Related papers: Extending DUNE: The dune-xt modules

Basing on the analysis by revealing the equivalence of modern networks, we find that both ResNet and DenseNet are essentially derived from the same "dense topology", yet they only differ in the form of connection -- addition (dubbed "inner…

The international collaboration designing and constructing the Deep Underground Neutrino Experiment (DUNE) at the Long-Baseline Neutrino Facility (LBNF) has developed a two-phase strategy for the implementation of this leading-edge,…

In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…

Let $\mathcal{X}$ be a class of $R$-modules. In this paper, we investigate \;$\mathcal{X}$-(f.g.)injective ((f.g.)projective) and DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and…

We introduce MixFunn, a novel neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability. The architecture comprises two key components: the mixed-function…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…

The Deep Underground Neutrino Experiment (DUNE) is a next-generation long-baseline neutrino oscillation experiment aimed at determining the neutrino mass hierarchy and the CP-violating phase. The DUNE physics program also includes the…

Despite the growing popularity of digital twin (DT) developments, there is a lack of common understanding and definition for important concepts of DT. It is needed to address this gap by building a shared understanding of DT before it…

The preponderance of matter over antimatter in the early universe, the dynamics of the supernovae that produced the heavy elements necessary for life, and whether protons eventually decay -- these mysteries at the forefront of particle…

In-band Network Telemetry (INT) and sketching algorithms are two promising directions for measuring network traffics in real time. To combine sketch with INT and preserve their advantages, a representative approach is to use INT to send a…

Digital network twins (DNTs), by representing a physical network using a virtual model, offer significant benefits such as streamlined network development, enhanced productivity, and cost reduction for next-generation (nextG) communication…

N-Variant Execution (NVX) systems utilize software diversity techniques for enhancing software security. The general idea is to run multiple different variants of the same program alongside each other while monitoring their run-time…

Let R be a commutative ring and C a semidualizing R-module. In this article, we introduce and investigate the notion of DC-projective complexes. We first prove that a complex X is DC-projective if and only if each degree of X is a…

We present a novel and flexible architecture for point cloud segmentation with dual-representation iterative learning. In point cloud processing, different representations have their own pros and cons. Thus, finding suitable ways to…

The Domain Mixed Unit (DMU) is a new neural arithmetic unit that learns a single parameter gate that mixes between log-space and linear-space representations while performing either addition (DMU add) or subtraction (DMU sub). Two…

The integration of digital twinning technologies is driving next-generation networks toward new capabilities, allowing operators to thoroughly understand network conditions, efficiently analyze valuable radio data, and innovate applications…

A process of extending sets which can be used as foundation for an alternative organization for Differential and Integral Calculus is presented.

In this paper, we collect the fundamental basic properties of jet modules in algebraic geometry and related properties of differential operators. We claim no originality but we want to provide a reference work for own research and the…

Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…

The Distributed object computing is a paradigm that allows objects to be distributed across a heterogeneous network, and allows each of the components to interoperate as a unified whole. A new generation of distributed applications, such as…