Ensemble Analysis of Adaptive Compressed Genome Sequencing Strategies

Acquiring genomes at single-cell resolution has many applications such as in the study of microbiota. However, deep sequencing and assembly of all of millions of cells in a sample is prohibitively costly. A property that can come to rescue is that deep sequencing of every cell should not be necessary to capture all distinct genomes, as the majority of cells are biological replicates. Biologically important samples are often sparse in that sense. In this paper, we propose an adaptive compressed method, also known as distilled sensing, to capture all distinct genomes in a sparse microbial community with reduced sequencing effort. As opposed to group testing in which the number of distinct events is often constant and sparsity is equivalent to rarity of an event, sparsity in our case means scarcity of distinct events in comparison to the data size. Previously, we introduced the problem and proposed a distilled sensing solution based on the breadth first search strategy. We simulated the whole process which constrained our ability to study the behavior of the algorithm for the entire ensemble due to its computational intensity. In this paper, we modify our previous breadth first search strategy and introduce the depth first search strategy. Instead of simulating the entire process, which is intractable for a large number of experiments, we provide a dynamic programming algorithm to analyze the behavior of the method for the entire ensemble. The ensemble analysis algorithm recursively calculates the probability of capturing every distinct genome and also the expected total sequenced nucleotides for a given population profile. Our results suggest that the expected total sequenced nucleotides grows proportional to $\log$ of the number of cells and proportional linearly with the number of distinct genomes

Corrected entropy of the rotating black hole solution of the new massive gravity using the tunneling method and Cardy formula

We study the AdS rotating black hole solution for the Bergshoeff-Hohm-Townsend (BHT) massive gravity in three dimensions. The field equations of the asymptotically AdS black hole of the static metric can be expressed as the first law of thermodynamics, i.e. $dE=TdS-PdV$. The corrected Hawking-like temperature and entropy of asymptotically AdS rotating black hole are calculated using the Cardy formula and the tunneling method. Comparison of these methods will help identify the unknown leading correction parameter $\beta_1$ in the tunneling method.Comment: 6 page

Resurrecting the exponential and inverse power-law potentials in non-canonical inflation

We study inflation within the framework of non-canonical scalar field. In this scenario, we obtain the inflationary observables such as the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index as well as the equilateral non-Gaussianity parameter. Then, we apply these results for the exponential and inverse power-law potentials. Our investigation shows that although the predictions of these potentials in the standard canonical inflation are completely ruled out by the Planck 2015 observations, their results in non-canonical scenario can lie inside the allowed regions of the Planck 2015 data. We also find that in non-canonical inflation, the predictions of the aforementioned potentials for the running of the scalar spectral index and the equilateral non-Gaussianity parameter are in well agreement with the Planck 2015 results. Furthermore, we show that in the context of non-canonical inflation, the graceful exit problem of the exponential and inverse power-law potentials is resolved.Comment: 18 pages, 3 figure