Related papers: Structural Foundations for Leading Digit Laws: Bey…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
State-of-the-art link prediction (LP) models demonstrate impressive benchmark results. However, popular benchmark datasets often assume that training, validation, and testing samples are representative of the overall dataset distribution.…
Are there hidden dynamical common patterns in the evolution of social and cultural history? While the growing availability of digitized social data invites us to answer this question, prevailing quantitative methods often rely on…
We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…
The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…
Benford's Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common…
Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
Rock discontinuities critically govern the mechanical behavior and stability of rock masses. Their internal distributions remain largely unobservable and are typically inferred from surface-exposed discontinuities using generative…
Despite the crucial role of inertial measurements in motion tracking and navigation systems, the time-consuming and resource-intensive nature of collecting extensive inertial data has hindered the development of robust machine learning…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…