Related papers: A Mereological Approach to Higher-Order Structure …
Many complex systems are representable as macroscopic set of elements which interact by simple rules. The complex macroscopically relevant phenomena are then the result of the generic emergence of a space-time multi-scale dynamics. Critical…
Imaging and hyperspectral data analysis is central to progress across biology, medicine, chemistry, and physics. The core challenge lies in converting high-resolution or high-dimensional datasets into interpretable representations that…
A monolithic process is a single recursive equation with data parameters, which only uses non-determinism, action prefixing, and recursion. We present a technique that decomposes such a monolithic process into multiple processes where each…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
In classical systems, we reexamine how macroscopic structures in equilibrium state connect with spatial con- straint on the systems: e.g., volume and density as the constraint for liquids in rigid box, and crystal lattice as the constraint…
We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-M\"obius element) to a class of M\"obius semigroups which includes certain settings…
The transition from microscopic to macroscopic in quantum mechanics can be seen from various points of view. It is often not merely a transition from quantum to classical mechanics in the sense of the Correspondence Principle. The fact that…
Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to…
A quite general interaction process of a multi-component system is analysed by the extended effective potential method liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of…
While the properties of materials at microscopic scales are well described by fundamental quantum mechanical equations and electronic structure theories, the emergent behavior of mesoscopic or macroscopic composites is no longer governed…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
Miquel dynamics is a discrete time dynamics for circle patterns, which relies on Miquel's six circle theorem. Previous work shows that the evolution of the circle centers satisfy the dSKP equation on the octahedral lattice $A_3$. As a…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
The conventional approach to the general Partial Information Decomposition (PID) problem has been redundancy-based: specifying a measure of redundant information between collections of source variables induces a PID via Moebius-Inversion…
Improvements in sequencing technologies and reduced experimental costs have resulted in a vast number of studies generating high-throughput data. Although the number of methods to analyze these "omics" data has also increased, computational…