Positive almost periodic solutions for a class of nonlinear Duffing equations with a deviating argument

In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results

Oracle-Efficient Pessimism: Offline Policy Optimization in Contextual Bandits

We consider offline policy optimization (OPO) in contextual bandits, where one is given a fixed dataset of logged interactions. While pessimistic regularizers are typically used to mitigate distribution shift, prior implementations thereof are either specialized or computationally inefficient. We present the first general oracle-efficient algorithm for pessimistic OPO: it reduces to supervised learning, leading to broad applicability. We obtain statistical guarantees analogous to those for prior pessimistic approaches. We instantiate our approach for both discrete and continuous actions and perform experiments in both settings, showing advantage over unregularized OPO across a wide range of configurations

Off-Policy Evaluation for Large Action Spaces via Policy Convolution

Developing accurate off-policy estimators is crucial for both evaluating and optimizing for new policies. The main challenge in off-policy estimation is the distribution shift between the logging policy that generates data and the target policy that we aim to evaluate. Typically, techniques for correcting distribution shift involve some form of importance sampling. This approach results in unbiased value estimation but often comes with the trade-off of high variance, even in the simpler case of one-step contextual bandits. Furthermore, importance sampling relies on the common support assumption, which becomes impractical when the action space is large. To address these challenges, we introduce the Policy Convolution (PC) family of estimators. These methods leverage latent structure within actions -- made available through action embeddings -- to strategically convolve the logging and target policies. This convolution introduces a unique bias-variance trade-off, which can be controlled by adjusting the amount of convolution. Our experiments on synthetic and benchmark datasets demonstrate remarkable mean squared error (MSE) improvements when using PC, especially when either the action space or policy mismatch becomes large, with gains of up to 5 - 6 orders of magnitude over existing estimators.Comment: Under review. 36 pages, 31 figure

Cloning, expression and characterization of alcohol dehydrogenases in the silkworm Bombyx mori

Alcohol dehydrogenases (ADH) are a class of enzymes that catalyze the reversible oxidation of alcohols to corresponding aldehydes or ketones, by using either nicotinamide adenine dinucleotide (NAD) or nicotinamide adenine dinucleotide phosphate (NADP), as coenzymes. In this study, a short-chain ADH gene was identified in Bombyx mori by 5′-RACE PCR. This is the first time the coding region of BmADH has been cloned, expressed, purified and then characterized. The cDNA fragment encoding the BmADH protein was amplified from a pool of silkworm cDNAs by PCR, and then cloned into E. coli expression vector pET-30a(+). The recombinant His-tagged BmADH protein was expressed in E. coli BL21 (DE3), and then purified by metal chelating affinity chromatography. The soluble recombinant BmADH, produced at low-growth temperature, was instrumental in catalyzing the ethanol-dependent reduction of NAD+, thereby indicating ethanol as one of the substrates of BmADH