“…We tested and compared latent Dirichlet allocation (LDA), Dirichlet multinomial mixture (DMM), GPU-DMM, biterm topic model, and nonnegative matrix factorization for identifying topics associated with tweets. …”
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“…METHODS: We introduced an improved four-layer supervised latent Dirichlet allocation (sLDA) approach called Hierarchical sLDA model, which categorized patient features in HDRs as patient feature-value pairs in one-hot way according to clinical guidelines for lab test of CHD. …”
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“…However, the huge dimensionality of microbial metagenomics datasets is a major challenge for the existing methods such as Dirichlet multinomial mixture (DMM) models. In the approach of the existing methods, the computational burden of identifying a small number of representative species from a large number of observed species remains a challenge. …”
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“…METHODS: We collected posts from Reddit and Xiaohongshu, conducted topic mining using the latent Dirichlet allocation model, and analyzed the characteristics of topics on different social media. …”
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“…We ran a suite of analyses using various Python packages, such as latent Dirichlet allocation, hierarchical latent Dirichlet allocation, and sentiment analysis. …”
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“…Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, inertia and ramification of ideals Part Three is devoted to Kummer's theory of cyclomatic fields, and includes Bernoulli numbers and the proof of Fermat's Last Theorem for regular prime exponents Finally, in Part Four, the emphasis is on analytical methods and it includes Dinchlet's Theorem on primes in arithmetic progressions, the theorem of Chebotarev and class number formulas A careful study of this book will provide a solid background to the learning of more recent topics…”
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“…The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). …”
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“…The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the  Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators,  extremal problems in polynomials and entire functions,  applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of  mechanical fields in media with inclusions and holes.  …”
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“…Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. …”
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“…The chapter moves on to include more advanced topics on generalized latent variable topic models based on hierarchical Dirichlet processes which recently have been developed in non-parametric Bayesian literature. …”
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“…This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. …”
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“…An introductory chapter contains some of the results involving characters of finite abelian groups by Lagrange, Gauss, and Dirichlet, which were part of the mathematical tradition from which Frobenius drew his inspiration. …”
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“…Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.…”
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“…In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. …”
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“…These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. …”
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“…This paper selects the Henan rainstorm event as a case study and extracts the theme characteristics by combining the life cycle theory and Latent Dirichlet Allocation (LDA) model. It integrates the Term Frequency–Inverse Document Frequency (TF-IDF) and Pointwise Mutual Information (PMI) algorithms as the theme-coding data source to build a dynamic theme propagation model for emergencies. …”
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“…A total of 19 topics were extracted through latent Dirichlet allocation and then transformed into structured data using a time series approach to analyze significant changes in trends. …”
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“…The numerical model is based on an inverse boundary problem of the parabolic equation with Dirichlet boundary conditions. To validate this model and characterize the diffusion of oxygen through the oxygen sensing materials, we designed a series of control/calibration experiments modeled after the device’s clinical application using oxygenation values in the physiological range expected for healthy tissue. …”
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“…After the sinusoidal, triangular, rectangular, and sawtooth functions that satisfy the Dirichlet condition are expanded into the Fourier sine series, the spectral density of the sine function is used to represent the corrugation function. …”
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“…We establish [Formula: see text] boundary regularity and existence results for the Dirichlet problem.…”
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