In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the Toeplitz structure and the fast Toeplitz matrix-vector product can be utilized to reduce the computational complexity from [Formula: see text] to...

This paper is devoted to the adaptive Morley element algorithms for a biharmonic eigenvalue problem in [Formula: see text] ([Formula: see text]). We combine the Morley element method with the shifted-inverse iteration including Rayleigh quotient iteration and the inverse iteration with fixed shift to propose multigrid discretization schemes in an adaptive fashion. We establish an inequality on ...

Semantic error detection and correction is an important task for applications such as fact checking, speech-to-text or grammatical error correction. Current approaches generally focus on relatively shallow semantics and do not account for numeric quantities. Our approach uses language models grounded in numbers within the text. Such groundings are easily achieved for recurrent neural language m...

This paper presents a platform aiming to assess the difficulty of administrative texts, mostly for editorial assistance purposes. The platform first offers a readability formula specialized for administrative texts, the development of which required the design of a dedicated annotation procedure. The resulting model correctly classifies 58% of the texts on a 5-levels scale and commits serious m...

Regular expressions with numerical occurrence indicators (#REs) are used in established text manipulation tools like Perl and Unix egrep, and in the recent W3C XML Schema Definition Language. Numerical occurrence indicators do not increase the expressive power of regular expressions, but they do increase the succinctness of expressions by an exponential factor. Therefore methods based on straig...

A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is deriv...

This Internet Appendix provides additional proofs and results that are left out of the main text of the paper due to space limitation. Section I of this appendix collects proofs of the corollaries to Proposition 1 in the main text. Section II presents a general dynamic model of investment and capital structure decisions that allows for shareholder recovery in default. Section III describes the ...

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of quantum field theory. The starting point this to truncate the interacting finite-dimensional space states spanned by eigenvectors free $H_0$ with eigenvalues below some energy cutoff $E_\text{max}$. In work, we show how treat systematically using effective theory methodology. We define integrating out a...