Related papers: Time Evolution of Complexity: A Critique of Three …
Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to…
At present, there is a great deal of confusion regarding complexity and its measures (reviews on complexity measures are found in, e.g. Lloyd, 2001 and Shalizi, 2006 and more references therein). Moreover, there is also confusion regarding…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary…
Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited…
A central goal of evolutionary biology is to explain the origins and distribution of diversity across life. Beyond species or genetic diversity, we also observe diversity in the circuits (genetic or otherwise) underlying complex functional…
In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…
In order to make a case for or against a trend in the evolution of complexity in biological evolution, complexity needs to be both rigorously defined and measurable. A recent information-theoretic (but intuitively evident) definition…
Explaining how and why some species evolved to have more complex social structures than others has been a long-term goal for many researchers in animal behavior because it would provide important insight into the links between evolution and…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical probabilities it…
We investigate time evolution of prepared vibrational state (system) coupled to a reservoir with dense spectrum of its vibrational states. We assume that the reservoir has an equidistant spectrum, and the system - reservoir coupling matrix…
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
Entanglement between a quantum system and its environment leads to loss of coherence in the former. In general, the temporal fate of coherences is complicated. Here, we establish the connection between decoherence of a central system and…
A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…
We present implementations of constant-time algorithms for connectivity tests and related problems. Some are implementations of slightly improved variants of previously known algorithms; for other problems we present new algorithms that…
In this paper we examine the concept of complexity as it applies to generative art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic measures of…