535 research outputs found
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
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 dimensions on simple-cubic and
body-centered-cubic lattices, with . 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 .Comment: 11 pages, 21 figure
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
Contact process with long-range interactions: a study in the ensemble of constant particle number
We analyze the properties of the contact process with long-range interactions
by the use of a kinetic ensemble in which the total number of particles is
strictly conserved. In this ensemble, both annihilation and creation processes
are replaced by an unique process in which a particle of the system chosen at
random leaves its place and jumps to an active site. The present approach is
particularly useful for determining the transition point and the nature of the
transition, whether continuous or discontinuous, by evaluating the fractal
dimension of the cluster at the emergence of the phase transition. We also
present another criterion appropriate to identify the phase transition that
consists of studying the system in the supercritical regime, where the presence
of a "loop" characterizes the first-order transition. All results obtained by
the present approach are in full agreement with those obtained by using the
constant rate ensemble, supporting that, in the thermodynamic limit the results
from distinct ensembles are equivalent
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