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Expanding on expansus : A new species of Scaphanocephalus from North America and the Caribbean based on molecular and morphological data
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null (Ed.)Abstract We continue the study of n -dependent groups, fields and related structures, largely motivated by the conjecture that every n -dependent field is dependent. We provide evidence toward this conjecture by showing that every infinite n -dependent valued field of positive characteristic is henselian, obtaining a variant of Shelah’s Henselianity Conjecture in this case and generalizing a recent result of Johnson for dependent fields. Additionally, we prove a result on intersections of type-definable connected components over generic sets of parameters in n -dependent groups, generalizing Shelah’s absoluteness of $$G^{00}$$ in dependent theories and relative absoluteness of $$G^{00}$$ in $$2$$ -dependent theories. In an effort to clarify the scope of this conjecture, we provide new examples of strictly $$2$$ -dependent fields with additional structure, showing that Granger’s examples of non-degenerate bilinear forms over dependent fields are $$2$$ -dependent. Along the way, we obtain some purely model-theoretic results of independent interest: we show that n -dependence is witnessed by formulas with all but one variable singletons; provide a type-counting criterion for $$2$$ -dependence and use it to deduce $$2$$ -dependence for compositions of dependent relations with arbitrary binary functions (the Composition Lemma); and show that an expansion of a geometric theory T by a generic predicate is dependent if and only if it is n -dependent for some n , if and only if the algebraic closure in T is disintegrated. An appendix by Martin Bays provides an explicit isomorphism in the Kaplan-Scanlon-Wagner theorem.more » « less
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Abstract Spirotrichonymphea, one of the six classes of phylum Parabasalia, are characterized by bearing many flagella in spiral rows, and they occur exclusively in the guts of termites. Phylogenetic relationships among the 13 described genera are not well understood due to complex morphological evolution and a paucity of molecular data. One such understudied genus isSpironympha. It has been variously considered a valid genus, a subgenus ofSpirotrichonympha, or an “immature” life cycle stage ofSpirotrichonympha. To clarify this, we sequenced the small subunit rRNA gene sequences ofSpironymphaandSpirotrichonymphacells isolated from the hindguts ofReticulitermesspecies andHodotermopsis sjostedtiand confirmed the molecular identity ofH. sjostedtisymbionts using fluorescence in situ hybridization.Spironymphaas currently circumscribed is polyphyletic, with bothH. sjostedtisymbiont species branching separately from the “true”SpironymphafromReticulitermes. Similarly, theSpirotrichonymphasymbiont ofH. sjostedtibranches separately from the “true”Spirotrichonymphafound inReticulitermes. Our data supportSpironymphafromReticulitermesas a valid genus most closely related toSpirotrichonympha, though its monophyly and interspecific relationships are not resolved in our molecular phylogenetic analysis. We propose three new genera to accommodate theH. sjostedtisymbionts and two new species ofSpirotrichonymphafromReticulitermes.more » « less
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Summary We discover a connection between the Benjamini–Hochberg procedure and the e-Benjamini–Hochberg procedure (Wang & Ramdas, 2022) with a suitably defined set of e-values. This insight extends to Storey’s procedure and generalized versions of the Benjamini–Hochberg procedure and the model-free multiple testing procedure of Barber & Candés (2015) with a general form of rejection rules. We further summarize these findings in a unified form. These connections open up new possibilities for designing multiple testing procedures in various contexts by aggregating e-values from different procedures or assembling e-values from different data subsets.more » « less
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Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the statistical tools for model discovery are well established in the context of linear regression, their generalization to nonlinear regression in material modeling is highly problem‐specific and insufficiently understood. Here we explore the potential of neural networks for automatic model discovery and induce sparsity by a hybrid approach that combines two strategies: regularization and physical constraints. We integrate the concept of Lp regularization for subset selection with constitutive neural networks that leverage our domain knowledge in kinematics and thermodynamics. We train our networks with both, synthetic and real data, and perform several thousand discovery runs to infer common guidelines and trends: L2 regularization or ridge regression is unsuitable for model discovery; L1 regularization or lasso promotes sparsity, but induces strong bias that may aggressively change the results; only L0 regularization allows us to transparently fine‐tune the trade‐off between interpretability and predictability, simplicity and accuracy, and bias and variance. With these insights, we demonstrate that Lp regularized constitutive neural networks can simultaneously discover both, interpretable models and physically meaningful parameters. We anticipate that our findings will generalize to alternative discovery techniques such as sparse and symbolic regression, and to other domains such as biology, chemistry, or medicine. Our ability to automatically discover material models from data could have tremendous applications in generative material design and open new opportunities to manipulate matter, alter properties of existing materials, and discover new materials with user‐defined properties.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S0031182024000647
