Related papers: Digital Repository of Mathematical Formulae
Orbital-free density functional theory (OF-DFT) runs at low computational cost that scales linearly with the number of simulated atoms, making it suitable for large-scale material simulations. It is generally considered that OF-DFT strictly…
Recently we proposed an information entropy based method for electronic structure calculations within the density-matrix functional theory(DMFT) (Phys. Rev. Lett. 128, 013001), dubbed as $i$-DMFT. Comments have been raised regarding the…
Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…
The online Markov decision process (MDP) is a generalization of the classical Markov decision process that incorporates changing reward functions. In this paper, we propose practical online MDP algorithms with policy iteration and…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
Reproducibility of computational results remains a challenge in materials science, as simulation workflows and parameters are often reported only in unstructured text and tables. While literature data are valuable for validation and reuse,…
We present SMPDF Web, a web interface for the construction of parton distribution functions (PDFs) with a minimal number of error sets needed to represent the PDF uncertainty of specific processes (SMPDF).
Spreadsheets are widely used by knowledge workers, especially in the industrial sector. Their methodology enables a well understood, easy and fast possibility to enter data. As filling out a spreadsheet is more accessible to common…
MathRepo, located at https://mathrepo.mis.mpg.de, is an online repository for mathematical research data. In mathematics, research data comes in many different flavours. For instance, in computer algebra it most often takes the form of…
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…
Mathematics education, a crucial and basic field, significantly influences students' learning in related subjects and their future careers. Utilizing artificial intelligence to interpret and comprehend math problems in education is not yet…
We propose exploiting symmetries (exact or approximate) of the Standard Model (SM) to search for physics Beyond the Standard Model (BSM) using the data-directed paradigm (DDP). Symmetries are very powerful because they provide two samples…
We consider the problem of finding the minimizer of a function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ of the finite-sum form $\min f(w) = 1/n\sum_{i}^n f_i(w)$. This problem has been studied intensively in recent years in the field of…
We present a novel game-theoretic formulation of Non-Negative Matrix Factorization (NNMF), a popular data-analysis method with many scientific and engineering applications. The game-theoretic formulation is shown to have favorable scaling…
Recommender systems need to optimize various types of user feedback, e.g., clicks, likes, and shares. A typical recommender system handling multiple types of feedback has two components: a multi-task learning (MTL) module, predicting…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
To shift the computational burden from real-time to offline in delay-critical power systems applications, recent works entertain the idea of using a deep neural network (DNN) to predict the solutions of the AC optimal power flow (AC-OPF)…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
The use of semantic technologies is gaining significant traction in science communication with a wide array of applications in disciplines including the Life Sciences, Computer Science, and the Social Sciences. Languages like RDF, OWL, and…
Online learning, where feature spaces can change over time, offers a flexible learning paradigm that has attracted considerable attention. However, it still faces three significant challenges. First, the heterogeneity of real-world data…