Children’s musical perception and creativity as a compositional model

The intention of this study was to understand more fully the process of creating musical composition. As a means to to this I created a compositional model, "Maya's Words", a conscious experiment which utilised the techniques I discovered and codified from children's compositions. By utilising rhe model as a working tool and the information extracted from the children's works I was able to draw together my own theories and observations concerning the process of musical composition and how it works. Within this study I have also examined my own process of musical composition and drawn, in a limited way, upon my work on the methodology behind the compositional procedures of composer Elisabeth Lutyens. The way in which the children used their own musical ideas in a flexible and original manner illustrated a mental state that seemed to be able to grasp thoughts from anywhere, without reference, for example, to tradition or style. This dexterity brought to my attention the notion that the children were using fragments of ideas/music/sound and integrating them into their own compositions. In the compositional model for this study I chose to compose in a way that utilised information from this study in many manifestations but it also had to be an organic growth as a means to be real and for me to have a true input into it a sa composer. It also had to incorporate many of the study elements into it otherwise it would not be a conscious experiment. The two forces here, for me haave worked in tandem as the flexibility of approach used by the children has allowed me to work in a flexible way in this compositional model and yet the uncomplicated way in which the children evaluated their own progressions has had a profound influence on me too and provided me with a method of self-evaluation which does not create self-inflicted damage to my own feelings about my composition. I hope in the same way that this study will allow composers a freedon of perspective that will open for them a new understanding of musical composition

Random graphs with clustering

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network.Comment: 5 pages, 2 figure

Competing epidemics on complex networks

Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance of one disease and dominance of the other as a function of their relative rates of growth. Close to this transition the final outcomes show strong dependence on stochastic fluctuations in the early stages of growth, dependence that decreases with increasing network size, but does so sufficiently slowly as still to be easily visible in systems with millions or billions of individuals. In most regions of the phase diagram we find that one disease eventually dominates while the other reaches only a vanishing fraction of the network, but the system also displays a significant coexistence regime in which both diseases reach epidemic proportions and infect an extensive fraction of the network.Comment: 14 pages, 5 figure

Directed percolation with incubation times

We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Levy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Levy parameter.Comment: 17 pages, 7 figures. v.2: minor correction

ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS

A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is derived on the basis of this relationship. An approximate expression for the nonlinear velocity is also determined by extending the concept of Lyapunov exponent to growth rate of finite perturbations.Comment: Tex file without figures- Figures and text in post-script available via anonymous ftp at ftp://wpts0.physik.uni-wuppertal.de/pub/torcini/jpa_le

Threshold effects for two pathogens spreading on a network

Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.Comment: 5 pages, 2 figure

High-precision Monte Carlo study of directed percolation in (d+1) dimensions

We present a Monte Carlo study of the bond and site directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \leq 7$. A dimensionless ratio is defined, and an analysis of its finite-size scaling produces improved estimates of percolation thresholds. We also report improved estimates for the standard critical exponents. In addition, we study the probability distributions of the number of wet sites and radius of gyration, for $1 \leq d \leq 7$.Comment: 11 pages, 21 figure

Random graphs containing arbitrary distributions of subgraphs

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly non-tree-like neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a new class of random graph models that incorporates general subgraphs, allowing for non-tree-like neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.Comment: 12 pages, 6 figures, 1 tabl

Emergence of diversity in a model ecosystem

The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)]. The competition is controlled by an interaction network with fixed links chosen by a Bernoulli process. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that patches of isolated meta-populations formed by the collapse of cyclic relations are essential for the transition to the state of high diversity.Comment: 7 pages, 6 figures. Accepted for publication in PRE. Typos corrected, Fig.3A and Fig.6 update

Ecosystems with mutually exclusive interactions self-organize to a state of high diversity

Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general unknown. Using lichen communities as an example, we propose a model for the evolution of mutually excluding organisms that compete for space. We suggest that chain-like or cyclic invasions involving three or more species open for creation of spatially separated sub-populations that subsequently can lead to increased diversity. In contrast to its non-spatial counterpart, our model predicts robust co-existence of a large number of species, in accordance with observations on lichen growth. It is demonstrated that large species diversity can be obtained on evolutionary timescales, provided that interactions between species have spatial constraints. In particular, a phase transition to a sustainable state of high diversity is identified.Comment: 4 pages, 4 figure