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Pediatric sleep is an important but often overlooked area in health informatics. We present PedSleepMAE, a generative model that fully leverages multimodal pediatric sleep signals including multichannel EEGs, respiratory signals, EOGs and EMG. This masked autoencoder-based model performs comparably to supervised learning models in sleep scoring and in the detection of apnea, hypopnea, EEG arousal and oxygen desaturation. Its embeddings are also shown to capture subtle differences in sleep signals coming from a rare genetic disorder. Furthermore, PedSleepMAE generates realistic signals that can be used for sleep segment retrieval, outlier detection, and missing channel imputation. This is the first general-purpose generative model trained on multiple types of pediatric sleep signals.

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One of the central problems in coding theory is to construct codes with best possible parameters and properties. A special class of codes called quasi-twisted (QT) codes is well-known to produce codes with good parameters. Most of the work on QT codes has been over the 1-generator case. In this work, we focus on 2-generator QT codes and generalize the ASR algorithm that has been very effective to produce new linear codes from 1-generator QT codes. As a result of implementing the generalized algorithm, we have found 103 2-generator QT codes that are new among the class of QT codes. Additionally, most of these codes possess the following additional properties: a) they have the same parameters as best known linear codes, and b) many of them have additional desired properties such as being LCD and dual-containing. Further, we have also found a binary 2-generator QT code that is new (record breaking) among all binary linear codes [1] and its extension yields another record breaking binary linear code.

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One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes over the binary field, we have found 113 binary QC codes that are new among the class of QC codes using an implementation of a fast cyclic partitioning algorithm and the highly effective ASR algorithm. Moreover, these codes have the following additional properties: a) they have the same parameters as best known linear codes, and b) many of the have additional desired properties such as being reversible, LCD, self-orthogonal or dual-containing. Additionally, we present an algorithm for the generation of new codes from QC codes using ConstructionX, and introduce 33 new record breaking linear codes over GF(2), GF(3) and GF(5) produced from this method.

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Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize this algorithm to constacyclic codes. As an application of the algorithm we found many constacyclic codes with good parameters and properties. In particular, we found 22 new codes that improve the minimum distances of best known linear codes (BKLCs).