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 Laminar Cortical Model for 3D Perception of Slanted and Curved Surfaces and of 2D Images: Developement, attention, and Bistability

A model of laminar visual cortical dynamics proposes how 3D boundary and surface representations of slated and curved 3D objects and 2D images arise. The 3D boundary representations emerge from interactions between non-classical horizontal receptive field interactions with intracorticcal and intercortical feedback circuits. Such non-classical interactions contextually disambiguate classical receptive field responses to ambiguous visual cues using cells that are sensitive to angles and disparity gradients with cortical areas V1 and V2. These cells are all variants of bipole grouping cells. Model simulations show how horizontal connections can develop selectively to angles, how slanted surfaces can activate 3D boundary representations that are sensitive to angles and disparity gradients, how 3D filling-in occurs across slanted surfaces, how a 2D Necker cube image can be represented in 3D, and how bistable Necker cuber percepts occur. The model also explains data about slant aftereffects and 3D neon color spreading. It shows how habituative transmitters that help to control developement also help to trigger bistable 3D percepts and slant aftereffects, and how attention can influence which of these percepts is perceived by propogating along some object boundaries.

Effects of Highlights on Gloss Perception

The perception of a glossy surface in a static monochromatic image can occur when a bright highlight is embedded in a compatible context of shading and a bounding contour. Some images naturally give rise to the impression that a surface has a uniform reflectance, characteristic of a shiny object, even though the highlight may only cover a small portion of the surface. Nonetheless, an observer may adopt an attitude of scrutiny in viewing a glossy surface, whereby the impression of gloss is partial and nonuniform at image regions outside of a higlight. Using a rating scale and small probe points to indicate image locations, differential perception of gloss within a single object is investigate in the present study. Observers' gloss ratings are not uniform across the surface, but decrease as a function of distance from highlight. When, by design, the distance from a highlight is uncoupled from the luminance value at corresponding probe points, the decrease in rated gloss correlates more with the distance than with the luminance change. Experiments also indicate that gloss ratings change as a function of estimated surface distance, rather than as a function of image distance. Surface continuity affects gloss ratings, suggesting that apprehension of 3D surface structure is crucial for gloss perception.

Linking Visual Cortex to Visual Perception: An Alternative to the Gestalt Bubble

Lehar's lively discussion builds on a critique of neural models of vision that is incorrect in its general and specific claims. He espouses a Gestalt perceptual approach, rather than one consistent with the "objective neurophysiological state of the visual system" (p. 1). Contemporary vision models realize his perceptual goals and also quantitatively explain neurophysiological and anatomical data.

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.

Laminar Cortical Dynamics of 3D Surface Perception: Stratification, transparency, and Neon Color Spreading

How does the laminar organization of cortical circuitry in areas VI and V2 give rise to 3D percepts of stratification, transparency, and neon color spreading in response to 2D pictures and 3D scenes? Psychophysical experiments have shown that such 3D percepts are sensitive to whether contiguous image regions have the same relative contrast polarity (dark-light or lightdark), yet long-range perceptual grouping is known to pool over opposite contrast polarities. The ocularity of contiguous regions is also critical for neon color spreading: Having different ocularity despite the contrast relationship that favors neon spreading blocks the spread. In addition, half visible points in a stereogram can induce near-depth transparency if the contrast relationship favors transparency in the half visible areas. It thus seems critical to have the whole contrast relationship in a monocular configuration, since splitting it between two stereogram images cancels the effect. What adaptive functions of perceptual grouping enable it to both preserve sensitivity to monocular contrast and also to pool over opposite contrasts? Aspects of cortical development, grouping, attention, perceptual learning, stereopsis and 3D planar surface perception have previously been analyzed using a 3D LAMINART model of cortical areas VI, V2, and V4. The present work consistently extends this model to show how like-polarity competition between VI simple cells in layer 4 may be combined with other LAMINART grouping mechanisms, such as cooperative pooling of opposite polarities at layer 2/3 complex cells. The model also explains how the Metelli Rules can lead to transparent percepts, how bistable transparency percepts can arise in which either surface can be perceived as transparent, and how such a transparency reversal can be facilitated by an attention shift. The like-polarity inhibition prediction is consistent with lateral masking experiments in which two f1anking Gabor patches with the same contrast polarity as the target increase the target detection threshold when they approach the target. It is also consistent with LAMINART simulations of cortical development. Other model explanations and testable predictions will also be presented.

Laminar Cortical Dynamics of Visual Form and Motion Interactions During Coherent Object Motion Perception

How do visual form and motion processes cooperate to compute object motion when each process separately is insufficient? A 3D FORMOTION model specifies how 3D boundary representations, which separate figures from backgrounds within cortical area V2, capture motion signals at the appropriate depths in MT; how motion signals in MT disambiguate boundaries in V2 via MT-to-Vl-to-V2 feedback; how sparse feature tracking signals are amplified; and how a spatially anisotropic motion grouping process propagates across perceptual space via MT-MST feedback to integrate feature-tracking and ambiguous motion signals to determine a global object motion percept. Simulated data include: the degree of motion coherence of rotating shapes observed through apertures, the coherent vs. element motion percepts separated in depth during the chopsticks illusion, and the rigid vs. non-rigid appearance of rotating ellipses.

Temporal Dynamics of Decision-Making during Motion Perception in the Visual Cortex

How does the brain make decisions? Speed and accuracy of perceptual decisions covary with certainty in the input, and correlate with the rate of evidence accumulation in parietal and frontal cortical "decision neurons." A biophysically realistic model of interactions within and between Retina/LGN and cortical areas V1, MT, MST, and LIP, gated by basal ganglia, simulates dynamic properties of decision-making in response to ambiguous visual motion stimuli used by Newsome, Shadlen, and colleagues in their neurophysiological experiments. The model clarifies how brain circuits that solve the aperture problem interact with a recurrent competitive network with self-normalizing choice properties to carry out probablistic decisions in real time. Some scientists claim that perception and decision-making can be described using Bayesian inference or related general statistical ideas, that estimate the optimal interpretation of the stimulus given priors and likelihoods. However, such concepts do not propose the neocortical mechanisms that enable perception, and make decisions. The present model explains behavioral and neurophysiological decision-making data without an appeal to Bayesian concepts and, unlike other existing models of these data, generates perceptual representations and choice dynamics in response to the experimental visual stimuli. Quantitative model simulations include the time course of LIP neuronal dynamics, as well as behavioral accuracy and reaction time properties, during both correct and error trials at different levels of input ambiguity in both fixed duration and reaction time tasks. Model MT/MST interactions compute the global direction of random dot motion stimuli, while model LIP computes the stochastic perceptual decision that leads to a saccadic eye movement.

Form Perception

National Science Foundation (SBE-0354378); Office of Naval Research (N00014-01-1-0624)

Neural Dynamics of Motion Perception, Recognition Learning, and Spatial Attention

Advanced Research Projects Agency (ONR N00014-92-J-4015); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-91-J-4100)

Variable Rate Working Memories for Phonetic Categorization and Invariant Speech Perception

Speech can be understood at widely varying production rates. A working memory is described for short-term storage of temporal lists of input items. The working memory is a cooperative-competitive neural network that automatically adjusts its integration rate, or gain, to generate a short-term memory code for a list that is independent of item presentation rate. Such an invariant working memory model is used to simulate data of Repp (1980) concerning the changes of phonetic category boundaries as a function of their presentation rate. Thus the variability of categorical boundaries can be traced to the temporal in variance of the working memory code.

Brightness Perception, Illusory Contours and Corticogeniculate Feedback

A neural network model of early visual processing offers an explanation of brightness effects often associated with illusory contours. Top-down feedback from the model's analog of visual cortical complex cells to model lateral geniculate nucleus (LGN) cells are used to enhance contrast at line ends and other areas of boundary discontinuity. The result is an increase in perceived brightness outside a dark line end, akin to what Kennedy (1979) termed "brightness buttons" in his analysis of visual illusions. When several lines form a suitable configuration, as in an Ehrenstein pattern, the perceptual effect of enhanced brightness can be quite strong. Model simulations show the generation of brightness buttons. With the LGN model circuitry embedded in a larger model of preattentive vision, simulations using complex inputs show the interaction of the brightness buttons with real and illusory contours.

A Gestalt Bubble Model of Visuosptial Perception

A neural network model is presented to account for the three dimensional perception of visual space by way of an analog Gestalt-like perceptual mechanism.

Laminar Cortical Dynamics of Visual Form and Motion Interactions During Coherent Object Motion Perception

How do visual form and motion processes cooperate to compute object motion when each process separately is insufficient? Consider, for example, a deer moving behind a bush. Here the partially occluded fragments of motion signals available to an observer must be coherently grouped into the motion of a single object. A 3D FORMOTION model comprises five important functional interactions involving the brain’s form and motion systems that address such situations. Because the model’s stages are analogous to areas of the primate visual system, we refer to the stages by corresponding anatomical names. In one of these functional interactions, 3D boundary representations, in which figures are separated from their backgrounds, are formed in cortical area V2. These depth-selective V2 boundaries select motion signals at the appropriate depths in MT via V2-to-MT signals. In another, motion signals in MT disambiguate locally incomplete or ambiguous boundary signals in V2 via MT-to-V1-to-V2 feedback. The third functional property concerns resolution of the aperture problem along straight moving contours by propagating the influence of unambiguous motion signals generated at contour terminators or corners. Here, sparse “feature tracking signals” from, e.g., line ends, are amplified to overwhelm numerically superior ambiguous motion signals along line segment interiors. In the fourth, a spatially anisotropic motion grouping process takes place across perceptual space via MT-MST feedback to integrate veridical feature-tracking and ambiguous motion signals to determine a global object motion percept. The fifth property uses the MT-MST feedback loop to convey an attentional priming signal from higher brain areas back to V1 and V2. The model's use of mechanisms such as divisive normalization, endstopping, cross-orientation inhibition, and longrange cooperation is described. Simulated data include: the degree of motion coherence of rotating shapes observed through apertures, the coherent vs. element motion percepts separated in depth during the chopsticks illusion, and the rigid vs. non-rigid appearance of rotating ellipses.

Cortical Dynamics of Visual Motion Perception: Short-Range and Long Range Apparent Motion

This article describes further evidence for a new neural network theory of biological motion perception that is called a Motion Boundary Contour System. This theory clarifies why parallel streams Vl-> V2 and Vl-> MT exist for static form and motion form processing among the areas Vl, V2, and MT of visual cortex. The Motion Boundary Contour System consists of several parallel copies, such that each copy is activated by a different range of receptive field sizes. Each copy is further subdivided into two hierarchically organized subsystems: a Motion Oriented Contrast Filter, or MOC Filter, for preprocessing moving images; and a Cooperative-Competitive Feedback Loop, or CC Loop, for generating emergent boundary segmentations of the filtered signals. The present article uses the MOC Filter to explain a variety of classical and recent data about short-range and long-range apparent motion percepts that have not yet been explained by alternative models. These data include split motion; reverse-contrast gamma motion; delta motion; visual inertia; group motion in response to a reverse-contrast Ternus display at short interstimulus intervals; speed-up of motion velocity as interfiash distance increases or flash duration decreases; dependence of the transition from element motion to group motion on stimulus duration and size; various classical dependencies between flash duration, spatial separation, interstimulus interval, and motion threshold known as Korte's Laws; and dependence of motion strength on stimulus orientation and spatial frequency. These results supplement earlier explanations by the model of apparent motion data that other models have not explained; a recent proposed solution of the global aperture problem, including explanations of motion capture and induced motion; an explanation of how parallel cortical systems for static form perception and motion form perception may develop, including a demonstration that these parallel systems are variations on a common cortical design; an explanation of why the geometries of static form and motion form differ, in particular why opposite orientations differ by 90°, whereas opposite directions differ by 180°, and why a cortical stream Vl -> V2 -> MT is needed; and a summary of how the main properties of other motion perception models can be assimilated into different parts of the Motion Boundary Contour System design.