Sound wave generation by a spherically symmetric outburst and AGN Feedback in Galaxy Clusters

We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind AGN feedback in the intra cluster medium (ICM). For a given density and pressure of the medium, the spatial structure and energy partition at a given time $t_{age}$ (since the onset of the outburst) are fully determined by the total injected energy $E_{inj}$ and the duration $t_b$ of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of $E_{inj}$ and $t_b$. For an instantaneous outburst with $t_b\rightarrow 0$, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is $\lesssim$12% of $E_{inj}$. As $t_b$ increases, the solution approaches the "slow piston" limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst $(E_{inj}, t_b$ and $t_{age})$ to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated $(E_{inj}, t_b$ and $t_{age})$ agree with numerical simulations tailored for these objects with $20-30\%$ accuracy.Comment: Accepted by MNRAS, add one figure in appendix and minor changes in text based on referee's commen

Integration by differentiation: new proofs, methods and examples

Recently, new methods were introduced which allow one to solve ordinary integrals by performing only derivatives. These studies were originally motivated by the difficulties of the quantum field theoretic path integral, and correspondingly, the results were derived by heuristic methods. Here, we give rigorous proofs for the methods to hold on fully specified function spaces. We then illustrate the efficacy of the new methods by applying them to the study of the surprising behavior of so-called Borwein integrals.Comment: Match published versio

Scaling Properties of Superoscillations and the Extension to Periodic Signals

Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more pronounced the desired superoscillatory behavior is to be, the more difficult it becomes to produce, or even only calculate, such highly fine-tuned wave forms in practice. Here, we investigate how this sensitivity to preparation errors scales for a method for constructing superoscillatory functions which is optimal in the sense that it minimizes the energetic expense. We thereby also arrive at very accurate approximations of functions which are so highly superoscillatory that they cannot be calculated numerically. We then investigate to what extent the scaling and sensitivity results for superoscillatory functions on the real line extend to the experimentally important case of superoscillatory functions that are periodic.Comment: 19 pages, 4 figure

Liver lesion segmentation informed by joint liver segmentation

We propose a model for the joint segmentation of the liver and liver lesions in computed tomography (CT) volumes. We build the model from two fully convolutional networks, connected in tandem and trained together end-to-end. We evaluate our approach on the 2017 MICCAI Liver Tumour Segmentation Challenge, attaining competitive liver and liver lesion detection and segmentation scores across a wide range of metrics. Unlike other top performing methods, our model output post-processing is trivial, we do not use data external to the challenge, and we propose a simple single-stage model that is trained end-to-end. However, our method nearly matches the top lesion segmentation performance and achieves the second highest precision for lesion detection while maintaining high recall.Comment: Late upload of conference version (ISBI

Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters II: impact of thermal conduction

We analyze the impact of thermal conduction on the appearance of a shock-heated gas shell which is produced when a spherically symmetric outburst of a supermassive black hole inflates bubbles of relativistic plasma at the center of a galaxy cluster. The presence of the hot and low-density shell can be used as an ancillary indicator for a high rate of energy release during the outburst, which is required to drive strong shocks into the gas. Here we show that conduction can effectively erase such shell, unless the diffusion of electrons is heavily suppressed. We conclude that a more robust proxy to the energy release rate is the ratio between the shock radius and bubble radius. We also revisited the issue of sound waves dissipation induced by thermal conduction in a scenario, where characteristic wavelength of the sound wave is set by the total energy of the outburst. For a fiducial short outburst model, the dissipation length does not exceed the cooling radius in a typical cluster, provided that the conduction is suppressed by a factor not larger than $\sim$100. For quasi-continuous energy injection neither the shock-heated shell nor the outgoing sound wave are important and the role of conduction is subdominant.Comment: 12 pages, 10 figures, MNRAS in pres

Metabolic Pathways Enhancement Confers Poor Prognosis in p53 Exon Mutant Hepatocellular Carcinoma.

RNA-Sequencing (RNA-Seq), the most commonly used sequencing application tool, is not only a method for measuring gene expression but also an excellent media to detect important structural variants such as single nucleotide variants (SNVs), insertion/deletion (Indels), or fusion transcripts. The Cancer Genome Atlas (TCGA) contains genomic data from a variety of cancer types and also provides the raw data generated by TCGA consortium. p53 is among the top 10 somatic mutations associated with hepatocellular carcinoma (HCC). The aim of the present study was to analyze concordant different gene profiles and the priori defined set of genes based on p53 mutation status in HCC using RNA-Seq data. In the study, expression profile of 11 799 genes on 42 paired tumor and adjacent normal tissues was collected, processed, and further stratified by the mutated versus normal p53 expression. Furthermore, we used a knowledge-based approach Gene Set Enrichment Analysis (GSEA) to compare between normal and p53 mutation gene expression profiles. The statistical significance (nominal P value) of the enrichment score (ES) genes was calculated. The ranked gene list that reflects differential expression between p53 wild-type and mutant genotypes was then mapped to metabolic process by KEGG, an encyclopedia of genes and genomes to assign functional meanings. These approaches enable us to identify pathways and potential target gene/pathways that are highly expressed in p53 mutated HCC. Our analysis revealed 2 genes, the hexokinase 2 (HK2) and Enolase 1 (ENO1), were conspicuous of red pixel in the heatmap. To further explore the role of these genes in HCC, the overall survival plots by Kaplan-Meier method were performed for HK2 and ENO1 that revealed high HK2 and ENO1 expression in patients with HCC have poor prognosis. These results suggested that these glycolysis genes are associated with mutated-p53 in HCC that may contribute to poor prognosis. In this proof-of-concept study, we proposed an approach for identifying novel potential therapeutic targets in human HCC with mutated p53. These approaches can take advantage of the massive next-generation sequencing (NGS) data generated worldwide and make more out of it by exploring new potential therapeutic targets

The ghost in the radiation: robust encodings of the black hole interior

We reconsider the black hole firewall puzzle, emphasizing that quantum error- correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation