along a straight line after foraging away in a distance of much more than thousands of times longer than its body length. Several kinds of information must be acquired during its trip, and the most important two are: path integration and visual navigation. Path integration is achieved by using sky light compass based on polarized light and odometer, while visual navigation relies on landmark based memory and matching. In this paper, a survey of research work on desert ant navigation from the viewpoint of information acquisition and fusion is presented, as well as the application of these kinds of information to navigate robots, especially bionic robots cruising in strange environment.

Insects such as ants and bees are capable of surprisingly good navigation, despite the small size and relative simplicity of their brains. Recent experimental research in our laboratory, summarized in this chapter, indicates that honeybees estimate the distance travelled to a food site in terms of the image motion that they experience en route. This finding has inspired us to design and build a robot that navigates using a visually-driven odometer.

The path integral approach is used for the calculation of the correlation functions of the XY Heisenberg chain. The obtained answers for the two-point correlators of the XX magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.