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.

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

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

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

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

Facilitating Stable Representations: Serial Dependence in Vision

We tested whether the intervening time between multiple glances influences the independence of the resulting visual percepts. Observers estimated how many dots were present in brief displays that repeated one, two, three, four, or a random number of trials later. Estimates made farther apart in time were more independent, and thus carried more information about the stimulus when combined. In addition, estimates from different visual field locations were more independent than estimates from the same location. Our results reveal a retinotopic serial dependence in visual numerosity estimates, which may be a mechanism for maintaining the continuity of visual perception in a noisy environment

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Organization of high-level visual cortex in human infants

How much of the structure of the human mind and brain is already specified at birth, and how much arises from experience? In this article, we consider the test case of extrastriate visual cortex, where a highly systematic functional organization is present in virtually every normal adult, including regions preferring behaviourally significant stimulus categories, such as faces, bodies, and scenes. Novel methods were developed to scan awake infants with fMRI, while they viewed multiple categories of visual stimuli. Here we report that the visual cortex of 4–6-month-old infants contains regions that respond preferentially to abstract categories (faces and scenes), with a spatial organization similar to adults. However, precise response profiles and patterns of activity across multiple visual categories differ between infants and adults. These results demonstrate that the large-scale organization of category preferences in visual cortex is adult-like within a few months after birth, but is subsequently refined through development.National Science Foundation (U.S.) (CCF-1231216

Neural Correlates of Visual Aesthetics – Beauty as the Coalescence of Stimulus and Internal State

How do external stimuli and our internal state coalesce to create the distinctive aesthetic pleasures that give vibrance to human experience? Neuroaesthetics has so far focused on the neural correlates of observing beautiful stimuli compared to neutral or ugly stimuli, or on neural correlates of judging for beauty as opposed to other judgments. Our group questioned whether this approach is sufficient. In our view, a brain region that assesses beauty should show beauty-level-dependent activation during the beauty judgment task, but not during other, unrelated tasks. We therefore performed an fMRI experiment in which subjects judged visual textures for beauty, naturalness and roughness. Our focus was on finding brain activation related to the rated beauty level of the stimuli, which would take place exclusively during the beauty judgment. An initial whole-brain analysis did not reveal such interactions, yet a number of the regions showing main effects of the judgment task or the beauty level of stimuli were selectively sensitive to beauty level during the beauty task. Of the regions that were more active during beauty judgments than roughness judgments, the frontomedian cortex and the amygdala demonstrated the hypothesized interaction effect, while the posterior cingulate cortex did not. The latter region, which only showed a task effect, may play a supporting role in beauty assessments, such as attending to one's internal state rather than the external world. Most of the regions showing interaction effects of judgment and beauty level correspond to regions that have previously been implicated in aesthetics using different stimulus classes, but based on either task or beauty effects alone. The fact that we have now shown that task-stimulus interactions are also present during the aesthetic judgment of visual textures implies that these areas form a network that is specifically devoted to aesthetic assessment, irrespective of the stimulus type