Related papers: Self-Referential Order
One of the most fundamental problems in science is to define {\it quantitatively} the complexity of organized matters, i.e., {\it organized complexity}. Although many measures have been proposed toward this aim in previous decades, there is…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in…
Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they…
The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules…
A novel paradigm for sorting is introduced, based upon resetting. Using simple examples, we demonstrate that sorting is achieved by resetting the velocity component(s) or orientation of the particles, rather than position. The objects to be…
Many applications, e.g., Web service composition, complex system design, team formation, etc., rely on methods for identifying collections of objects or entities satisfying some functional requirement. Among the collections that satisfy the…
We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that…
Targeted and uniform interventions to a system are crucial for unveiling causal relationships. While several methods have been developed to leverage interventional data for causal structure learning, their practical application in…
A new graph-based order parameter is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system, and is transferable to all structural geometries. Three sets of data are…
Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been…
Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason…
While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and…
We study how macroscopic observational constraints restrict admissible microscopic explanatory structures when no intrinsic order or dynamics is assumed a priori. Starting from an unordered collection of measurement outcomes, we formulate…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…
We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…
We propose a concept of disordered resonant media, which are characterized by random variations of their parameters along the light propagation direction. In particular, a simple model of disorder considered in the paper implies random…
We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve…