Search results for " dimensionality"
showing 10 items of 129 documents
Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization
1996
The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.
Surface tension and interfacial fluctuations in d-dimensional Ising model
2005
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…
The use of Markovian metapopulation models: a comparison of three methods reducing the dimensionality of transition matrices.
2001
The use of Markovian models is an established way for deriving the complete distribution of the size of a population and the probability of extinction. However, computationally impractical transition matrices frequently result if this mathematical approach is applied to natural populations. Binning, or aggregating population sizes, has been used to permit a reduction in the dimensionality of matrices. Here, we present three deterministic binning methods and study the errors due to binning for a metapopulation model. Our results indicate that estimation errors of the investigated methods are not consistent and one cannot make generalizations about the quality of a method. For some compared o…
Role of geometry and anisotropic diffusion for modelling PO2 profiles in working red muscle
1990
A 3-dimensional analytical model of O2 diffusion in heavily working muscle is proposed which considers anisotropic, myoglobin (Mb)-facilitated O2 diffusion inside the muscle fiber and a carrier-free layer separating erythrocytes and fiber. The model is used to study the effects of some commonly applied simplifying assumptions (reduced dimensionality, neglected anisotropy) on the resulting PO2 distributions: (1) In order not to underestimate PO2 drops near erythrocytes, modelling O2 transport in 3 dimensions is important. (2) For a capillary-to-fiber ratio of 1, the results from the 2-dimensional version of the present model and from a Krogh-type model which incorporates a carrier-free layer…
Unifying vectors and matrices of different dimensions through nonlinear embeddings
2020
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…
Monitoring of chicken meat freshness by means of a colorimetric sensor array
2012
A new optoelectronic nose to monitor chicken meat ageing has been developed. It is based on 16 pigments prepared by the incorporation of different dyes (pH indicators, Lewis acids, hydrogenbonding derivatives, selective probes and natural dyes) into inorganic materials (UVM-7, silica and alumina). The colour changes of the sensor array were characteristic of chicken ageing in a modi¿ed packaging atmosphere (30% CO2¿70% N2). The chromogenic array data were processed with qualitative (PCA) and quantitative (PLS) tools. The PCA statistical analysis showed a high degree of dispersion, with nine dimensions required to explain 95% of variance. Despite this high dimensionality, a tridimensional re…
Incommensurate phases of a bosonic two-leg ladder under a flux
2016
A boson two--leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and Density Matrix Renormalization Group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is $\rho \pi$ and close to it, where $\rho$ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung-rung correlation function and the spin-spin and charge-charge static structure factors.
Dynamic integration of classifiers in the space of principal components
2003
Recent research has shown the integration of multiple classifiers to be one of the most important directions in machine learning and data mining. It was shown that, for an ensemble to be successful, it should consist of accurate and diverse base classifiers. However, it is also important that the integration procedure in the ensemble should properly utilize the ensemble diversity. In this paper, we present an algorithm for the dynamic integration of classifiers in the space of extracted features (FEDIC). It is based on the technique of dynamic integration, in which local accuracy estimates are calculated for each base classifier of an ensemble, in the neighborhood of a new instance to be pr…
The situational version of the Brief Cope: Dimensionality and relationships with goal-related variables
2015
This study is aimed at investigating the dimensionality of the situational version of the Brief COPE, a questionnaire that is frequently used to assess a broad range of coping responses to specific difficulties, by comparing five different factor models highlighted in previous studies. It also aimed at exploring the relationships among coping responses, personal goal commitment and progress. The study involved 606 adults (male = 289) ranging in age from 19 to 71. Using confirmatory factor analysis, we compared five models and assessed relationships of coping responses with goal commitment and progress. The results confirmed the theoretical factor structure of the situational Brief COPE. All…
Extraction of Endmembers from Spectral Mixtures
1999
Abstract Linear spectral mixture modeling (LSMM) divides each ground resolution element into its constituent materials using endmembers which represent the spectral characteristics of the cover types. However, it is difficult to identify and estimate the spectral signature of pure components or endmembers which form the scene, since they vary with the scale and purpose of the study. We propose three different methods to estimate the spectra of pure components from a set of unknown mixture spectra. Two of the methods consist in different optimization procedures based on objective functions defined from the coordinate axes of the dominant factors. The third one consists in the design of a neu…