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We develop an analytical framework to appropriately model and adequately analyze A/B tests in presence of nonparametric nonstationarities in the targeted business metrics. A/B tests, also known as online randomized controlled experiments, have been used at scale by data-driven enterprises to guide decisions and test innovative ideas to improve core business metrics. Meanwhile, nonstationarities, such as the time-of-day effect and the day-of-week effect, can often arise nonparametrically in key business metrics involving purchases, revenue, conversions, customer experiences, and so on. First, we develop a generic nonparametric stochastic model to capture nonstationarities in A/B test experiments, where each sample represents a visit or action associated with a time label. We build a practically relevant limiting regime to facilitate analyzing large-sample estimator performances under nonparametric nonstationarities. Second, we show that ignoring or inadequately addressing nonstationarities can cause standard A/B test estimators to have suboptimal variance and nonvanishing bias, therefore leading to loss of statistical efficiency and accuracy. We provide a new estimator that views time as a continuous strata and performs poststratification with a data-dependent number of stratification levels. Without making parametric assumptions, we prove a central limit theorem for the proposed estimator and show that the estimator attains the best achievable asymptotic variance and is asymptotically unbiased. Third, we propose a time-grouped randomization that is designed to balance treatment and control assignments at granular time scales. We show that when the time-grouped randomization is integrated to standard experimental designs to generate experiment data, simple A/B test estimators can achieve asymptotically optimal variance. A brief account of numerical experiments are conducted to illustrate the analysis. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.01205 . 

This work presents a general strategy for integrating photoresponsive molecules into liquid crystal elastomers (LCEs) using Diels–Alder chemistry. The method introduces various photochromes, offering a scalable route for multifunctional LCEs. 

Spatiotemporal mode-locking in a laser with anomalous dispersion is investigated. Mode-locked states with varying modal content can be observed, but we find it difficult to observe highly-multimode states. We describe the properties of these mode-locked states and compare them to the results of numerical simulations. Prospects for the generation of highly-multimode states and lasers based on multimode soliton formation are discussed. 

Kerr beam cleaning in graded-index multimode fiber has been investigated in experiments with sub-nanosecond pulses and in experiments with femtosecond pulses at wavelengths where the dispersion is normal. We report a theoretical and experimental study of this effect with femtosecond pulses and anomalous dispersion. In this regime, only weak beam cleaning is observed experimentally, along with strong temporal evolution of the pulse. Numerical simulations exhibit the qualitative trends of the experiments. 

The commercially available polyelectrolyte complex poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) is ubiquitous in organic and hybrid electronics. As such, it has often been used as a benchmark material for fundamental studies and the development of new electronic devices. Yet, most studies on PEDOT:PSS have focused on its electronic conductivity in dry environments, with less consideration given to its ion transport, coupled ionic-electronic transport, and charge storage properties in aqueous environments. These properties are essential for applications in bioelectronics (sensors, actuators), charge storage devices, and electrochromic displays. Importantly, past studies on mixed ionic-electronic transport in PEDOT:PSS neglected to consider how the molecular structure of PSS affects mixed ionic-electronic transport. Herein, we therefore investigated the effect of the molecular weight and size distribution of PSS on the electronic properties and morphology of PEDOT:PSS both in dry and aqueous environments, and overall performance in organic electrochemical transistors (OECTs). Using reversible addition–fragmentation chain transfer (RAFT) polymerization with two different chain transfer agents, six PSS samples with monomodal, narrow ( Đ = 1.1) and broad ( Đ = 1.7) size distributions and varying molecular weights were synthesized and used as matrices for PEDOT. We found that using higher molecular weight of PSS ( M n = 145 kg mol −1 ) and broad dispersity led to OECTs with the highest transconductance (up to 16 mS) and [ μC *] values (∼140 F cm −1 V −1 s −1 ) in PEDOT:PSS, despite having a lower volumetric capacitance ( C * = 35 ± 4 F cm −3 ). The differences were best explained by studying the microstructure of the films by atomic force microscopy (AFM). We found that heterogeneities in the PEDOT:PSS films (interconnected and large PEDOT- and PSS-rich domains) obtained from high molecular weight and high dispersity PSS led to higher charge mobility ( μ OECT ∼ 4 cm 2 V −1 s −1 ) and hence transconductance. These studies highlight the importance of considering molecular weight and size distribution in organic mixed ionic-electronic conductor, and could pave the way to designing high performance organic electronics for biological interfaces. 

ABSTRACT We continue to investigate the design, synthesis, and characterization of electrically and ionically active conjugated polythiophene copolymers for integrating a variety of biomedical devices with living tissue. This paper will describe some of our most recent results, including the development of several new monomers that can tailor the surface chemistry, adhesion, and biointegration of these materials with neural cells. Our efforts have focused on copolymers of 3,4 ethylenedioxythiophene (EDOT), functionalized variants of EDOT (including EDOT-acid and the trifunctional EPh), and dopamine (DOPA). The resulting PEDOT-based copolymers have electrical, optical, mechanical, and adhesive properties that can be precisely tailored by fine tuning the chemical composition and structure. Here we present results on EDOT-dopamine bifunctional monomers and their corresponding polymers. We discuss the design and synthesis of an EDOT-cholesterol that combines the thiophene with a biological moiety known to exhibit surface-active behaviour. We will also introduce EDOT-aldehyde and EDOT-maleimide monomers and show how they can be used as the starting point for a wide variety of functionalized monomers and polymers.