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Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In…
It is crucial to learn the shared structures among functional predictors, as these structures characterize how predictor components exert common effects and, more generally, how predictors are homogeneously associated with the response.…
The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a…
Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and…
Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…
Design patterns are elegant and well-tested solutions to recurrent software development problems. They are the result of software developers dealing with problems that frequently occur, solving them in the same or a slightly adapted way. A…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
One of the major problems in modeling natural signals is that signals with very similar structure may locally have completely different measurements, e.g., images taken under different illumination conditions, or the speech signal captured…
Multimode fibres (MMF) are remarkable high-capacity information channels owing to the large number of transmitting fibre modes, and have recently attracted significant renewed interest in applications such as optical communication, imaging,…
Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently…
A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these…
Wireless foundation models (WFMs) have recently demonstrated promising capabilities, jointly performing multiple wireless functions and adapting effectively to new environments. However, while current WFMs process only one modality,…
Current multimodal and multitask foundation models like 4M or UnifiedIO show promising results, but in practice their out-of-the-box abilities to accept diverse inputs and perform diverse tasks are limited by the (usually rather small)…
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
Fusing measurements from multiple, heterogeneous, partial sources, observing a common object or process, poses challenges due to the increasing availability of numbers and types of sensors. In this work we propose, implement and validate an…
Conceptualizing a porous media as a network of conductors sets a compromise between the oversimplifying conceptualization of the media as a bundle of capillary tubes and the computationally expensive and unobtainable detailed description of…
In the present work, we describe a framework for modeling how models can be built that integrates concepts and methods from a wide range of fields. The information schism between the real-world and that which can be gathered and considered…
In data modelling, product information has most often been handled separately from process information. The integration of product and process models in a unified data model could provide the means by which information could be shared…