Environmental Anchoring of Head Direction in a Computational Model of Retrosplenial Cortex

Allocentric (world-centered) spatial codes driven by path integration accumulate error unless reset by environmental sensory inputs that are necessarily egocentric (body-centered). Previous models of the head direction system avoided the necessary transformation between egocentric and allocentric reference frames by placing visual cues at infinity. Here we present a model of head direction coding that copes with exclusively proximal cues by making use of a conjunctive representation of head direction and location in retrosplenial cortex. Egocentric landmark bearing of proximal cues, which changes with location, is mapped onto this retrosplenial representation. The model avoids distortions due to parallax, which occur in simple models when a single proximal cue card is used, and can also accommodate multiple cues, suggesting how it can generalize to arbitrary sensory environments. It provides a functional account of the anatomical distribution of head direction cells along Papez' circuit, of place-by-direction coding in retrosplenial cortex, the anatomical connection from the anterior thalamic nuclei to retrosplenial cortex, and the involvement of retrosplenial cortex in navigation. In addition to parallax correction, the same mechanism allows for continuity of head direction coding between connected environments, and shows how a head direction representation can be stabilized by a single within arena cue. We also make predictions for drift during exploration of a new environment, the effects of hippocampal lesions on retrosplenial cells, and on head direction coding in differently shaped environments. SIGNIFICANCE STATEMENT: The activity of head direction cells signals the direction of an animal's head relative to landmarks in the world. Although driven by internal estimates of head movements, head direction cells must be kept aligned to the external world by sensory inputs, which arrive in the reference frame of the sensory receptors. We present a computational model, which proposes that sensory inputs are correctly associated to head directions by virtue of a conjunctive representation of place and head directions in the retrosplenial cortex. The model allows for a stable head direction signal, even when the sensory input from nearby cues changes dramatically whenever the animal moves to a different location, and enables stable representations of head direction across connected environments

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

Sculpting the Extra Dimensions: Inflation from Codimension-2 Brane Back-reaction

We construct an inflationary model in 6D supergravity that is based on explicit time-dependent solutions to the full higher-dimensional field equations, back-reacting to the presence of a 4D inflaton rolling on a space-filling codimension-2 source brane. Fluxes in the bulk stabilize all moduli except the `breathing' modulus (that is generically present in higher-dimensional supergravities). Back-reaction to the inflaton roll causes the 4D Einstein-frame on-brane geometry to expand, a(t) ~ t^p, as well as exciting the breathing mode and causing the two off-brane dimensions to expand, r(t) ~ t^q. The model evades the general no-go theorems precluding 4D de Sitter solutions, since adjustments to the brane-localized inflaton potential allow the power p to be dialed to be arbitrarily large, with the 4D geometry becoming de Sitter in the limit p -> infinity (in which case q = 0). Slow-roll solutions give accelerated expansion with p large but finite, and q = 1/2. Because the extra dimensions expand during inflation, the present-day 6D gravity scale can be much smaller than it was when primordial fluctuations were generated - potentially allowing TeV gravity now to be consistent with the much higher gravity scale required at horizon-exit for observable primordial gravity waves. Because p >> q, the 4 on-brane dimensions expand more quickly than the 2 off-brane ones, providing a framework for understanding why the observed four dimensions are presently so much larger than the internal two. If uplifted to a 10D framework with 4 dimensions stabilized, the 6D evolution described here could describe how two of the six extra dimensions evolve to become much larger than the others, as a consequence of the enormous expansion of the 4 large dimensions we can see.Comment: 27 pages + appendices, 2 figure

Braneworld inflation

We discuss various realizations of the four dimensional braneworld inflation in warped geometries of string theory. In all models the inflaton field is represented by a Dp probe brane scalar specifying its position in the warped throat of the compactification manifold. We study existing inflationary throat local geometries, and construct a new example. The inflationary brane is either a D3- or a D5-brane of type IIB string theory. In the latter case the inflationary brane is wrapping a two-cycle of the compactification manifold. We discuss some phenomenological aspects of the model where slow-roll conditions are under computational control.Comment: 31 pages + 6 figures, v2: published PRD versio

A model of head direction and landmark coding in complex environments

Environmental information is required to stabilize estimates of head direction (HD) based on angular path integration. However, it is unclear how this happens in real-world (visually complex) environments. We present a computational model of how visual feedback can stabilize HD information in environments that contain multiple cues of varying stability and directional specificity. We show how combinations of feature-specific visual inputs can generate a stable unimodal landmark bearing signal, even in the presence of multiple cues and ambiguous directional specificity. This signal is associated with the retrosplenial HD signal (inherited from thalamic HD cells) and conveys feedback to the subcortical HD circuitry. The model predicts neurons with a unimodal encoding of the egocentric orientation of the array of landmarks, rather than any one particular landmark. The relationship between these abstract landmark bearing neurons and head direction cells is reminiscent of the relationship between place cells and grid cells. Their unimodal encoding is formed from visual inputs via a modified version of Oja's Subspace Algorithm. The rule allows the landmark bearing signal to disconnect from directionally unstable or ephemeral cues, incorporate newly added stable cues, support orientation across many different environments (high memory capacity), and is consistent with recent empirical findings on bidirectional HD firing reported in the retrosplenial cortex. Our account of visual feedback for HD stabilization provides a novel perspective on neural mechanisms of spatial navigation within richer sensory environments, and makes experimentally testable predictions

Brane Induced Gravity: Codimension-2

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tensions branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, but the crossover from 5D to 6D is not. This shows how the vacuum energy problem manifests in BIG: instead of tuning vacuum energy to adjust the 4D curvature, generically one must tune it to get the desired crossover scales and the hierarchy between the scales governing the 4D \to 5D \to 6D transitions. In the near-critical limit, linearized perturbation theory remains under control below the crossover scale, and we find that linearized gravity around the vacuum looks like a scalar-tensor theory.Comment: 16 pages latex, 2 .eps figs, based on the talks given at the "Sowers Workshop", Virginia Tech, May 14-18, 2007, "Cosmology and Strings" workshop at ICTP, Trieste, Italy, July 9-13, 2007, "Dark Energy In the Universe", Hakone, Japan, Sep 1-4, 2007 and "Zagreb Workshop 2007", Zagreb, Croatia, Nov 9-11, 2007; v2: added reference

D-Brane Dynamics and NS5 Rings

We consider the classical motion of a probe D-brane moving in the background geometry of a ring of NS5 branes, assuming that the latter are non-dynamical. We analyse the solutions to the Dirac-Born-Infield (DBI) action governing the approximate dynamics of the system. In the near horizon (throat) approximation we find several exact solutions for the probe brane motion. These are compared to numerical solutions obtained in more general cases. One solution of particular interest is when the probe undergoes oscillatory motion through the centre of the ring (and perpendicular to it). By taking the ring radius sufficiently large, this solution should remain stable to any stringy corrections coming from open-strings stretching between the probe and the NS5-branes along the ring.Comment: 17 pages, Latex, 8 figures; References adde

Transplanckian energy production and slow roll inflation

In this paper we investigate how the energy density due to a non-standard choice of initial vacuum affects the expansion of the universe during inflation. To do this we introduce source terms in the Friedmann equations making sure that we respect the relation between gravity and thermodynamics. We find that the energy production automatically implies a slow rolling cosmological constant. Hence we also conclude that there is no well defined value for the cosmological constant in the presence of sources. We speculate that a non-standard vacuum can provide slow roll inflation on its own.Comment: 16 pages, 2 figures, version 2: minor corrections to section 4 and references adde