Related papers: Structure-aware divergences for comparing probabil…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…
The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…
Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements. When the relative abundances of types can be measured well, we often observe heavy-tailed…
The relationships between diversity, productivity and scale determine much of the structure and robustness of complex biological and social systems. While arguments for the link between specialization and productivity are common, diversity…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
This study introduces a novel model that effectively captures asymmetric structures in multivariate contingency tables with ordinal categories. Leveraging the principle of maximum entropy, our approach employs f-divergence to provide a…
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…
Attention networks have proven to be an effective approach for embedding categorical inference within a deep neural network. However, for many tasks we may want to model richer structural dependencies without abandoning end-to-end training.…
The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…
We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied,…
In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Establishing correspondences between two images requires both local and global spatial context. Given putative correspondences of feature points in two views, in this paper, we propose Order-Aware Network, which infers the probabilities of…