The effects of age-of-acquisition and frequency-of-occurrence in visual word recognition: Further evidence from the Dutch language

It has been claimed that the frequency eOEect in visual word naming is an artefact of age-of-acquisition: Words are named faster not because they are encountered more often in texts, but because they have been acquired earlier. In a series of experiments using immediate naming, lexical decision, and masked priming, we found that frequency had a clear eOEect in lexical tasks when age-of-acquisition is controlled for. At the same time, age-ofacquisition was a significant variable in all tasks, whereas imageability had no effect. These results corroborate findings previously reported in English and Dutch

Behind the Scenes at American Anthropologist

Behind the Scenes at American Anthropologis

Explanatory Proofs and Beautiful Proofs

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples drawn from mathematical practice, and the account proposed here is compared to other accounts in the literature. The concept of a proof that explains is closely intertwined with other important concepts, such as a brute force proof, a mathematical coincidence, unification in mathematics, and natural properties. Ultimately, this paper concludes that the features of a proof that would contribute to its explanatory power would also contribute to its beauty, but that these two virtues are not the same; a beautiful proof need not be explanatory

Efficient Doubling on Genus Two Curves over Binary Fields

In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes. This paper investigates how to compute faster doubling over fields of characteristic two. We derive explicit doubling formulae making strong use of the defining equation of the curve. We analyze how many field operations are needed depending on the curve making clear how much generality one loses by the respective choices. Note, that none of the proposed types is known to be weak – one only could be suspicious because of the more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only half the time of an addition. Combined with a sliding window method this leads to fast computation of scalar multiples. We also speed up the general case

Quantitative Comparison of Abundance Structures of Generalized Communities: From B-Cell Receptor Repertoires to Microbiomes

The \emph{community}, the assemblage of organisms co-existing in a given space and time, has the potential to become one of the unifying concepts of biology, especially with the advent of high-throughput sequencing experiments that reveal genetic diversity exhaustively. In this spirit we show that a tool from community ecology, the Rank Abundance Distribution (RAD), can be turned by the new MaxRank normalization method into a generic, expressive descriptor for quantitative comparison of communities in many areas of biology. To illustrate the versatility of the method, we analyze RADs from various \emph{generalized communities}, i.e.\ assemblages of genetically diverse cells or organisms, including human B cells, gut microbiomes under antibiotic treatment and of different ages and countries of origin, and other human and environmental microbial communities. We show that normalized RADs enable novel quantitative approaches that help to understand structures and dynamics of complex generalize communities

Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works as a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDEs, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.Comment: 26 pages, 8 figures; ICML 2023 (oral); updated with expanded appendices and ancillary files. Code available at https://github.com/haerski/EPGP. For animations, see https://mathrepo.mis.mpg.de/EPGP/index.html. For a presentation see https://icml.cc/virtual/2023/oral/25571. The paper and all ancillary files are released under CC-B