Related papers: On Structure and Organization: An Organizing Princ…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
We define and construct a new data structure, the tables, this structure generalizes the (finite) $k$-sets sets of Eilenberg \cite{Ei}, it is versatile (one can vary the letters, the words and the coefficients). We derive from this…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize…
The characterization of large-scale structural organization of social networks is an important interdisciplinary problem. We show, by using scaling analysis and numerical computation, that the following factors are relevant for models of…
We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a…
We study the question of how concepts that have structure get represented in the brain. Specifically, we introduce a model for hierarchically structured concepts and we show how a biologically plausible neural network can recognize these…
Self-organization is frequently observed in active collectives, from ant rafts to molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying…
From subcellular structures to entire organisms, many natural systems generate complex organisation through self-organisation: local interactions that collectively give rise to global structure without any blueprint of the outcome. Yet a…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
The underlying structure of natural language is hierarchical; words combine into phrases, which in turn form clauses. An awareness of this hierarchical structure can aid machine learning models in performing many linguistic tasks. However,…
Based on laboratory based growth of plant-like structures from inorganic materials, we present new theory for the emergence of plant structure at a range of scales dictated by levels of ionization (charge density), which can be traced…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
It is proposed that self-organisation (SO) in non-equilibrium systems is governed by a general principle: it emerges when a minute subset of system configurations are exceptionally stable and long-lived to survive the noise generated by the…
This chapter reviews four notions of system structure, three of which are contextual and classic (i.e. the complete computational structure linked to a state space model, the sparsity pattern of a transfer function, and the interconnection…
Our technologies complexify our environments. Thus, new technologies need to deal with more and more complexity. Several efforts have been made to deal with this complexity using the concept of self-organization. However, in order to…
We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…