On the equality of Hausdorff and box counting dimensions

By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.Comment: CYCLER Paper 93mar001 Latex file with 3 PostScript figures (needs psfig.sty

Full oxide heterostructure combining a high-Tc diluted ferromagnet with a high-mobility conductor

We report on the growth of heterostructures composed of layers of the high-Curie temperature ferromagnet Co-doped (La,Sr)TiO3 (Co-LSTO) with high-mobility SrTiO3 (STO) substrates processed at low oxygen pressure. While perpendicular spin-dependent transport measurements in STO//Co-LSTO/LAO/Co tunnel junctions demonstrate the existence of a large spin polarization in Co-LSTO, planar magnetotransport experiments on STO//Co-LSTO samples evidence electronic mobilities as high as 10000 cm2/Vs at T = 10 K. At high enough applied fields and low enough temperatures (H < 60 kOe, T < 4 K) Shubnikov-de Haas oscillations are also observed. We present an extensive analysis of these quantum oscillations and relate them with the electronic properties of STO, for which we find large scattering rates up to ~ 10 ps. Thus, this work opens up the possibility to inject a spin-polarized current from a high-Curie temperature diluted oxide into an isostructural system with high-mobility and a large spin diffusion length.Comment: to appear in Phys. Rev.

Phase shift in experimental trajectory scaling functions

For one dimensional maps the trajectory scaling functions is invariant under coordinate transformations and can be used to compute any ergodic average. It is the most stringent test between theory and experiment, but so far it has proven difficult to extract from experimental data. It is shown that the main difficulty is a dephasing of the experimental orbit which can be corrected by reconstructing the dynamics from several time series. From the reconstructed dynamics the scaling function can be accurately extracted.Comment: CYCLER Paper 93mar008. LaTeX, LAUR-92-3053. Replaced with a version with all figure

Expanding direction of the period doubling operator

We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a ``Perron-Frobenius type operator'', to study the linearization of the period doubling operator at its fixed point. We then use a sequence of linear operators with finite ranks to study this induced operator. The proof is constructive. One can calculate the expanding direction and the rate of expansion of the period doubling operator at the fixed point

On the athermal character of structural phase transitions

The significance of thermal fluctuations on nucleation in structural first-order phase transitions has been examined. The prototype case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.Comment: 5 pages, 4 figures, accepted in Phys. Rev. Let

Towards tunable consensus clustering for studying functional brain connectivity during affective processing

In the past decades, neuroimaging of humans has gained a position of status within neuroscience, and data-driven approaches and functional connectivity analyses of functional magnetic resonance imaging (fMRI) data are increasingly favored to depict the complex architecture of human brains. However, the reliability of these findings is jeopardized by too many analysis methods and sometimes too few samples used, which leads to discord among researchers. We propose a tunable consensus clustering paradigm that aims at overcoming the clustering methods selection problem as well as reliability issues in neuroimaging by means of first applying several analysis methods (three in this study) on multiple datasets and then integrating the clustering results. To validate the method, we applied it to a complex fMRI experiment involving affective processing of hundreds of music clips. We found that brain structures related to visual, reward, and auditory processing have intrinsic spatial patterns of coherent neuroactivity during affective processing. The comparisons between the results obtained from our method and those from each individual clustering algorithm demonstrate that our paradigm has notable advantages over traditional single clustering algorithms in being able to evidence robust connectivity patterns even with complex neuroimaging data involving a variety of stimuli and affective evaluations of them. The consensus clustering method is implemented in the R package “UNCLES” available on http://cran.r-project.org/web/packages/UNCLES/index.html

Bounded Rational Decision-Making with Adaptive Neural Network Priors

Bounded rationality investigates utility-optimizing decision-makers with limited information-processing power. In particular, information theoretic bounded rationality models formalize resource constraints abstractly in terms of relative Shannon information, namely the Kullback-Leibler Divergence between the agents' prior and posterior policy. Between prior and posterior lies an anytime deliberation process that can be instantiated by sample-based evaluations of the utility function through Markov Chain Monte Carlo (MCMC) optimization. The most simple model assumes a fixed prior and can relate abstract information-theoretic processing costs to the number of sample evaluations. However, more advanced models would also address the question of learning, that is how the prior is adapted over time such that generated prior proposals become more efficient. In this work we investigate generative neural networks as priors that are optimized concurrently with anytime sample-based decision-making processes such as MCMC. We evaluate this approach on toy examples.Comment: Published in ANNPR 2018: Artificial Neural Networks in Pattern Recognitio

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated unstable manifold. An unstable manifold defines a family of Lorenz maps and we prove that each infinitely renormalizable combinatorial type (satisfying the above conditions) has a unique representative within such a family. We also prove that each infinitely renormalizable map has no wandering intervals and that the closure of the forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Electron-phonon interaction in a local region

The paper reports on a study of electron-phonon interaction within a limited nanosized region. We invoked the modified Fr\"{o}hlich's Hamiltonian to calculate the electron self-energy, as well as the elastic and inelastic scattering cross sections. New effects have been revealed, more specifically: a bound state forms within the limited nanosized region, electrons undergo resonant elastic scattering, with strong inelastic scattering being possible from this state even at low electron energies. The effect of scattering on the magnetic-field-independent dephasing time, in particular, in a diamond-decorated carbon nanotube, has been determined. The effect of strong inelastic electron scattering on thermal resistance at the metal-insulator interface is discussed.Comment: 13 pages, 2 figure