Integrated Analysis and Synthesis of the Dynamic Behaviour of a Carbonate Field

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Signatures of primordial gravitational waves in matter power spectrum

We simulate the evolution of a dust universe from $z=1089$ to $z=0$ by numerically integrating the Einstein's equation for a spatially flat Friedmann-Lemaire-Robertson-Walker (FLRW) background spacetime with scalar perturbations which are derived from the matter power spectrum produced with the Code for Anisotropies in the Microwave Background (CAMB). To investigate the effects of primordial gravitational waves (GWs) on the inhomogeneity of the universe, we add an additional decaying, divergenceless and traceless primordial tensor perturbation with its initial amplitude being $3\times 10^{-4}$ to the above metric. We find that this primordial tensor perturbation suppresses the matter power spectrum by about $0.01\%$ at $z=0$ for modes with wave number similar to its. This suppression may be a possible probe of a GWs background in the future.Comment: 8 pages, 5 figure

Multi-Label Zero-Shot Human Action Recognition via Joint Latent Ranking Embedding

Human action recognition refers to automatic recognizing human actions from a video clip. In reality, there often exist multiple human actions in a video stream. Such a video stream is often weakly-annotated with a set of relevant human action labels at a global level rather than assigning each label to a specific video episode corresponding to a single action, which leads to a multi-label learning problem. Furthermore, there are many meaningful human actions in reality but it would be extremely difficult to collect/annotate video clips regarding all of various human actions, which leads to a zero-shot learning scenario. To the best of our knowledge, there is no work that has addressed all the above issues together in human action recognition. In this paper, we formulate a real-world human action recognition task as a multi-label zero-shot learning problem and propose a framework to tackle this problem in a holistic way. Our framework holistically tackles the issue of unknown temporal boundaries between different actions for multi-label learning and exploits the side information regarding the semantic relationship between different human actions for knowledge transfer. Consequently, our framework leads to a joint latent ranking embedding for multi-label zero-shot human action recognition. A novel neural architecture of two component models and an alternate learning algorithm are proposed to carry out the joint latent ranking embedding learning. Thus, multi-label zero-shot recognition is done by measuring relatedness scores of action labels to a test video clip in the joint latent visual and semantic embedding spaces. We evaluate our framework with different settings, including a novel data split scheme designed especially for evaluating multi-label zero-shot learning, on two datasets: Breakfast and Charades. The experimental results demonstrate the effectiveness of our framework.Comment: 27 pages, 10 figures and 7 tables. Technical report submitted to a journal. More experimental results/references were added and typos were correcte

Random restricted partitions

We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions of all of the parts together and that of the largest part as $n$ tends to infinity while $m$ is fixed or tends to infinity. In particular, if $m$ goes to infinity not fast enough, the largest part satisfies the central limit theorem. The second measure is very general. It includes the Dirichlet distribution and the uniform distribution as special cases. We derive the asymptotic distributions of the parts jointly and that of the largest part by taking limit of $n$ and $m$ in the same manner as that in the first probability measure.Comment: 32 page