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This work aims to jointly estimate the arrival rate of customers to a market and the nested logit model that forecasts hierarchical customer choices from an assortment of products. The estimation is based on censored transactional data, where lost sales are not recorded. The goal is to determine the arrival rate, customer taste coefficients, and nest dissimilarity parameters that maximize the likelihood of the observed data. The problem is formulated as a maximum likelihood estimation model that addresses two prevailing challenges in the existing literature: Estimating demand fromdata with unobservable lost salesand capturingcustomer taste heterogeneity arising from hierarchical choices. However, the model is intractable to solve or analyze due to the nonconcavity of the likelihood function in both taste coefficients and dissimilarity parameters. We characterize conditions under which the model parameters are identifiable. Our results reveal that the parameter identification is influenced by thediversity of products and nests. We also develop a sequential minorization-maximization algorithm to solve the problem, by which the problem boils down to solving a series of convex optimization models with simple structures. Then, we show the convergence of the algorithm by leveraging the structural properties of these models. We evaluate the performance of the algorithm by comparing it with widely used benchmarks, using both synthetic and real data. Our findings show that the algorithm consistently outperforms the benchmarks in maximizing in-sample likelihood and ranks among the top two in out-of-sample prediction accuracy. Moreover, our algorithm is particularly effective in estimating nested logit models with low dissimilarity parameters, yielding higher profitability compared to the benchmarks. 

DNA has shown great biocompatibility, programmable mechanical properties, and precise structural addressabil- ity at the nanometer scale, rendering it a material for constructing versatile nanorobots for biomedical applica- tions. Here, we present the design principle, synthesis, and characterization of a DNA nanorobotic hand, called DNA NanoGripper, that contains a palm and four bendable fingers as inspired by naturally evolved human hands, bird claws, and bacteriophages. Each NanoGripper finger consists of three phalanges connected by three rotat- able joints that are bendable in response to the binding of other entities. NanoGripper functions are enabled and driven by the interactions between moieties attached to the fingers and their binding partners. We demonstrate that the NanoGripper can be engineered to effectively interact with and capture nanometer-scale objects, includ- ing gold nanoparticles, gold NanoUrchins, and SARS-CoV-2 virions. With multiple DNA aptamer nanoswitches programmed to generate a fluorescent signal that is enhanced on a photonic crystal platform, the NanoGripper functions as a highly sensitive biosensor that selectively detects intact SARS-CoV-2 virions in human saliva with a limit of detection of ~100 copies per milliliter, providing a sensitivity equal to that of reverse transcription quanti- tative polymerase chain reaction (RT-qPCR). Quantified by flow cytometry assays, we demonstrated that the NanoGripper-aptamer complex can effectively block viral entry into the host cells, suggesting its potential for in- hibiting virus infections. The design, synthesis, and characterization of a sophisticated nanomachine that can be tailored for specific applications highlight a promising pathway toward feasible and efficient solutions to the de- tection and potential inhibition of virus infections.