相关论文: Aesthetic complexity
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be…
Many widely different problems have a common mathematical structure wherein limited knowledge lead to ambiguity that can be captured conveniently using a concept of invisibility that requires the introduction of negative values for…
Pictures in physics education go beyond instructional functions and serve affective roles, such as attracting attention, creating fascination, and fostering engagement with the depicted content. Recognizing the importance of these affective…
The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
The disorder and a simple convex measure of complexity are studied for rank ordered power law distributions, indicative of criticality, in the case where the total number of ranks is large. It is found that a power law distribution may…
We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…
Accurate evaluation of human aesthetic preferences represents a major challenge for creative evolutionary and generative systems research. Prior work has tended to focus on feature measures of the artefact, such as symmetry, complexity and…
Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…
The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
This chapter does not deal with specific tools and techniques for managing complex systems, but proposes some basic concepts that help us to think and speak about complexity. We review classical thinking and its intrinsic drawbacks when…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
The wholeness, conceived and developed by Christopher Alexander, is what exists to some degree or other in space and matter, and can be described by precise mathematical language. However, it remains somehow mysterious and elusive, and…
Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space.…
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
As urban critic Jane Jacobs conceived, a city is essentially the problem of organized complexity. What underlies the complexity refers to a structural factor, called living structure, which is defined as a mathematical structure composed of…