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Precise spatial patterning of cell fate during morphogenesis requires accurate inference of cellular position. In making such inferences from morphogen profiles, cells must contend with inherent stochasticity in morphogen production, transport, sensing and signalling. Motivated by the multitude of signalling mechanisms in various developmental contexts, we show how cells may utilise multiple tiers of processing (compartmentalisation) and parallel branches (multiple receptor types), together with feedback control, to bring about fidelity in morphogenetic decoding of their positions within a developing tissue. By simultaneously deploying specific and nonspecific receptors, cells achieve a more accurate and robust inference. We explore these ideas in the patterning of Drosophila melanogaster wing imaginal disc by Wingless morphogen signalling, where multiple endocytic pathways participate in decoding the morphogen gradient. The geometry of the inference landscape in the high dimensional space of parameters provides a measure for robustness and delineates stiff and sloppy directions. This distributed information processing at the scale of the cell highlights how local cell autonomous control facilitates global tissue scale design.

Understanding how organisms make transitive inferences is critical to understanding their general ability to learn serial relationships. In this context, transitive inference (TI) can be understood as a specific heuristic that applies broadly to many different serial learning tasks, which have been the focus of hundreds of studies involving dozens of species. In the present study, monkeys learned the order of 7-item lists of photographic stimuli by trial and error, and were then tested on “derived” lists. These derived test lists combined stimuli from multiple training lists in ambiguous ways, sometimes changing their order relative to training. We found that subjects displayed strong preferences when presented with novel test pairs, even when those pairs were drawn from different training lists. These preferences were helpful when test pairs had an ordering congruent with their ranks during training, but yielded consistently below-chance performance when pairs had an incongruent order relative to training. This behavior can be explained by the joint contributions of transitive inference and another heuristic that we refer to as “positional inference.” Positional inferences play a complementary role to transitive inferences in facilitating choices between novel pairs of stimuli. The theoretical framework that best explains both transitive and positional inferences is a spatial model that represents both the position of each stimulus and its uncertainty. A computational implementation of this framework yields accurate predictions about both correct responses and errors on derived lists.

Estimating the genomic location and length of identical-by-descent (IBD) segments among individuals is a crucial step in many genetic analyses. However, the exponential growth in the size of biobank and direct-to-consumer genetic data sets makes accurate IBD inference a significant computational challenge. Here we present the templated positional Burrows–Wheeler transform (TPBWT) to make fast IBD estimates robust to genotype and phasing errors. Using haplotype data simulated over pedigrees with realistic genotyping and phasing errors, we show that the TPBWT outperforms other state-of-the-art IBD inference algorithms in terms of speed and accuracy. For each phase-aware method, we explore the false positive and false negative rates of inferring IBD by segment length and characterize the types of error commonly found. Our results highlight the fragility of most phased IBD inference methods; the accuracy of IBD estimates can be highly sensitive to the quality of haplotype phasing. Additionally, we compare the performance of the TPBWT against a widely used phase-free IBD inference approach that is robust to phasing errors. We introduce both in-sample and out-of-sample TPBWT-based IBD inference algorithms and demonstrate their computational efficiency on massive-scale data sets with millions of samples. Furthermore, we describe the binary file format for TPBWT-compressed haplotypes that results in fast and efficient out-of-sample IBD computes against very large cohort panels. Finally, we demonstrate the utility of the TPBWT in a brief empirical analysis, exploring geographic patterns of haplotype sharing within Mexico. Hierarchical clustering of IBD shared across regions within Mexico reveals geographically structured haplotype sharing and a strong signal of isolation by distance. Our software implementation of the TPBWT is freely available for noncommercial use in the code repository (https://github.com/23andMe/phasedibd, last accessed January 11, 2021).

Disassembling is an important process in the maintenance, reparation, and disposal of mechanical as well as structural systems. More often than not, however, disassembling processes are not prepared in advance; we need to organize the disassembling process based on the obtained arrangement information of the constituent parts of the system. In this study, we deal with a disassembling process inference based on the positional relations matrix. On the basis of the positional relations matrix, the geometrical constraints among the parts can be expressed in a general form. The developed disassembling process inference based on the matrix is considered to be practical. We have evaluated the practicality of the proposed disassembling process inference based on a number of disassembling problems which were generated by means of a problem-generation system based on random number generator. The obtained evaluation demonstrated that the proposed approach does not always result in the optimal disassembling process but provides a fairly appropriate disassembling process in general, and the required computational cost is considerably small. We concluded that the proposed disassembling process inference is practical enough.

Arabic automatic speech recognition (ASR) faces distinct challenges due to its complex morphology, dialectal variations, and the presence of diacritical marks that strongly influence pronunciation and meaning. This study introduces a lightweight approach for diacritical Arabic ASR that employs a Transformer encoder architecture enhanced with Relative Positional Encoding (RPE) and Connectionist Temporal Classification (CTC) loss, eliminating the need for a conventional decoder. A two-stage training process was applied: initial pretraining on Modern Standard Arabic (MSA), followed by progressive three-phase fine-tuning on diacritical Arabic datasets. The proposed model achieves a WER of 22.01% on the SASSC dataset, improving over traditional systems (best 28.4% WER) while using only ≈14 M parameters. In comparison, XLSR-Large (300 M parameters) achieves a WER of 12.17% but requires over 20× more parameters and substantially higher training and inference costs. Although XLSR attains lower error rates, the proposed model is far more practical for resource-constrained environments, offering reduced complexity, faster training, and lower memory usage while maintaining competitive accuracy. These results show that encoder-only Transformers with RPE, combined with CTC training and systematic architectural optimization, can effectively model Arabic phonetic structure while maintaining computational efficiency. This work establishes a new benchmark for resource-efficient diacritical Arabic ASR, making the technology more accessible for real-world deployment.

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

This chapter contains sections titled: Introduction The Concept of Functional Genomics Approaches to Functional Genomics Functional Genomics Approaches Suitable for Aquaculture Acknowledgments References