“…This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and poly-Bernoulli numbers. …”
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“…The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. …”
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“…To test this hypothesis, we measured three dental topographic metrics: Relief Index (RFI), Dirichlet Normal Energy (DNE), and Orientation Patch Count Rotated (OPCR) in 57 extant carnivoran species. …”
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“…Since all periodic curves that meet the Dirichlet conditions can be formed by superposition of sinusoidal curves, taking the “lowest frequency” part that reflects the main characteristics of the curve as the target configuration can simplify the motion control function of snake robots’ gaits. …”
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“…To qualitatively and quantitatively understand the CHO literature, we have conducted topic modeling using a CHO bioprocess bibliome manually compiled in 2016, and compared the topics uncovered by the Latent Dirichlet Allocation (LDA) models with the human labels of the CHO bibliome. …”
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“…This study proposes a two-stage natural language processing-based model that utilizes Latent Dirichlet Allocation to identify critical topics related to each type of legal case or judgment and the Valence Aware Dictionary Sentiment Reasoner algorithm to assess people's sentiments on those topics. …”
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“…This study describes the growth of research publications from 1991 to 2021 in the Web of Science database and points out current research landscapes in the fields of HIV/AIDS and substance use. Latent Dirichlet Allocation was used for classifying 21 359 papers into corresponding topics. …”
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“…The study analyzed local family education policy documents, extracting six major themes using the Latent Dirichlet Allocation (LDA) model, and presented them according to the calculated mean theme probability. …”
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“…We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. …”
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“…Here, we demonstrate that mean–variability association is ubiquitous across technologies, highlighting the inadequacy of the very popular Dirichlet-multinomial distribution. We show that sccomp accurately fits experimental data, significantly improving performance over state-of-the-art algorithms. …”
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“…The frequency of behaviours was calculated and compared using Dirichlet regression. Despite the SOM models having higher Kappa (>95%) and overall accuracy (>95%) compared with the RF models (64–76% and 70–86%, respectively), the RF models predicted behaviours more consistently between mounting locations. …”
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“…Based on the transaction data of the ‘Renrendai’ platform, this paper analyzed the linguistic features and extracted the content of loan descriptions using a latent Dirichlet allocation (LDA) theme model. To further explore the value of loan descriptions in predicting lending success, this paper conducts a prediction study based on a support vector machine model. …”
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“…METHODS: Overall, 207,038 posts by 41,400 users were collected from June 1, 2017, to June 1, 2022, in a popular online forum. We applied Latent Dirichlet Allocation (LDA), an unsupervised machine learning model, to organize the posts into topics. …”
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“…Then, the database is analyzed using the LDA (Latent Dirichlet Analysis) cluster analysis method. The TF-IDF (Term Frequency-Inverse Document Frequency) algorithm processes the data to obtain critical technical words. …”
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“…The satisfaction factors were extracted using Latent Dirichlet Allocation (LDA) and grouped into three dimensions; information quality, system quality, and service quality. …”
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“…Examples are the naïve Bayes multinomial model (MM), the Dirichlet compound multinomial model (DCM) and the exponential-family approximation of the DCM (EDCM), as well as support vector machines (SVM). …”
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“…Our model extends a hierarchical Dirichlet process mixture model to allow data fusion on a gene-by-gene basis. …”
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“…The electromagnetic field distribution in the non-homogeneous domain was defined as an internal Dirichlet problem using the finite element method. …”
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“…Here, we review advances and the application of multinomial-Dirichlet likelihood methods of inference for identifying genome regions that have been subject to natural selection with the F(ST) estimates. …”
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“…Our software jointly infers the global mutational parameters at the nucleotide level, the branch lengths of the tree and a Dirichlet process governing across-site variation at the amino acid level. …”
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