Robust Transmissions in Wireless Powered Multi-Relay Networks with Chance Interference Constraints

In this paper, we consider a wireless powered multi-relay network in which a multi-antenna hybrid access point underlaying a cellular system transmits information to distant receivers. Multiple relays capable of energy harvesting are deployed in the network to assist the information transmission. The hybrid access point can wirelessly supply energy to the relays, achieving multi-user gains from signal and energy cooperation. We propose a joint optimization for signal beamforming of the hybrid access point as well as wireless energy harvesting and collaborative beamforming strategies of the relays. The objective is to maximize network throughput subject to probabilistic interference constraints at the cellular user equipment. We formulate the throughput maximization with both the time-switching and power-splitting schemes, which impose very different couplings between the operating parameters for wireless power and information transfer. Although the optimization problems are inherently non-convex, they share similar structural properties that can be leveraged for efficient algorithm design. In particular, by exploiting monotonicity in the throughput, we maximize it iteratively via customized polyblock approximation with reduced complexity. The numerical results show that the proposed algorithms can achieve close to optimal performance in terms of the energy efficiency and throughput.Comment: 14 pages, 8 figure

Numerical analysis of a time discretized method for nonlinear filtering problem with L\'evy process observations

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter solution. Then we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis

Cancer LncRNA Census reveals evidence for deep functional conservation of long noncoding RNAs in tumorigenesis.

Long non-coding RNAs (lncRNAs) are a growing focus of cancer genomics studies, creating the need for a resource of lncRNAs with validated cancer roles. Furthermore, it remains debated whether mutated lncRNAs can drive tumorigenesis, and whether such functions could be conserved during evolution. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, we introduce the Cancer LncRNA Census (CLC), a compilation of 122 GENCODE lncRNAs with causal roles in cancer phenotypes. In contrast to existing databases, CLC requires strong functional or genetic evidence. CLC genes are enriched amongst driver genes predicted from somatic mutations, and display characteristic genomic features. Strikingly, CLC genes are enriched for driver mutations from unbiased, genome-wide transposon-mutagenesis screens in mice. We identified 10 tumour-causing mutations in orthologues of 8 lncRNAs, including LINC-PINT and NEAT1, but not MALAT1. Thus CLC represents a dataset of high-confidence cancer lncRNAs. Mutagenesis maps are a novel means for identifying deeply-conserved roles of lncRNAs in tumorigenesis

Analyses of non-coding somatic drivers in 2,658 cancer whole genomes.

The discovery of drivers of cancer has traditionally focused on protein-coding genes1-4. Here we present analyses of driver point mutations and structural variants in non-coding regions across 2,658 genomes from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium5 of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). For point mutations, we developed a statistically rigorous strategy for combining significance levels from multiple methods of driver discovery that overcomes the limitations of individual methods. For structural variants, we present two methods of driver discovery, and identify regions that are significantly affected by recurrent breakpoints and recurrent somatic juxtapositions. Our analyses confirm previously reported drivers6,7, raise doubts about others and identify novel candidates, including point mutations in the 5' region of TP53, in the 3' untranslated regions of NFKBIZ and TOB1, focal deletions in BRD4 and rearrangements in the loci of AKR1C genes. We show that although point mutations and structural variants that drive cancer are less frequent in non-coding genes and regulatory sequences than in protein-coding genes, additional examples of these drivers will be found as more cancer genomes become available

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts

The Spectral Method for the Cahn-Hilliard Equation with Concentration-Dependent Mobility

This paper is concerned with the numerical approximations of the Cahn-Hilliard-type equation with concentration-dependent mobility. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method for the space and the implicit Euler method for the time. Numerical experiments are carried out to illustrate the theoretical analysis

Mixed Weak Galerkin Method for Heat Equation with Random Initial Condition

This paper is devoted to the numerical analysis of weak Galerkin mixed finite element method (WGMFEM) for solving a heat equation with random initial condition. To set up the finite element spaces, we choose piecewise continuous polynomial functions of degree j+1 with j≥0 for the primary variables and piecewise discontinuous vector-valued polynomial functions of degree j for the flux ones. We further establish the stability analysis of both semidiscrete and fully discrete WGMFE schemes. In addition, we prove the optimal order convergence estimates in L2 norm for scalar solutions and triple-bar norm for vector solutions and statistical variance-type convergence estimates. Ultimately, we provide a few numerical experiments to illustrate the efficiency of the proposed schemes and theoretical analysis