Related papers: Digital Repository of Mathematical Formulae
Information technology and data science development stimulate transformation in many fields of scientific knowledge. In recent years, a large number of specialized systems for information and knowledge management have been created in…
Over the years, RDF streaming was explored in research and practice from many angles, resulting in a wide range of RDF stream definitions. This variety presents a major challenge in discussing and integrating streaming systems, due to the…
The natural orbital functional theory (NOFT) has emerged as an alternative formalism to both density functional (DF) and wavefunction methods. In NOFT, the electronic structure is described in terms of the natural orbitals (NOs) and their…
The open-source python package diffpy.mpdf, part of the DiffPy suite for diffraction and pair distribution function analysis, provides a user-friendly approach for performing magnetic pair distribution function (mPDF) analysis. The package…
Machine learning potentials (MLPs) developed from extensive datasets constructed from density functional theory (DFT) calculations have become increasingly appealing for many researchers. This paper presents a framework of polynomial-based…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral analysis of nonlinear dynamical systems, with a plethora of…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…
Reinforcement learning with human feedback~(RLHF) is critical for aligning Large Language Models (LLMs) with human preference. Compared to the widely studied offline version of RLHF, \emph{e.g.} direct preference optimization (DPO), recent…
Digital Twins (DTs) are virtual representations of physical systems synchronized in real time through Internet of Things (IoT) sensors and computational models. In industrial applications, DTs enable predictive maintenance, fault diagnosis,…
Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to…
This paper describes an approach to the representation and processing of ontologies in the Semantic Web, based on the ICMAUS theory of computation and AI. This approach has strengths that complement those of languages based on the Resource…
The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…
Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by…
With rapid progress in deep learning, neural networks have been widely used in scientific research and engineering applications as surrogate models. Despite the great success of neural networks in fitting complex systems, two major…
The Web is our primary source of all kinds of information today. This includes information about software as well as associated materials, like source code, documentation, related publications and change logs. Such data is of particular…
Metal-organic frameworks (MOFs) are nanoporous compounds composed of metal ions and organic linkers. MOFs play an important role in industrial applications such as gas separation, gas purification, and electrolytic catalysis. Important MOF…
Both the notion of Property Graphs (PG) and the Resource Description Framework (RDF) are commonly used models for representing graph-shaped data. While there exist some system-specific solutions to convert data from one model to the other,…
Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…