{"title":"覆盖面、连续性和视觉皮层结构。","authors":"Wolfgang Keil, Fred Wolf","doi":"10.1186/2042-1001-1-17","DOIUrl":null,"url":null,"abstract":"<p><strong>Background: </strong>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.</p><p><strong>Results: </strong>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 the 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.</p><p><strong>Conclusions: </strong>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.</p>","PeriodicalId":89606,"journal":{"name":"Neural systems & circuits","volume":"1 ","pages":"17"},"PeriodicalIF":0.0000,"publicationDate":"2011-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3283456/pdf/","citationCount":"0","resultStr":"{\"title\":\"Coverage, continuity, and visual cortical architecture.\",\"authors\":\"Wolfgang Keil, Fred Wolf\",\"doi\":\"10.1186/2042-1001-1-17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><strong>Background: </strong>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.</p><p><strong>Results: </strong>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 the 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.</p><p><strong>Conclusions: </strong>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. 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引用次数: 0
摘要
背景:许多哺乳动物的初级视觉皮层包含一个连续的视觉空间表征,并叠加有大致重复的非周期性方位偏好图。最近研究发现,方位偏好图(OPMs)服从统计规律,而这些规律在食肉动物进化过程中相距甚远的物种之间显然是不变的。在此,我们研究了大脑皮层图谱优化的最著名模型之一--弹性网(EN)模型--能否再现这种常见的设计。弹性网模型生成的表征能在刺激空间覆盖率和地图连续性之间进行最佳权衡。虽然该模型已被大量研究采用,但迄今为止还没有关于预测 OPMs 精确布局的分析结果:结果:我们提出了一种数学方法,用于分析计算 EN 模型预测的皮层表征,以实现刺激位置和方向的联合映射。我们发现,在以前研究过的所有情况下,预测的 OPM 布局都是完全周期性的。通过对 EN 参数空间进行无偏搜索,我们发现了一种新的非周期性 OPM 体系,其针轮密度低于实验结果。在一个极端极限中,出现了与实验观测结果定量相似的非周期性 OPM。这些布局的稳定来自于强大的非局部相互作用,而不是覆盖-连续-妥协:我们的研究结果表明,由非局部抑制性相互作用主导的刺激表征优化模型原则上能够正确预测常见的 OPM 设计。他们质疑视觉皮层特征表征可以用覆盖-连续-妥协来解释。
Coverage, continuity, and visual cortical architecture.
Background: 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.
Results: 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 the 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.
Conclusions: 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.