No abstract

In alternative theories of gravity, designed to produce cosmic acceleration at the current epoch, the growth of large scale structure can be modified. We study the potential of upcoming and future tomographic surveys such as DES and LSST, with the aid of CMB and supernovae data, to detect departures from the growth of cosmic structure expected within General Relativity. We employ parametric forms to quantify the potential time-and scale-dependent variation of the effective gravitational constant, and the differences between the two Newtonian potentials. We then apply the Fisher matrix technique to forecast the errors on the modified growth parameters from galaxy clustering, weak lensing, CMB, and their cross-correlations across multiple photometric redshift bins. We find that even with conservative assumptions about the data, DES will produce nontrivial constraints on modified growth, and that LSST will do significantly better.

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully reproduce these receptive fields. We further prove, mathematically, that sparseness and decorrelation are the key ingredients that allow for synaptically local plasticity rules to optimize a cooperative, linear generative image model formed by the neural representation. Finally, we discuss several interesting emergent properties of our network, with the intent of bridging the gap between theoretical and experimental studies of visual cortex.