Solution of a one-dimensional stochastic model with branching and coagulation reactions

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical Review E (September 2001

Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A + A -> A, despite differences between the two models in other statistical measures, such as the interparticle distribution function

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001

Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment

LUX-ZEPLIN (LZ) is a next-generation dark matter direct detection experiment that will operate 4850 feet underground at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, USA. Using a two-phase xenon detector with an active mass of 7 tonnes, LZ will search primarily for low-energy interactions with weakly interacting massive particles (WIMPs), which are hypothesized to make up the dark matter in our galactic halo. In this paper, the projected WIMP sensitivity of LZ is presented based on the latest background estimates and simulations of the detector. For a 1000 live day run using a 5.6-tonne fiducial mass, LZ is projected to exclude at 90% confidence level spin-independent WIMP-nucleon cross sections above 1.4 × 10-48cm2 for a 40 GeV/c2 mass WIMP. Additionally, a 5σ discovery potential is projected, reaching cross sections below the exclusion limits of recent experiments. For spin-dependent WIMP-neutron(-proton) scattering, a sensitivity of 2.3 × 10−43 cm2 (7.1 × 10−42 cm2) for a 40 GeV/c2 mass WIMP is expected. With underground installation well underway, LZ is on track for commissioning at SURF in 2020

Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020

We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe

The evolution of lung cancer and impact of subclonal selection in TRACERx

Lung cancer is the leading cause of cancer-associated mortality worldwide. Here we analysed 1,644 tumour regions sampled at surgery or during follow-up from the first 421 patients with non-small cell lung cancer prospectively enrolled into the TRACERx study. This project aims to decipher lung cancer evolution and address the primary study endpoint: determining the relationship between intratumour heterogeneity and clinical outcome. In lung adenocarcinoma, mutations in 22 out of 40 common cancer genes were under significant subclonal selection, including classical tumour initiators such as TP53 and KRAS. We defined evolutionary dependencies between drivers, mutational processes and whole genome doubling (WGD) events. Despite patients having a history of smoking, 8% of lung adenocarcinomas lacked evidence of tobacco-induced mutagenesis. These tumours also had similar detection rates for EGFR mutations and for RET, ROS1, ALK and MET oncogenic isoforms compared with tumours in never-smokers, which suggests that they have a similar aetiology and pathogenesis. Large subclonal expansions were associated with positive subclonal selection. Patients with tumours harbouring recent subclonal expansions, on the terminus of a phylogenetic branch, had significantly shorter disease-free survival. Subclonal WGD was detected in 19% of tumours, and 10% of tumours harboured multiple subclonal WGDs in parallel. Subclonal, but not truncal, WGD was associated with shorter disease-free survival. Copy number heterogeneity was associated with extrathoracic relapse within 1 year after surgery. These data demonstrate the importance of clonal expansion, WGD and copy number instability in determining the timing and patterns of relapse in non-small cell lung cancer and provide a comprehensive clinical cancer evolutionary data resource

The artificial intelligence-based model ANORAK improves histopathological grading of lung adenocarcinoma

The introduction of the International Association for the Study of Lung Cancer grading system has furthered interest in histopathological grading for risk stratification in lung adenocarcinoma. Complex morphology and high intratumoral heterogeneity present challenges to pathologists, prompting the development of artificial intelligence (AI) methods. Here we developed ANORAK (pyrAmid pooliNg crOss stReam Attention networK), encoding multiresolution inputs with an attention mechanism, to delineate growth patterns from hematoxylin and eosin-stained slides. In 1,372 lung adenocarcinomas across four independent cohorts, AI-based grading was prognostic of disease-free survival, and further assisted pathologists by consistently improving prognostication in stage I tumors. Tumors with discrepant patterns between AI and pathologists had notably higher intratumoral heterogeneity. Furthermore, ANORAK facilitates the morphological and spatial assessment of the acinar pattern, capturing acinus variations with pattern transition. Collectively, our AI method enabled the precision quantification and morphology investigation of growth patterns, reflecting intratumoral histological transitions in lung adenocarcinoma

Evolutionary characterization of lung adenocarcinoma morphology in TRACERx

Lung adenocarcinomas (LUADs) display a broad histological spectrum from low-grade lepidic tumors through to mid-grade acinar and papillary and high-grade solid, cribriform and micropapillary tumors. How morphology reflects tumor evolution and disease progression is poorly understood. Whole-exome sequencing data generated from 805 primary tumor regions and 121 paired metastatic samples across 248 LUADs from the TRACERx 421 cohort, together with RNA-sequencing data from 463 primary tumor regions, were integrated with detailed whole-tumor and regional histopathological analysis. Tumors with predominantly high-grade patterns showed increased chromosomal complexity, with higher burden of loss of heterozygosity and subclonal somatic copy number alterations. Individual regions in predominantly high-grade pattern tumors exhibited higher proliferation and lower clonal diversity, potentially reflecting large recent subclonal expansions. Co-occurrence of truncal loss of chromosomes 3p and 3q was enriched in predominantly low-/mid-grade tumors, while purely undifferentiated solid-pattern tumors had a higher frequency of truncal arm or focal 3q gains and SMARCA4 gene alterations compared with mixed-pattern tumors with a solid component, suggesting distinct evolutionary trajectories. Clonal evolution analysis revealed that tumors tend to evolve toward higher-grade patterns. The presence of micropapillary pattern and ‘tumor spread through air spaces’ were associated with intrathoracic recurrence, in contrast to the presence of solid/cribriform patterns, necrosis and preoperative circulating tumor DNA detection, which were associated with extra-thoracic recurrence. These data provide insights into the relationship between LUAD morphology, the underlying evolutionary genomic landscape, and clinical and anatomical relapse risk