Chimera States for Coupled Oscillators

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure

Self-organization and the selection of pinwheel density in visual cortical development

Self-organization of neural circuitry is an appealing framework for understanding cortical development, yet its applicability remains unconfirmed. Models for the self-organization of neural circuits have been proposed, but experimentally testable predictions of these models have been less clear. The visual cortex contains a large number of topological point defects, called pinwheels, which are detectable in experiments and therefore in principle well suited for testing predictions of self-organization empirically. Here, we analytically calculate the density of pinwheels predicted by a pattern formation model of visual cortical development. An important factor controlling the density of pinwheels in this model appears to be the presence of non-local long-range interactions, a property which distinguishes cortical circuits from many nonliving systems in which self-organization has been studied. We show that in the limit where the range of these interactions is infinite, the average pinwheel density converges to $\pi$. Moreover, an average pinwheel density close to this value is robustly selected even for intermediate interaction ranges, a regime arguably covering interaction-ranges in a wide range of different species. In conclusion, our paper provides the first direct theoretical demonstration and analysis of pinwheel density selection in models of cortical self-organization and suggests to quantitatively probe this type of prediction in future high-precision experiments.Comment: 22 pages, 3 figure

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

Automated Glaucoma Detection Using Hybrid Feature Extraction in Retinal Fundus Images

Glaucoma is one of the most common causes of blindness. Robust mass screening may help to extend the symptom-free life for affected patients. To realize mass screening requires a cost-effective glaucoma detection method which integrates well with digital medical and administrative processes. To address these requirements, we propose a novel low cost automated glaucoma diagnosis system based on hybrid feature extraction from digital fundus images. The paper discusses a system for the automated identification of normal and glaucoma classes using higher order spectra (HOS), trace transform (TT), and discrete wavelet transform (DWT) features. The extracted features are fed to a support vector machine (SVM) classifier with linear, polynomial order 1, 2, 3 and radial basis function (RBF) in order to select the best kernel for automated decision making. In this work, the SVM classifier, with a polynomial order 2 kernel function, was able to identify glaucoma and normal images with an accuracy of 91.67%, and sensitivity and specificity of 90% and 93.33%, respectively. Furthermore, we propose a novel integrated index called Glaucoma Risk Index (GRI) which is composed from HOS, TT, and DWT features, to diagnose the unknown class using a single feature. We hope that this GRI will aid clinicians to make a faster glaucoma diagnosis during the mass screening of normal/glaucoma images

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Reprogramming of orientation columns in visual cortex : a domino effect

Abstract : Cortical organization rests upon the fundamental principle that neurons sharing similar properties are co-located. In the visual cortex, neurons are organized into orientation columns. In a column, most neurons respond optimally to the same axis of an oriented edge, that is, the preferred orientation. This orientation selectivity is believed to be absolute in adulthood. However, in a fully mature brain, it has been established that neurons change their selectivity following sensory experience or visual adaptation. Here, we show that after applying an adapter away from the tested cells, neurons whose receptive fields were located remotely from the adapted site also exhibit a novel selectivity in spite of the fact that they were not adapted. These results indicate a robust reconfiguration and remapping of the orientation domains with respect to each other thus removing the possibility of an orientation hole in the new hypercolumn. These data suggest that orientation columns transcend anatomy, and are almost strictly functionally dynamic

A Multi-Component Model of the Developing Retinocollicular Pathway Incorporating Axonal and Synaptic Growth

During development, neurons extend axons to different brain areas and produce stereotypical patterns of connections. The mechanisms underlying this process have been intensively studied in the visual system, where retinal neurons form retinotopic maps in the thalamus and superior colliculus. The mechanisms active in map formation include molecular guidance cues, trophic factor release, spontaneous neural activity, spike-timing dependent plasticity (STDP), synapse creation and retraction, and axon growth, branching and retraction. To investigate how these mechanisms interact, a multi-component model of the developing retinocollicular pathway was produced based on phenomenological approximations of each of these mechanisms. Core assumptions of the model were that the probabilities of axonal branching and synaptic growth are highest where the combined influences of chemoaffinity and trophic factor cues are highest, and that activity-dependent release of trophic factors acts to stabilize synapses. Based on these behaviors, model axons produced morphologically realistic growth patterns and projected to retinotopically correct locations in the colliculus. Findings of the model include that STDP, gradient detection by axonal growth cones and lateral connectivity among collicular neurons were not necessary for refinement, and that the instructive cues for axonal growth appear to be mediated first by molecular guidance and then by neural activity. Although complex, the model appears to be insensitive to variations in how the component developmental mechanisms are implemented. Activity, molecular guidance and the growth and retraction of axons and synapses are common features of neural development, and the findings of this study may have relevance beyond organization in the retinocollicular pathway

Visual Cells Remember Earlier Applied Target: Plasticity of Orientation Selectivity

BACKGROUND: A canonical proposition states that, in mature brain, neurons responsive to sensory stimuli are tuned to specific properties installed shortly after birth. It is amply demonstrated that that neurons in adult visual cortex of cats are orientation-selective that is they respond with the highest firing rates to preferred oriented stimuli. METHODOLOGY/PRINCIPAL FINDINGS: In anesthetized cats, prepared in a conventional fashion for single cell recordings, the present investigation shows that presenting a stimulus uninterruptedly at a non-preferred orientation for twelve minutes induces changes in orientation preference. Across all conditions orientation tuning curves were investigated using a trial by trial method. Contrary to what has been previously reported with shorter adaptation duration, twelve minutes of adaptation induces mostly attractive shifts, i.e. toward the adapter. After a recovery period allowing neurons to restore their original orientation tuning curves, we carried out a second adaptation which produced three major results: (1) more frequent attractive shifts, (2) an increase of their magnitude, and (3) an additional enhancement of responses at the new or acquired preferred orientation. Additionally, we also show that the direction of shifts depends on the duration of the adaptation: shorter adaptation in most cases produces repulsive shifts, whereas adaptation exceeding nine minutes results in attractive shifts, in the same unit. Consequently, shifts in preferred orientation depend on the duration of adaptation. CONCLUSION/SIGNIFICANCE: The supplementary response improvements indicate that neurons in area 17 keep a memory trace of the previous stimulus properties, thereby upgrading cellular performance. It also highlights the dynamic nature of basic neuronal properties in adult cortex since repeated adaptations modified both the orientation tuning selectivity and the response strength to the preferred orientation. These enhanced neuronal responses suggest that the range of neuronal plasticity available to the visual system is broader than anticipated