Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

A Neural Model of Surface Perception: Lightness, Anchoring, and Filling-in

This article develops a neural model of how the visual system processes natural images under variable illumination conditions to generate surface lightness percepts. Previous models have clarified how the brain can compute the relative contrast of images from variably illuminate scenes. How the brain determines an absolute lightness scale that "anchors" percepts of surface lightness to us the full dynamic range of neurons remains an unsolved problem. Lightness anchoring properties include articulation, insulation, configuration, and are effects. The model quantatively simulates these and other lightness data such as discounting the illuminant, the double brilliant illusion, lightness constancy and contrast, Mondrian contrast constancy, and the Craik-O'Brien-Cornsweet illusion. The model also clarifies the functional significance for lightness perception of anatomical and neurophysiological data, including gain control at retinal photoreceptors, and spatioal contrast adaptation at the negative feedback circuit between the inner segment of photoreceptors and interacting horizontal cells. The model retina can hereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A later model cortical processing stages, boundary representations gate the filling-in of surface lightness via long-range horizontal connections. Variants of this filling-in mechanism run 100-1000 times faster than diffusion mechanisms of previous biological filling-in models, and shows how filling-in can occur at realistic speeds. A new anchoring mechanism called the Blurred-Highest-Luminance-As-White (BHLAW) rule helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural images under variable lighting conditions.

A Neuromorphic Model for Achromatic and Chromatic Surface Representation of Natural Images

This study develops a neuromorphic model of human lightness perception that is inspired by how the mammalian visual system is designed for this function. It is known that biological visual representations can adapt to a billion-fold change in luminance. How such a system determines absolute lightness under varying illumination conditions to generate a consistent interpretation of surface lightness remains an unsolved problem. Such a process, called "anchoring" of lightness, has properties including articulation, insulation, configuration, and area effects. The model quantitatively simulates such psychophysical lightness data, as well as other data such as discounting the illuminant, the double brilliant illusion, and lightness constancy and contrast effects. The model retina embodies gain control at retinal photoreceptors, and spatial contrast adaptation at the negative feedback circuit between mechanisms that model the inner segment of photoreceptors and interacting horizontal cells. The model can thereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A new anchoring mechanism, called the Blurred-Highest-Luminance-As-White (BHLAW) rule, helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural color images under variable lighting conditions, and is compared with the popular RETINEX model.