Related papers: On Structure and Organization: An Organizing Princ…
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
We present a theory for modeling the structure of information and a language (Quanta) expressing the theory. Unlike Shannon's information theory, which focuses on the amount of information in an information system, we focus on the structure…
This paper describes some biologically-inspired processes that could be used to build the sort of networks that we associate with the human brain. New to this paper, a 'refined' neuron will be proposed. This is a group of neurons that by…
Humans possess the capability to reason at an abstract level and to structure information into abstract categories, but the underlying neural processes have remained unknown. Experimental evidence has recently emerged for the organization…
In this paper we try to define the difference between hierarchical organization and self-organization. Organization is defined as a structure with a function. So we can define the difference between hierarchical organization and…
Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…
Contract theories have been proposed to formally support distributed and decentralized system design while ensuring safe system integration. In this paper we propose hypercontracts, a generic model with a richer structure for its underlying…
Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…
Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity…
The microscopic organization of dynamical systems coupled via higher-order interactions plays a pivotal role in understanding their collective behavior. In this paper, we introduce a framework for systematically investigating the impact of…
Students, after they leave our care, are called to solve the diverse problems of the world, so we should teach to increase transfer: the ability to apply fundamental principles to new problems and contexts. This ability is rare. The…
Self-organization can be broadly defined as the ability of a system to display ordered spatio-temporal patterns solely as the result of the interactions among the system components. Processes of this kind characterize both living and…
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
We investigate the self-organization of point-particles with short-range interactions modeled via simple 1D and 2D Hubbard-like models. We show how various properties emerge such as, boson-like ordering leading to topological structures in…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…