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, 2011 The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate.
Gershenson, Carlos
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Restricted Complexity, General Complexity [PDF]
Worldviews, Science and Us, 2006 Why has the problematic of complexity appeared so late?
Morin, Edgar
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Complex complex landscapes [PDF]
Physical Review Research, 2021 We study the saddle-points of the $p$-spin model -- the best understood example of a `complex' (rugged) landscape -- when its $N$ variables are complex. These points are the solutions to a system of $N$ random equations of degree $p-1$. We solve for $\overline{\mathcal N}$, the number of solutions averaged over randomness in the $N\to\infty$ limit.
Jaron Kent-Dobias, Jorge Kurchan
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Complexes from Complexes [PDF]
Foundations of Computational Mathematics, 2021 This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a systematic procedure which, starting from well-understood differential complexes such as the de Rham complex, derives new ...
Kaibo Hu, Douglas N. Arnold
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Studying Complexity is Complex [PDF]
Journal of General Internal Medicine, 2007 This supplement contains 9 articles that arose from a Department of Veterans Affairs sponsored State of the Art (SOTA) conference “Managing Complexity in Chronic Care.” It is appropriate that these articles appear in the Journal of General Internal Medicine.
Hayden B. Bosworth +3 more
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, 2021 Horizon 2045 (H2045) is a 25-year initiative to end the nuclear weapons century. We urgently need to manage the intertwined existential risks of the Anthropocene—the geological era that began with the 1945 Trinity Test and is characterized by humankind’s
Center for Complexity,
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The complexity of cutting complexes [PDF]
Discrete & Computational Geometry, 1989 This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections.
Chazelle, B. +2 more
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Circuit complexity, proof complexity, and polynomial identity testing [PDF]
, 2014 We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have ...
Grochow, Joshua A., Pitassi, Toniann
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Complexity and Multiple Complexes
Mathematische Zeitschrift, 1987 In this chapter we introduce the notion of the complexity of a module and explore some related ideas. Complexity was first defined by Jon Alperin in the late 1970’s and it helped to motivate much of the development of the homological properties of modules.
Jon F. Carlson +3 more
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Simplicial complexes and complex systems [PDF]
European Journal of Physics, 2018 © 2018 European Physical Society. We provide a short introduction to the field of topological data analysis (TDA) and discuss its possible relevance for the study of complex systems. TDA provides a set of tools to characterise the shape of data, in terms of the presence of holes or cavities between the points.
Renaud Lambiotte +3 more
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