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This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its…
Suppose an experiment is conducted on pairs of objects with outcome responses a continuous variable measuring the interactions among the pairs. Furthermore, assume the response variable is hard to measure numerically but easy to be coded…
Complex systems can be described at myriad different scales, and their causal workings often have multiscale structure (e.g., a computer can be described at the microscale of its hardware circuitry, the mesoscale of its machine code, and…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that…
The $\sigma$ profile is presented as a tool to analyze the organization of systems at different scales, and how this organization changes in time. Describing structures at different scales as goal-oriented agents, one can define $\sigma \in…
The paper reviews two prominent approaches for the measurement of technological complexity: the method of reflection and the assessment of technologies' combinatorial difficulty. It discusses their central underlying assumptions and…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
Complexity is an inherent attribute of any project. The purpose of defining and documenting complexity is to have an early warning tool allowing a project team to focus on certain areas and aspects of the project in order to prevent and…
A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary transformations, such as translations, scalings, projections…
We present a computational framework for analyzing and quantifying system flexibility. Our framework incorporates new features that include: general uncertainty characterizations that are constructed using composition of sets, procedures…
We study various novel complexity measures for two-sided matching mechanisms, applied to the two canonical strategyproof matching mechanisms, Deferred Acceptance (DA) and Top Trading Cycles (TTC). Our metrics are designed to capture the…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
This paper provides a precise and scientific definition of complexity and coupling, grounded in the functional domain, particularly within industrial control and automation systems (iCAS). We highlight the widespread ambiguity in defining…