Topological Schemas of Memory Spaces

Hippocampal cognitive map---a neuronal representation of the spatial environment---is broadly discussed in the computational neuroscience literature for decades. More recent studies point out that hippocampus plays a major role in producing yet another cognitive framework that incorporates not only spatial, but also nonspatial memories---the memory space. However, unlike cognitive maps, memory spaces have been barely studied from a theoretical perspective. Here we propose an approach for modeling hippocampal memory spaces as an epiphenomenon of neuronal spiking activity. First, we suggest that the memory space may be viewed as a finite topological space---a hypothesis that allows treating both spatial and nonspatial aspects of hippocampal function on equal footing. We then model the topological properties of the memory space to demonstrate that this concept naturally incorporates the notion of a cognitive map. Lastly, we suggest a formal description of the memory consolidation process and point out a connection between the proposed model of the memory spaces to the so-called Morris' schemas, which emerge as the most compact representation of the memory structure.Comment: 24 pages, 8 Figures, 1 Suppl. Figur

Stability analysis of black holes in massive gravity: a unified treatment

We consider the analytic solutions of massive (bi)gravity which can be written in a simple form using advanced Eddington-Finkelstein coordinates. We analyse the stability of these solutions against radial perturbations. First we recover the previously obtained result on the instability of the bidiagonal bi-Schwarzschild solutions. In the non-bidiagonal case (which contains, in particular, the Schwarzschild solution with Minkowski fiducial metric) we show that generically there are physical spherically symmetric perturbations, but no unstable modes.Comment: 4 pages; v2: matches the published versio

Gravitational focusing of Imperfect Dark Matter

Motivated by the projectable Horava--Lifshitz model/mimetic matter scenario, we consider a particular modification of standard gravity, which manifests as an imperfect low pressure fluid. While practically indistinguishable from a collection of non-relativistic weakly interacting particles on cosmological scales, it leaves drastically different signatures in the Solar system. The main effect stems from gravitational focusing of the flow of Imperfect Dark Matter passing near the Sun. This entails strong amplification of Imperfect Dark Matter energy density compared to its average value in the surrounding halo. The enhancement is many orders of magnitude larger than in the case of Cold Dark Matter, provoking deviations of the metric in the second order in the Newtonian potential. Effects of gravitational focusing are prominent enough to substantially affect the planetary dynamics. Using the existing bound on the PPN parameter $\beta_{PPN}$, we deduce a stringent constraint on the unique constant of the model.Comment: 34 pages, 1 figure. Clarifications and references added. Matches published versio

Dressing a black hole with a time-dependent Galileon

We present a class of exact scalar-tensor black holes for a shift-symmetric part of the Horndeski action. The action includes a higher order scalar tensor interaction term. We find that for a static and spherically symmetric space-time, the scalar field, if time dependent, can be non-trivial and regular thus circumventing in an interesting way no-hair arguments for gallileons. Furthermore, within this class we find a stealth Schwarzschild and a partially self-tuned de-Sitter Schwarzschild black hole, both exhibiting a non trivial and regular space and time dependent scalar. In the latter solution the bulk vacuum energy is screened from a necessarily smaller geometric effective de Sitter vacuum via an integration constant associated to the time dependent scalar field.Comment: v2: references added; v3: matches published versio

Caustic free completion of pressureless perfect fluid and k-essence

Both k-essence and the pressureless perfect fluid develop caustic singularities at finite time. We further explore the connection between the two and show that they belong to the same class of models, which admits the caustic free completion by means of the canonical complex scalar field. Specifically, the free massive/self-interacting complex scalar reproduces dynamics of pressureless perfect fluid/shift-symmetric k-essence under certain initial conditions in the limit of large mass/sharp self-interacting potential. We elucidate a mechanism of resolving caustic singularities in the complete picture. The collapse time is promoted to complex number. Hence, the singularity is not developed in real time. The same conclusion holds for a collection of collisionless particles modelled by means of the Schroedinger equation, or ultra-light axions (generically, coherent oscillations of bosons in the Bose--Einstein condensate state).Comment: 20 pages, 2 figures; clarifications and references added. Matches published versio