Indexing User Uploaded Videos For Late Arriving Reference Content

Disclosed herein is a mechanism for indexing user uploaded videos. This mechanism can be used, for example, to detect unauthorized media content items in instances where the reference content is uploaded or otherwise received after the receipt of user uploaded video content. More particularly, the mechanism can create a video index of user uploaded video content or a subset of user uploaded video content that has met one or more criterion (e.g., a video that has been viewed at least a predetermined number of times) and a reference index of reference content including references files that have been activated subsequent to receiving corresponding user uploaded video content. Accordingly, activated reference content can be compared against the video index and user uploaded video content can be compared against the reference index to determine whether there is matching content

On the asymptotic behaviour of cosmic density-fluctuation power spectra

We study the small-scale asymptotic behaviour of the cosmic density-fluctuation power spectrum in the Zel'dovich approximation. For doing so, we extend Laplace's method in arbitrary dimensions and use it to prove that this power spectrum necessarily develops an asymptotic tail proportional to $k^{-3}$ , irrespective of the cosmological model and the power spectrum of the initial matter distribution. The exponent $-3$ is set only by the number of spatial dimensions. We derive the complete asymptotic series of the power spectrum and compare the leading- and next-to-leading-order terms to derive characteristic scales for the onset of non-linear structure formation, independent of the cosmological model and the type of dark matter. Combined with earlier results on the mean-field approximation for including particle interactions, this asymptotic behaviour is likely to remain valid beyond the Zel'dovich approximation. Due to their insensitivity to cosmological assumptions, our results are generally applicable to particle distributions with positions and momenta drawn from a Gaussian random field. We discuss an analytically solvable toy model to further illustrate the formation of the $k^{-3}$ asymptotic tail.Comment: 22 pages, 4 figues, to be submitted to SciPost Physics Added arguments to section 1 and section 5, results unchange

Backwards integration and strategic delegation

We analyze the effects of downstream firms’ acquisition of pure cash flow rights in an efficient upstream supplier when all firms compete in prices. With an acquisition, downstream firms internalize the effects of their actions on their rivals’ sales. Double marginalization is enhanced. Whereas full vertical integration would lead to decreasing, passive backwards ownership leads to increasing downstream prices and is more profitable, as long as competition is sufficiently intensive. Downstream acquirers strategically abstain from vertical control, inducing the efficient supplier to commit to high prices. All results are sustained when upstream suppliers are allowed to charge two part tariffs