Related papers: Complexity and Coupling: A Functional Domain Appro…
Computational functionalism about consciousness is often criticized for relying on observer-relative interpretations of physical systems. This paper proposes a mathematical refinement of functionalism that avoids this problem. The central…
In Model-Based Design of Cyber-Physical Systems (CPS), it is often desirable to develop several models of varying fidelity. Models of different fidelity levels can enable mathematical analysis of the model, control synthesis, faster…
We address the challenge of product configuration in the context of increasing customer demand for diverse and complex products. We propose a solution through a curated selection of product model benchmarks formulated in the COOM language,…
The paper argues that attracting more economists and adopting a more-precise definition of dynamic complexity might help econophysics acquire more attention in the economics community and bring new lymph to economic research. It may be…
Causality and causal inference have emerged as core research areas at the interface of modern statistics and domains including biomedical sciences, social sciences, computer science, and beyond. The field's inherently interdisciplinary…
This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
The growing complexity of software systems and the influence of software-supported decisions in our society awoke the need for software that is transparent, accountable, and trustworthy. Explainability has been identified as a means to…
We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
In recent years economic complexity has grown into an active field of fundamental and applied research. Yet, despite important advances, the policy implications of economic complexity remain unclear or misunderstood. Here I organize the…
Component-based design paradigm is of paramount importance due to prolific growth in the complexity of modern-day systems. Since the components are developed primarily by multi-party vendors and often assembled to realize the overall…
Interconnected networks are mathematical representation of systems where two or more simple networks are coupled to each other. Depending on the coupling weight between the two components, the interconnected network can function in two…
The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks---communication systems require electricity, while the normal functioning of the power grid relies on communication…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…
Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates…
Computation nowadays is becoming inherently concurrent, either because of characteristics of the hardware (with multicore processors becoming omnipresent) or due to the ubiquitous presence of distributed systems (incarnated in the…