Related papers: Digital Repository of Mathematical Formulae
We address the challenge of developing an orthogonal time-frequency space (OTFS)-based non-orthogonal multiple access (NOMA) system where each user is modulated using orthogonal pulses in the delay Doppler domain. Building upon the concept…
The combination of density functional theory with dynamical mean-field theory (DFT+DMFT) has become a powerful first-principles approach to tackle strongly correlated materials in condensed matter physics. The wide use of this approach…
Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…
This demonstration presents an infrastructure for computing multilingual semantic relatedness and correlation for twelve natural languages by using three distributional semantic models (DSMs). Our demonsrator - DInfra (Distributional…
Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then…
The convergence of deep learning and formal mathematics has spurred research in formal verification. Statement autoformalization, a crucial first step in this process, aims to translate informal descriptions into machine-verifiable…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Projection-free online learning, which eschews the projection operation via less expensive computations such as linear optimization (LO), has received much interest recently due to its efficiency in handling high-dimensional problems with…
We have made an attempt to reproduce 17 objects of the IMAGINARY Open Mathematics Exhibition (www.imaginary.org) using low-cost, desktop 3D printers. The IMAGINARY open math is an international project by the Mathematisches…
This paper is devoted to the problems of ontology-based mathematical knowledge management and representation. The main attention is paid to the development of a formal model for the representation of mathematical statements in the Open…
NIFTY, "Numerical Information Field Theory", is a software package designed to enable the development of signal inference algorithms that operate regardless of the underlying spatial grid and its resolution. Its object-oriented framework is…
The frequent directions (FD) technique is a deterministic approach for online sketching that has many applications in machine learning. The conventional FD is a heuristic procedure that often outputs rank deficient matrices. To overcome the…
A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory…
The abundance of the data in the Internet facilitates the improvement of extraction and processing tools. The trend in the open data publishing encourages the adoption of structured formats like CSV and RDF. However, there is still a…
The generation of input files for density functional theory (DFT) programs must often be manually done by researchers. If one wishes to produce a maximally localized wannier functions (MLWFs) the calculation consists of several separate…
There are many case studies for which the formulation of RDF constraints and the validation of RDF data conforming to these constraint is very important. As a part of the collaboration with the W3C and the DCMI working groups on RDF…
In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the…
Digital Twins (DTs) represent digital counterparts of physical systems, assets, or processes, referred to as the actual twin (AT). DTs integrate heterogeneous data, models, and semantic technologies to support monitoring, simulation,…
To deal with non-stationary online problems with complex constraints, we investigate the dynamic regret of online Frank-Wolfe (OFW), which is an efficient projection-free algorithm for online convex optimization. It is well-known that in…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of Applied…