Related papers: An Algorithmic Information Theory approach to the …
Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…
A self-replicating system where the elements belonging to a solution category can replicate themselves by copying their own informations, is considered. The information carried by each element is defined by an element of all the n multiple…
Despite the obvious advantage of simple life forms capable of fast replication, different levels of cognitive complexity have been achieved by living systems in terms of their potential to cope with environmental uncertainty. Against the…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…
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…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
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…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous…
Many systems of interest exhibit nested emergent layers with their own rules and regularities, and our knowledge about them seems naturally organised around these levels. This paper proposes that this type of hierarchical emergence arises…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
Replicability requires that algorithmic conclusions remain consistent when rerun on independently drawn data. A central structural question is composition: given $k$ problems each admitting a $\rho$-replicable algorithm with sample…