Related papers: On computational irreducibility and the predictabi…
This article presents a formal model demonstrating that genuine autonomy, the ability of a system to self-regulate and pursue objectives, fundamentally implies computational unpredictability from an external perspective. we establish…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach…
Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
In studying the predictability of emergent phenomena in complex systems, Israeli & Goldenfeld (Phys. Rev. Lett., 2004; Phys. Rev. E, 2006) showed how to coarse-grain (elementary) cellular automata (CA). Their algorithm for finding…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Non-Hermitian evolution is mathematically invertible, yet finite dynamic range imposes a sharp operational limit on reversibility. We identify Precision-Induced Irreversibility (PIR): amplification, mode mixing (as warranted by…
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular…
We exhaustively explore the reprogrammability capabilities and the intrinsic universality of the Cartesian product $P \times C$ of the space $P$ of all possible computer programs of increasing size and the space $C$ of all possible…
The ability to control complex networks is of crucial importance across a wide range of applications in natural and engineering sciences. However, issues of both theoretical and numerical nature introduce fundamental limitations to…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how…
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…
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…