Search results for "curse of dimensionality"

Very large magnetoresistance inFe0.28TaS2single crystals

2015

There is great interest in understanding the physics of magnetic ordering and electronic transport in materials of reduced dimensionality with strong spin-orbit coupling. This paper presents magnetotransport measurements of Fe${}_{0.28}$TaS${}_{2}$ single crystals, which are found to exhibit very large magnetoresistance (MR) for magnetic fields along the easy axis. The authors believe that such a large MR arises from spin disorder scattering and propose to use this mechanism as a design principle for materials with large MR. Further tests are needed to fully rule out contributions from a more conventional anisotropic MR mechanism.

2016

The wealth of sensory data coming from different modalities has opened numerous opportunities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. However, multimodal architectures must rely on models able to adapt to changes in the data distribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation problem as d…

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

1993

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest…

Integrated Generation of High-dimensional Entangled Photon States and Their Coherent Control

2017

Exploiting a frequency-domain approach, we demonstrate the generation of high-dimensional entangled quantum states with a Hilbert-space dimensionality larger than 100 from an on-chip nonlinear microcavity, and introduce a coherent control platform using standard telecommunications components.

On the dynamics of confined particles: a laser test

2017

Reduced dimensionality systems (RDS) are materials extending along one or two dimensions much more than the other(s). The degrees of freedom of the small dimension are not explored by the electrons since their energy is very large. The time dependent wave function of a particle in a short nanotube, taken as a paradigm of the RDS family, is calculated by solving the Klein–Gordon equation; the confining condition produces a small change in the mass of the particles and of the energy levels. These changes are of relativistic origin and therefore small, but can be measured by use of a weak resonant laser field which produces cumulative effects in the time development of the wave function. The s…

Exchange-correlation potential with a proper long-range behavior for harmonically confined electron droplets

2010

The exchange-correlation potentials stemming from the local-density approximation and several generalized-gradient approximations are known to have incorrect asymptotic decay. This failure is independent of the dimensionality but so far the problem has been corrected---within the mentioned approximations---only in three dimensions. Here we provide a cured exchange-correlation potential for two-dimensional harmonically confined systems that cover a wide range of applications in quantum Hall and semiconductor physics, especially in quantum-dot modeling. The given potential is a generalized-gradient approximation and we demonstrate that it agrees very well with the analytic result of a two-ele…

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…