Lorentsen Livingston (butterturn9)

The continuously expanding toolbox of nonlinear time series analysis techniques has recently highlighted the importance of dynamical complexity to understand the behavior of the complex solar wind-magnetosphere-ionosphere-thermosphere coupling system and its components. Here, we apply new such approaches, mainly a series of entropy methods to the time series of the Earth's magnetic field measured by the Swarm constellation. We show successful applications of methods, originated from information theory, to quantitatively study complexity in the dynamical response of the topside ionosphere, at Swarm altitudes, focusing on the most intense magnetic storm of solar cycle 24, that is, the St. Patrick's Day storm, which occurred in March 2015. These entropy measures are utilized for the first time to analyze data from a low-Earth orbit (LEO) satellite mission flying in the topside ionosphere. These approaches may hold great potential for improved space weather nowcasts and forecasts.Taylor's law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor's law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson-Dirichlet processes and demonstrate how a non-trivial Taylor's law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity (i) written language (from a Gutenberg corpus); (ii) an online music website (Last.fm); (iii) Twitter hashtags; (iv) an online collaborative tagging system (Del.icio.us). While Taylor's law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor's law is a fundamental complement to Zipf's and Heaps' laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation.Unique k-SAT is the promised version of k-SAT where the given formula has 0 or 1 solution and is proved to be as difficult as the general k-SAT. For any k ≥ 3 , s ≥ f ( k , d ) and ( s + d ) / 2 > k - 1 , a parsimonious reduction from k-CNF to d-regular (k,s)-CNF is given. Here regular (k,s)-CNF is a subclass of CNF, where each clause of the formula has exactly k distinct variables, and each variable occurs in exactly s clauses. A d-regular (k,s)-CNF formula is a regular (k,s)-CNF formula, in which the absolute value of the difference between positive and negative occurrences of every variable is at most a nonnegative integer d. We prove that for all k ≥ 3 , f ( k , d ) ≤ u ( k , d ) + 1 and f ( k , d + 1 ) ≤ u ( k , d ) . The critical function f ( k , d ) is the maximal value of s, such that every d-regular (k,s)-CNF formula is satisfiable. In this study, u ( k , d ) denotes the minimal value of s such that there exists a uniquely satisfiable d-regular (k,s)-CNF formula. selleckchem We further show that for s ≥ f ( k , d ) + 1 and ( s + d ) / 2 > k - 1 , there exists a uniquely satisfiable d-regular ( k , s + 1 ) -CNF formula. Moreover, for k ≥ 7 , we have that u ( k , d ) ≤ f ( k , d ) + 1 .In this article, I develop a formal model of free will for complex systems based on emergent properties and adaptive selection. The model is based on a process ontology in which a free choice is a singular process that takes a system from one macrostate to another. I quantify the model by introducing a formal measure of the 'freedom' of a singular choice. The 'free will' of a system, then, is emergent from the aggregate freedom of the choice processes carried out by the system. The focus in th