Related papers: Digital Repository of Mathematical Formulae

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender…

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Systems that rely on Machine Learning (ML systems) have differing demands on system quality compared to traditional systems. Such quality demands, known as non-functional requirements (NFRs), may differ in their definition, scope, and…

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…

Recommender systems are a kind of data filtering that guides the user to interesting and valuable resources within an extensive dataset. by providing suggestions of products that are expected to match their preferences. However, due to data…

SWiM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge represented in the domain-specific structural semantic markup language OMDoc. It motivates users to contribute to collections of mathematical…

Online solvers for partially observable Markov decision processes have been applied to problems with large discrete state spaces, but continuous state, action, and observation spaces remain a challenge. This paper begins by investigating…

Devising dynamic pricing policy with always valid online statistical learning procedure is an important and as yet unresolved problem. Most existing dynamic pricing policy, which focus on the faithfulness of adopted customer choice models,…

According to the modern paradigms of software engineering, standard tasks are best accomplished by reusable open source libraries. We describe OpenOrbitalOptimizer: a reusable open source C++ library for the iterative solution of coupled…

Non-negative matrix factorization (NMF) is a fundamental matrix decomposition technique that is used primarily for dimensionality reduction and is increasing in popularity in the biological domain. Although finding a unique NMF is generally…

Neural Fields (NFs) have gained momentum as a tool for compressing various data modalities - e.g. images and videos. This work leverages previous advances and proposes a novel NF-based compression algorithm for 3D data. We derive two…

Density functional theory (DFT) is an indispensable ab initio method in both quantum chemistry and condensed matter physics. Based on recent advancements in reduced density matrix functional theory (RDMFT), a variant of DFT that is believed…

Solutions to the classic problems of dealing with heterogeneous data and making entire collections interoperable while ensuring that any annotation, which includes the recognition-and-reward system of scientific publishing, need to fit into…

In this paper, we consider online continuous DR-submodular maximization with linear stochastic long-term constraints. Compared to the prior work on online submodular maximization, our setting introduces the extra complication of stochastic…

Reinforcement learning (RL) algorithms involve the deep nesting of highly irregular computation patterns, each of which typically exhibits opportunities for distributed computation. We argue for distributing RL components in a composable…

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…

Orbital-free density functional theory (OF-DFT) provides an alternative approach for calculating the molecular electronic energy, relying solely on the electron density. In OF-DFT, both the ground-state density is optimized variationally to…

Current foundation models (FMs) rely on token representations that directly fragment continuous real-world multimodal data into discrete tokens. They limit FMs to learning real-world knowledge and relationships purely through statistical…

Physical reasoning is a remarkable human ability that enables rapid learning and generalization from limited experience. Current AI models, despite extensive training, still struggle to achieve similar generalization, especially in…