A Stochastic Formulation of the Bass Model of New-Product Diffusion

In the past several decades, new-product diffusion models has been an active area of research in marketing (see, e.g., Mahajan, Muller, and Wind 2000, and Mahajan and Wind 1986). Such models are useful because they can provide important insights into the timing of initial purchase of new products by consumers. Much of the work in this area has been spawned by a seminal paper of Bass (1969), in which it was postulated that the trajectory of cumulative adoptions of a new product follows a deterministic function whose instantaneous growth rate depends on two parameters, one of which captures a consumer?s intrinsic tendency to purchase, independent of the number of previous adopters, and the other captures a positive force of influence on a consumer by previous adopters. While Bass?s model, or the Bass Model (BM), yields an S-shaped cumulative-adoptions curve that has proven to provide excellent empirical fit for a wide range of new-product-adoptions data sets (especially for consumer durables), there also has been a common belief (see, e.g., Eliashberg and Chatterjee 1986) that it would be of interest to have an appropriate stochastic version of his model. The purpose of this paper is to formulate and study a stochastic counterpart of the BM. Inspired by a very early paper of Taga and Isii (1959), we formulate the trajectory of cumulative number of adoptions as a pure birth process with a set of state-dependent birth rates that are judiciously chosen to closely parallel the roles played by the two parameters in the deterministic BM. We demonstrate that with our choice of birth rates, the resulting pure birth process exhibits characteristics that resemble those in the BM. In particular, we show that the fraction of individuals who have adopted the product by time t in our formulation agrees with (converges in probability to) the corresponding deterministic fraction in a BM with the same pair of parameters, when the total number of consumers in the target population approaches infinity. Our formulation, therefore, supports and expands the BM by having explicit micro-level stochastic interactions amongst individual adopters.Pure Birth Processes, Diffusion Models, New-Product Adoptions, Epidemics,

Association of the CHRNA3 Locus with Lung Cancer Risk and Prognosis in Chinese Han Population

IntroductionRecent genome-wide association studies in Caucasians revealed association with lung cancer risk of single nucleotide polymorphisms (SNPs) in the locus containing two nicotine acetylcholine receptor CHRNA genes. However, the reported risk SNPs are extremely rare in Asians. This study sought to identify other variants on CHRNA3 associated with lung cancer susceptibility and to explore whether SNPs of CHRNA3 are of prognostic factors in patients with non-small cell lung cancer (NSCLC) in Chinese Han population.MethodsA case-control study of 529 cases and 567 controls was performed to study the association of three SNPs (rs3743076, rs3743078, and rs3743073) in CHRNA3 with lung cancer risk in Chinese Han population using logistic regression models. The relationship between CHRNA3 polymorphisms with overall survival among 122 patients with advanced stage (stage IIIb and IV) NSCLC were evaluated using Cox multiple model based on the International Association for the Study of Lung Cancer recommended tumor, node, metastasis new staging.ResultsPatients with genotypes TG or GG for the novel SNP rs3743073 in CHRNA3 gene, compared with those with TT, showed an increased risk of lung cancer (adjusted odds ratio = 1.91; 95% confidence interval, 1.38–2.63; p = 9.67 × 10−5) and worst survival (adjusted hazard ratio = 2.35; 95% confidence interval, 1.05–5.26; p = 0.04) in patients with advanced stage NSCLC based on International Association for the Study of Lung Cancer recommended tumor, node, metastasis new staging.ConclusionsThese results suggest that the rs3743073 polymorphism in CHRNA3 is predictive for lung cancer risk and prognostic in advanced stage NSCLC in Chinese Han population

Storage of multiple single-photon pulses emitted from a quantum dot in a solid-state quantum memory

Quantum repeaters are critical components for distributing entanglement over long distances in presence of unavoidable optical losses during transmission. Stimulated by Duan-Lukin-Cirac-Zoller protocol, many improved quantum-repeater protocols based on quantum memories have been proposed, which commonly focus on the entanglement-distribution rate. Among these protocols, the elimination of multi-photons (multi-photon-pairs) and the use of multimode quantum memory are demonstrated to have the ability to greatly improve the entanglement-distribution rate. Here, we demonstrate the storage of deterministic single photons emitted from a quantum dot in a polarization-maintaining solid-state quantum memory; in addition, multi-temporal-mode memory with $1$, $20$ and $100$ narrow single-photon pulses is also demonstrated. Multi-photons are eliminated, and only one photon at most is contained in each pulse. Moreover, the solid-state properties of both sub-systems make this configuration more stable and easier to be scalable. Our work will be helpful in the construction of efficient quantum repeaters based on all-solid-state devicesComment: Published version, including supplementary materia

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