Abstract Let R be an S-graded ring inducing S, that is, a ring which is the direct sum of a family of its additive subgroups indexed by a nonempty set S, under the assumption that the product of homogeneous elements is again homogeneous. We introduce a graded version of the subring and discuss its homogeneity, where U(R) denotes the group of units of R. Communicated by Pavel Kolesnikov

Abstract We study the graded isoradical of a ring graded by a group. In particular, we compare the graded isoradical and the classical isoradical of a graded ring, examine the question of how the (graded) isoradical of a graded ring depends on the classical isoradical of a ring which corresponds to the identity element of the grading group, and we also give some sufficient conditions under which the classical isoradical of a graded ring is homogeneous.

Principled computational approaches for tumor phylogeny reconstruction via single-cell sequencing typically aim to build the most likely perfect phylogeny tree from the noisy genotype matrix - which represents genotype calls of single-cells. This problem is NP-hard, and as a result, existing approaches aim to solve relatively small instances of it through combinatorial optimization techniques or Bayesian inference. As expected, even when the goal is to infer basic topological features of the tumor phylogeny - rather than reconstructing the topology entirely, these approaches could be prohibitively slow. In this paper, we introduce fast deep-learning solutions to the problems of inferring whether the most likely tree has a linear (chain) or branching topology and whether a perfect phylogeny is feasible from a given genotype matrix. We also present a reinforcement learning approach for reconstructing the most likely tumor phylogeny. This preliminary work demonstrates that data-driven approaches can reconstruct key features of tumor evolution.

Motivation Recent advances in single cell sequencing (SCS) offer an unprecedented insight into tumor emergence and evolution. Principled approaches to tumor phylogeny reconstruction via SCS data are typically based on general computational methods for solving an integer linear program (ILP), or a constraint satisfaction program (CSP), which, although guaranteeing convergence to the most likely solution, are very slow. Others based on Monte Carlo Markov Chain (MCMC) or alternative heuristics not only offer no such guarantee, but also are not faster in practice. As a result, novel methods that can scale up to handle the size and noise characteristics of emerging SCS data are highly desirable to fully utilize this technology. Results We introduce PhISCS-BnB, a Branch and Bound algorithm to compute the most likely perfect phylogeny (PP) on an input genotype matrix extracted from a SCS data set. PhISCS-BnB not only offers an optimality guarantee, but is also 10 to 100 times faster than the best available methods on simulated tumor SCS data. We also applied PhISCS-BnB on a large melanoma data set derived from the sub-lineages of a cell line involving 24 clones with 3574 mutations, which returned the optimal tumor phylogeny in less than 2 hours. The resulting phylogeny also agrees with bulk exome sequencing data obtained from in vivo tumors growing out from the same cell line. Availability https://github.com/algo-cancer/PhISCS-BnB

In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the observations are high-dimensional (e.g. images). For this reason, previous works have considered partial models, which model only part of the observation. In this paper, we show that partial models can be causally incorrect: they are confounded by the observations they don't model, and can therefore lead to incorrect planning. To address this, we introduce a general family of partial models that are provably causally correct, yet remain fast because they do not need to fully model future observations.

Abstract We present a small collection of examples and counterexamples for selected problems, mostly in spectral graph theory, that have occupied our minds over a number of years without being completely resolved.

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. Joana Carlevaro-Fita, Andrés Lanzós et al. present the Cancer LncRNA Census (CLC), a manually curated dataset of 122 long noncoding RNAs (lncRNAs) with experimentally-validated functions in cancer based on data from the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium. CLC lncRNAs have unique gene features, and a number display evidence for cancer-driving functions that are conserved from humans to mice.

Multi-omics datasets represent distinct aspects of the central dogma of molecular biology. Such high-dimensional molecular profiles pose challenges to data interpretation and hypothesis generation. ActivePathways is an integrative method that discovers significantly enriched pathways across multiple datasets using statistical data fusion, rationalizes contributing evidence and highlights associated genes. As part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2658 cancers across 38 tumor types, we integrated genes with coding and non-coding mutations and revealed frequently mutated pathways and additional cancer genes with infrequent mutations. We also analyzed prognostic molecular pathways by integrating genomic and transcriptomic features of 1780 breast cancers and highlighted associations with immune response and anti-apoptotic signaling. Integration of ChIP-seq and RNA-seq data for master regulators of the Hippo pathway across normal human tissues identified processes of tissue regeneration and stem cell regulation. ActivePathways is a versatile method that improves systems-level understanding of cellular organization in health and disease through integration of multiple molecular datasets and pathway annotations. Multi-omics datasets pose major challenges to data interpretation and hypothesis generation owing to their high-dimensional molecular profiles. Here, the authors develop ActivePathways method, which uses data fusion techniques for integrative pathway analysis of multi-omics data and candidate gene discovery.

The discovery of driver mutations is one of the key motivations for cancer genome sequencing. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2658 cancers across 38 tumour types, we describe DriverPower, a software package that uses mutational burden and functional impact evidence to identify driver mutations in coding and non-coding sites within cancer whole genomes. Using a total of 1373 genomic features derived from public sources, DriverPower’s background mutation model explains up to 93% of the regional variance in the mutation rate across multiple tumour types. By incorporating functional impact scores, we are able to further increase the accuracy of driver discovery. Testing across a collection of 2583 cancer genomes from the PCAWG project, DriverPower identifies 217 coding and 95 non-coding driver candidates. Comparing to six published methods used by the PCAWG Drivers and Functional Interpretation Working Group, DriverPower has the highest F1 score for both coding and non-coding driver discovery. This demonstrates that DriverPower is an effective framework for computational driver discovery. Analysis of cancer genome sequencing data has enabled the discovery of driver mutations. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium the authors present DriverPower, a software package that identifies coding and non-coding driver mutations within cancer whole genomes via consideration of mutational burden and functional impact evidence.

We present SVclone, a computational method for inferring the cancer cell fraction of structural variant (SV) breakpoints from whole-genome sequencing data. SVclone accurately determines the variant allele frequencies of both SV breakends, then simultaneously estimates the cancer cell fraction and SV copy number. We assess performance using in silico mixtures of real samples, at known proportions, created from two clonal metastases from the same patient. We find that SVclone’s performance is comparable to single-nucleotide variant-based methods, despite having an order of magnitude fewer data points. As part of the Pan-Cancer Analysis of Whole Genomes (PCAWG) consortium, which aggregated whole-genome sequencing data from 2658 cancers across 38 tumour types, we use SVclone to reveal a subset of liver, ovarian and pancreatic cancers with subclonally enriched copy-number neutral rearrangements that show decreased overall survival. SVclone enables improved characterisation of SV intra-tumour heterogeneity. The authors present SVclone, a computational method for inferring the cancer cell fraction of structural variants from whole-genome sequencing data.

The type and genomic context of cancer mutations depend on their causes. These causes have been characterized using signatures that represent mutation types that co-occur in the same tumours. However, it remains unclear how mutation processes change during cancer evolution due to the lack of reliable methods to reconstruct evolutionary trajectories of mutational signature activity. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole-genome sequencing data from 2658 cancers across 38 tumour types, we present TrackSig, a new method that reconstructs these trajectories using optimal, joint segmentation and deconvolution of mutation type and allele frequencies from a single tumour sample. In simulations, we find TrackSig has a 3–5% activity reconstruction error, and 12% false detection rate. It outperforms an aggressive baseline in situations with branching evolution, CNA gain, and neutral mutations. Applied to data from 2658 tumours and 38 cancer types, TrackSig permits pan-cancer insight into evolutionary changes in mutational processes. Cancers evolve as they progress under differing selective pressures. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, the authors present the method TrackSig the estimates evolutionary trajectories of somatic mutational processes from single bulk tumour data.